Keywords: Optimization : Theory and Algorithms, Machine Learning and Control
Abstract: Geometry arises in a myriad ways across the sciences, and quite naturally also within AI and optimization. In this talk I wish to share with you examples where geometry helps us understand problems in machine learning, optimization, and sampling. For instance, when sampling from densities supported on a manifold, understanding geometry and the impact of curvature are crucial; surprisingly, progress on geometric sampling theory helps us understand certain generalization properties of SGD for deep-learning! Another fascinating viewpoint afforded by geometry is in non-convex optimization: geometry can either help us make training algorithms more practical for deep learning, it can reveal tractability despite non-convexity (e.g., via geodesic convexity), or it can simply help us understand important ideas better (e.g., eigenvectors, LLM training and inference, etc.)

My hope is to offer the audience insights into geometric thinking, and to share with them some new tools that can help us make progress on modeling, algorithms, and applications. To make my discussion concrete, I will recall a few foundational results arising from our research, provide several examples, and note some open problems.

Keywords: Applications of Algebraic and Differential Geometry in Systems Theory, Computations in Systems Theory, Optimization : Theory and Algorithms
Abstract: Generically nonconvex tasks such as optimal control, peak estimation, and reachable set estimation can be posed as infinite-dimensional but convex LPs in terms of auxiliary functions. The computational bottleneck when discretizing these programs involve the universal quantification jointly over time, state, and input (e.g., Lie derivative nonpositivity in continuous-time). Decomposition techniques to reduce dimensionality can be applied to simplify the complexity of discretization (e.g., sum-of-squares, gridding, sampling). This work extends prior work treating continuous-time input-affine dynamics under vertex or box constraints on inputs by considering continuous-time or discrete-time systems under semidefinite-representable uncertainty. The disturbance variables are eliminated using parameterized robust counterparts without introducing conservatism under mild compactness and regularity conditions. Effectiveness is demonstrated on data-driven peak-estimation of a discrete-time dynamical system.

Keywords: Computations in Systems Theory, Applications of Algebraic and Differential Geometry in Systems Theory, Optimization : Theory and Algorithms
Abstract: Peak estimation involves bounding extreme values of state functions along system trajectories, such as finding the maximum current draw on a transmission line, or the maximum speed obtained by an aircraft. The nonconvex but finite-dimensional peak estimation problem (in terms of optimizing over the initial condition and stopping time) can be lifted into a primal-dual pair of infinite-dimensional linear programs in auxiliary functions/occupation measures. Under mild assumptions, this lifting provides an exact reformulation.

This work focuses on the setting where the dynamics and auxiliary function are chosen to be signomials (linear combinations of exponentials with possibly non-integer exponents). The infinite-dimensional linear constraints are truncated into sum-of-arithmetic-geometric-exponential nonnegativity certificates, which can be represented by relative entropy or dual-power-cone expressions. Our method is applicable to problems in chemical reaction networks, in which the generalized mass action kinetics can be transformed into signomial dynamics under a logarithmic mapping.

Keywords: Infinite Dimensional Systems Theory, Large Scale Systems, Stochastic Modeling and Stochastic Systems Theory
Abstract: We consider the question of whether a linear functional L on an unital commutative real algebra A can be represented as integral w.r.t. a compactly supported Radon measure on the character space of A? We present a characterization in terms of growth conditions on (L(a^n))_n. We compare our result with characterizations in terms of non-negativity conditions of L on Archimedean quadratic modules, and continuity conditions of L w.r.t. submultiplicative seminorms on A. We show that these conditions are directly mutually equivalent and we will relate each of these conditions to a different technique solving the moment problem.The main novelty is that we also establish an exact characterization of the compact support of the representing Radon measure purely in terms of L, instead of just a containment. See M. Infusino, S. Kuhlmann, T. Kuna, P. Michalski, {it An Intrinsic Characterization of Moment Functionals in the Compact Case}, International Mathematics Research Notices, textbf{2023}, 3, %pp. 2281–2303 (2023) for details and further results.

Keywords: Optimization : Theory and Algorithms, Numerical and Symbolic Computations
Abstract: The moment-SOS (sum of squares) hierarchy is a powerful approach for solving globally non-convex polynomial optimization problems (POPs) at the price of solving a family of convex semidefinite optimization problems (called moment-SOS relaxations) of increasing size, controlled by an integer, the relaxation order. We say that a relaxation of a given order is exact if solving the relaxation actually solves the POP globally. In this note, we study the geometry of the exactness cone, defined as the set of polynomial objective functions for which the relaxation is exact. Generalizing previous foundational work on quadratic optimization on real varieties, we prove by elementary arguments that the exactness cones are unions of semidefinite representable cones monotonically embedded for increasing relaxation order.

Keywords: Artificial Intelligence, Machine Learning and Control, Neural Networks

Keywords: Infinite Dimensional Systems Theory, Nonlinear Filtering and Estimation, Linear Systems
Abstract: The problem of optimal state estimation via deterministic Kalman filtering in the frequency domain is considered for a class of single-output Riesz-spectral systems on specific Hilbert state spaces. It is reported that the spectral factorization problem can be solved by symmetric extraction of poles and zeros, which leads to a tractable computational method in order to calculate the optimal output injection in the Kalman filter problem for such systems. The results and methods turn out to be applicable to the class of Sturm-Liouville operators with pointwise measurement.

Keywords: Networked Control Systems, Optimal Control, Transportation Systems
Abstract: We study regularized optimal mass transport over networks in the important situation where the initial and final goods distribution is only known on a subset of the state space. We show that, in spite of the meager information, it is possible to characterize the most likely flow on the given network. As an important by-product, we get the most likely initial and final marginals on the whole state space.

Keywords: Robust and H-Infinity Control, Optimal Control, Linear Systems
Abstract: This paper employs the chain-scattering description two-port framework to identify the relationship between the feedback closed-loop poles of a standard control configuration (SCC) system and the spectral zeros of the off-diagonal (P12 and P21 respectively) SCC plant matrix in H∞/H2 control design. By leveraging the symmetric nature of the coprime factorization techniques, the resulting closed-loop poles for H∞ control solutions for a sufficiently large γ are found to approach the spectral zeros of P12 and P21 respectively and will become the same as that of the H2 optimal control solution. This identified property provides an easy technique for determining the closed-loop poles from a designed SCC plant prior to solving the H∞/H2 controller so that an effective SCC plant construction via weighting function selection can be implemented for robust control realization. The main contributions of this paper include the identification, proof and formulation of the identified property from two specific design problems, which play a crucial role in obtaining H∞/H2 control solutions. Two lemmas that disclose this feature are presented for both H2 optimal control and H∞ sub-optimal control solutions. Using MATLAB/Control Toolbox, an illustrated example is given to verify the identified property.

Keywords: Robust and H-Infinity Control, Optimal Control, Stochastic Control and Estimation
Abstract: We introduce a generalisation to the finite-horizon mixed H_2/H_infty control method for linear stochastic systems with additive noise by considering {it affine plus integral} state-feedback controls and disturbances instead of the more common ones in a linear state-feedback form. This in particular permits achieving robust performance with respect to a wider class of disturbances and an improved tracking performance. The solution to this problem is obtained in an explicit-closed form by the completion of squares method, and the controller gains are expressed in terms of solutions to coupled Riccati and linear ordinary differential equations.

Keywords: Robust and H-Infinity Control, Networked Control Systems, Hybrid Systems
Abstract: We study event-triggered control for discrete-time systems with the H_infty (induced ell_2) performance measure. We construct event-triggered controllers generating sampling intervals no smaller than those of the optimal time-triggered controller under the same H_infty performance bound gamma. The design philosophy is based on a parametrization of discrete, possibly nonlinear and time-varying, gamma-suboptimal controllers and triggering events via the Q parameter that renders the parametrization sampled-data. We characterize through the associated difference Riccati equation a class of signals that causes our event-triggered controllers to generate the optimal time-triggered sampling pattern.

Keywords: Machine Learning and Control, Neural Networks, Linear Systems

Keywords: Machine Learning and Control, Numerical and Symbolic Computations
Abstract: Many applications require numerical solutions to differential equations for a large number of initial conditions and/or system parameters. For example, the analysis of fatigue effects and lifetime prediction of technological systems such as wind energy converters (WECs) often requires a comparison of design site conditions with real site conditions by simulating models of WECs for a large number of different conditions. This contribution evaluates the effectiveness of neural network (NN) enhanced integrators. NNs learn the integration errors, the approximation of which are then used as an additive correction term for the numerical schemes. The resulting integrators are compared with well-established methods in numerical studies, with a particular focus on computational requirements. The analytical properties will be addressed in terms of local errors. Classical Runge-Kutta methods and symplectic integrators are considered.

Keywords: Neural Networks, Artificial Intelligence, Optimization : Theory and Algorithms
Abstract: Operators on function spaces are a versatile tool to describe maps between functions. An example of this is a map from the initial condition of a partial differential equation (PDE) to the solution at a final time. A popular choice to encode operators for this task is a Deep Operator Network (DeepONet), a model that approximates an operator by simultaneously learning two sub-networks. DeepONets are usually optimized iteratively on large datasets to find the optimal internal network parameters. A recently introduced algorithm from our group allows the numerical construction of neural network parameters by sampling from a data-dependent probability distribution. Here, we apply this idea to POD DeepONet parameter sampling, a variation of the original model. We demonstrate the approach on solutions to Burgers’ equation and show that our sampling method can achieve comparable accuracy while being orders of magnitude faster in training than the iteratively trained model.

Keywords: Quantum Control
Abstract: We develop a fourth-order Magnus expansion based quantum algorithm for the simulation of many-body problems involving two-level quantum systems with time-dependent Hamiltonians, H(t). A major hurdle in the utilization of the Magnus expansion is the appearance of a commutator term which leads to prohibitively long circuits. We present a technique for eliminating this commutator and find that a single time-step of the resulting algorithm is only marginally costlier than that required for time-stepping with a time-independent Hamiltonian making the proposed algorithm a suitable candidate for simulation of time-dependent Hamiltonians on near-term quantum devices. The significance of this problem to computational quantum chemistry and physics, the suspected exponential difficulty for classical computers, and the demonstrably linear growth in terms of number of qubits required, makes Hamiltonian simulation problems for many-body systems an important class of candidates for demonstrating quantum advantage.

Keywords: Neural Networks, Numerical and Symbolic Computations, Optimal Control
Abstract: Deep learning is widely used in tasks including image recognition and generation, in learning dynamical systems from data and many more. It is important to construct learning architectures with theoretical guarantees to permit safety in the applications. There has been considerable progress in this direction lately. In particular, symplectic networks were shown to have the non vanishing gradient property, essential for numerical stability. On the other hand, architectures based on higher order numerical methods were shown to be efficient in many tasks where the learned function has an underlying dynamical structure. In this work we construct symplectic networks based on higher order explicit methods with non vanishing gradient property and test their efficiency on various examples.

Keywords: Robotics, Large Scale Systems
Abstract: Data-driven model reduction methods provide a nonintrusive way of constructing computationally efficient surrogates of high-fidelity models for real-time control of soft robots. This work leverages the Lagrangian nature of the model equations to derive structure-preserving linear reduced-order models via Lagrangian Operator Inference and compares their performance with prominent linear model reduction techniques through an anguilliform swimming soft robot model example with 231,336 degrees of freedom. The case studies demonstrate that preserving the underlying Lagrangian structure leads to learned models with higher predictive accuracy and robustness to unseen inputs.

Keywords: Large Scale Systems, Systems on Graphs, Stability
Abstract: This paper investigates the synthesis problem for synchronization of heterogeneous multi-agent systems, which aims at characterizing the allowable diversities among the agents for which a uniform controller can be designed to achieve synchronization. We introduce a matrix phase alignment principle and employ it to solve the simultaneous stabilization problem of a collection of semi-stable systems. By applying this result, we elucidate the allowable diversity in terms of phase alignment of the residue matrices of the agents at their persistent modes. Moreover, when the problem is solvable, a controller design method is provided.

Keywords: Linear Systems, Dissipativity
Abstract: By virtue of the well-known KYP lemma, there is a dissipativity characterization of the system gain (positive realness, respectively) for multivariable linear time-invariant (LTI) systems. Recently, a new notion of system phase for multivariable LTI systems was defined. In this extended abstract, we shed light on the dissipativity characterization of the phase and establish its connections to optimal control problems. The results not only share similarity with the understandings of gain and positive realness, but also exhibit conceptual differences due to the asymmetry of phase properties. Furthermore, the results pave the road for a comprehensive study of phase theory in time domain.

Keywords: Linear Systems, Large Scale Systems
Abstract: This study explores the frequency-wise phases of linear time-invariant networks with n-ports, utilizing recently defined phases of complex matrices. These phase descriptions provide a quantitative measure of the widely recognized concept of passivity in networks. Furthermore, the study investigates a comprehensive set of matrix operations induced by all conceivable n-port network connections. A scalable phase-preserving criterion is formulated, allowing for effective determination of the phase range of the integrated network. This analysis maintains scalability by relying solely on the phase properties of individual subnetworks under the considered matrix operations.

Keywords: Mathematical Theory of Networks and Circuits, Operator Theoretic Methods in Systems Theory
Abstract: The understanding of singular values of matrices and operators is rather mutual and has been applied widely in science and engineering. In recent years, some studies have begun to focus on the phases of matrices and operators. The purpose of our research is to explore the `mixed' singular value and phase properties of matrices and operators. We establish a series of mixed singular value and phase majorization inequalities for a class of accretive matrices and operators. One occasion where the results can be applied is the study of the impedance matrices induced by connections of two n-port networks.

Keywords: Robust and H-Infinity Control, Linear Systems, Stability
Abstract: In this presentation, we first review the historical matrix small gain theorem and the recent matrix small phase theorem. Then we propose and study a matrix sectored-disk problem in which we wish to determine the invertibility of a matrix with mixed gain and phase uncertainty. The matrix sectored-disk problem can then be carried on to the robust feedback stability problem for multiple-input-multiple-output (MIMO) linear time-invariant (LTI) systems involving sectored-disk uncertainty, namely, dynamic uncertainty subject to simultaneous gain and phase constraints. This problem is thereby called an LTI system sectored-disk problem.

Keywords: Stability, Linear Systems, Robust and H-Infinity Control
Abstract: The search for multipliers for guaranteeing robust stability of a feedback interconnection is a common theme in the control theory literature, and under mild conditions the existence of a multiplier is a both necessary and sufficient condition for robust stability. Here, we further develop this and show that if the feedback is robustly stable against certain structured uncertainties, then there always exists a multiplier that takes a corresponding form. More precisely, robust stability against certain gain-type perturbations implies that there exists a multiplier that is of phase-type. Analogously, robust stability against certain phase-type perturbations implies that there exists a gain-type multiplier. The results are meaningfully instructive in the search for a valid multiplier for establishing robust closed-loop stability, and cover the well-known small-gain and the recent small-phase theorems.

Keywords: Machine Learning and Control, Operator Theoretic Methods in Systems Theory, System Identification
Abstract: This manuscript presents a framework for resolving inverse problems through the use of operator approximations over vector valued RKHSs. This generalizes Koopman based methods for data driven methods in dynamical systems, and three examples of this framework are presented.

Keywords: Machine Learning and Control, Operator Theoretic Methods in Systems Theory, System Identification
Abstract: Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system.

Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics.

This manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.

Keywords: Nonlinear Filtering and Estimation, Infinite Dimensional Systems Theory, Operator Theoretic Methods in Systems Theory
Abstract: A novel approach is reported for the observer design of nonlinear systems based on a Koopman operator framework. Using the adjoint of the Liouville operator (or Koopman generator), we define a dual Koopman system on a reproducing kernel Hilbert space, which is associated with a nonlinear dynamics. For a given class of dynamics, we build a Luenberger observer that estimates the state of the (linear) Koopman dual system. Then, the (infinite dimensional) estimated state yields an estimation of the (finite dimensional) state of the nonlinear dynamics. Moreover, we introduce new concepts of observability and detectability for the dual Koopman system, which are shown to be equivalent to observability and detectability of the finite dimensional nonlinear system, and we characterize them in terms of spectral properties.

Keywords: Operator Theoretic Methods in Systems Theory, Machine Learning and Control, System Identification
Abstract: This paper presents a new technique for norm-convergent dynamic mode decomposition of deterministic systems. The developed method utilizes recent results on singular dynamic mode decomposition where it is shown that by appropriate selection of domain and range Hilbert spaces, the Liouville operator (also known as the Koopman generator) can be made to be compact. In this paper, it is shown that by selecting appropriate collections of finite basis functions in the domain and the range, a novel finite-rank representation of the Liouville operator may be obtained. It is also shown that the model resulting from dynamic mode decomposition of the finite-rank representation is closely related to regularized regression using the so-called occupation kernels as basis functions.

Keywords: Dissipativity, Linear Systems
Abstract: This work is concerned with interconnected networks with non-identical subsystems. We investigate the output consensus of the network where the dynamics are subject to external disturbance and/or reference input. For a network of output-feedback passive subsystems, we first introduce an index that characterises the gap between a pair of adjacent subsystems by the difference of their input-output trajectories. The set of these indices quantifies the level of heterogeneity of the networks. We then provide a condition in terms of the level of heterogeneity and the connectivity of the networks for ensuring the output consensus of the interconnected network.

Keywords: Stability, Networked Control Systems, Optimization : Theory and Algorithms
Abstract: This study considers the problem of using district heating systems as ancillary services for primary frequency control in power networks. We propose a novel power sharing scheme for heating networks that ensures an optimal power allocation among the different heat sources, without having a prior knowledge of the disturbances. We also show that the stability of the combined heat and power network is maintained when this control scheme is used. Simulations demonstrate the benefits the proposed scheme can provide.

Keywords: Transportation Systems, Networked Control Systems, Information Theory
Abstract: We study an information design problem in transportation networks when users are strategic and the network state is uncertain. An omniscient planner observes the network state and discloses information to the users to minimize the expected travel time at the equilibrium. Since public signals are known to be inefficient in achieving optimality, we focus on private signals. We formulate and analyze the problem for arbitrary network topologies and delay functions. Then, we focus on networks with an arbitrary number of parallel links and affine delay functions, and provide sufficient and necessary conditions for optimality.

Keywords: Transportation Systems, Process Control
Abstract: Nodal demand satisfaction in potential flow networks often requires a scheduled manipulation of edge resistances. The actuators used to implement the resistance variations can broadly be classified into (i) discrete (edge fully OPEN or CLOSED) and (ii) continuous (continuously vary edge resistance). Previously, we presented theoretical bounds on the ratio of time required to transport a given quantum of material with either type of actuators assuming that that all sinks are at the same potential. In the present work, we extend the results to a class of networks with demand nodes at different potentials. Based on our findings, we conjecture that the bounds remain the same irrespective of whether the sinks are at the same potentials or not.

Keywords: Large Scale Systems, Networked Control Systems, Systems on Graphs
Abstract: It is known that in a growing string network of homogeneous agents, there are fundamental limitations on the local feedback control capability to regulate non-local dynamics over larger spacial range. In this note, we study this problem in the infinite (2D) lattice by deriving one of the sensitivity functions in the infinite sensitivity matrix. The analytical solution is obtained by employing spacial discrete Fourier transform. The result may shed light on practical control problems in large-scale finite lattices, as the finite lattice sensitivity function is expected to converge point-wise to the infinite one in the sense of H_2.

Keywords: Feedback Control Systems, Large Scale Systems, Optimal Control
Abstract: The Hamilton-Jacobi-Bellman (HJB) equation is a challenging first-order fully nonlinear PDE cast over mathbb{R}^d, where d can be arbitrarily large, and thus intractable through conventional grid based methods. In this context we propose to approximate the value function together with its gradient in a data-driven approach, learning a surrogate model for the value function via adaptive sampling of the solution of the HJB. The value function is represented in Functional Tensor Train format and it has been successfully applied to optimal control problems up to dimension 100. However, the dimension of the value function is still that of the state space, leading to a very large number of unknowns in the approximation ansatz and training data. A possible way to tackle this problem is given by the application of Proper Orthogonal Decomposition techniques. In contrast to existing techniques, we propose a Statistical Proper Orthogonal Decomposition (SPOD) which takes into account controlled trajectories treating boundary conditions and initial conditions as random variables. The corresponding reduced basis is chosen to minimize the empirical risk for the controlled solution and we will show its application to the vorticity stabilization of the 2D Navier-Stokes equations.

Keywords: Infinite Dimensional Systems Theory, Large Scale Systems, Optimal Control
Abstract: Motivated by multi-agent systems, we study discrete-time finite-horizon optimal control problems in probability spaces, whereby the state of the system is a probability measure. We show that, in many instances, the solution of dynamic programming in probability spaces results from two ingredients: (i) the solution of dynamic programming in the “ground space” (i.e., the space on which the probability measures live) and (ii) the solution of an optimal transport problem. From a multi-agent control perspective, a separation principle holds: The ”low-level control of the agents of the fleet” (how to reach the destination?) and “fleet-level control” (who goes where?) are decoupled. This extended abstract is based on our recent paper (Terpin, Lanzetti, and Dörfler, 2023).

Keywords: Nonlinear Systems and Control, Operator Theoretic Methods in Systems Theory, Stability
Abstract: We present a state-feedback design method ensuring exponential stability for nonlinear systems using measurement data only. Our approach combines Koopman theory and robust control to explicitly account for approximation errors due to finitely many data samples. The proposed controller design is framed as a semidefinite program in terms of linear matrix inequalities, allowing for an efficient solution. Finally, we demonstrate the efficacy of the proposed feedback design procedure in a numerical example.

Keywords: Optimal Control, Stochastic Control and Estimation, Nonlinear Systems and Control
Abstract: We propose to analyze and solve stochastic nonlinear optimal control problems by formulating them as convex optimization problems subject to a partial differential equation (PDE). Such PDE based formulations do not only enable us to analyze global minimizers but also to apply modern operator-based learning methods. We outline on how such a framework can be used for the development of effective data-driven nonlinear optimal control algorithms.

Keywords: Stochastic Modeling and Stochastic Systems Theory, Large Scale Systems, Systems Biology
Abstract: The totally asymmetric simple exclusion process (TASEP) is a stochastic model for the unidirectional dynamics of interacting particles on a 1D-lattice that is much used in systems biology and statistical physics. Its master equation describes the evolution of the probability distribution on the state space. The size of the master equation grows exponentially with the length of the lattice. It is known that the complexity of the system may be reduced using mean field approximations. We provide a rigorous derivation and a stochastic interpretation of these approximations and present numerical results on their accuracy for a number of relevant cases.

Keywords: Optimization : Theory and Algorithms

Keywords: Systems Biology, Stochastic Modeling and Stochastic Systems Theory

Keywords: Mechanical Systems, Physical Systems Theory

Keywords: Stability, Nonlinear Systems and Control, Adaptive Control
Abstract: We consider feedback stabilization of the discrete-time integrator restricted to magnitude feedback. This prototype problem captures the complexities of controlling systems with even non-linearities near their extremum points. This challenge is present in diverse problems such as wood chip refiner control, inverted pendulum systems based on height measurements, and antenna alignment utilizing signal power. Although effective adaptive controllers exist for these systems, it is not yet known if there is any stabilizing solution that is causal, linear, and time-invariant. This has led to the conjecture that no such controller exists. In this note, we present a first attempt at validating the conjecture by proving a partial result. In particular, our results show that the system is not strongly stabilizable.

Keywords: Feedback Control Systems, Control of Distributed Parameter Systems, Large Scale Systems
Abstract: The mathcal{H}_2 optimal control problem has been solved for simple sub-classes of poset-causal systems such as the two player problem, but the methods used there do not seem to extend easily to broader sub-classes of poset-causal systems. In this talk we consider the challenges of extending results to more intricate sub-classes of poset causal systems. Furthermore we present several strategies for constructing feasible structured controllers for mathcal{H}_2 optimal control problem for general poset-causal systems, taking various optimality considerations into account along the way.

Keywords: Feedback Control Systems, Operator Theoretic Methods in Systems Theory, System Identification
Abstract: We consider a new class of passive iFIR controllers. These are the parallel of an integrator and a finite impulse response filter. A data-driven design method based on virtual reference feedback tuning is illustrated, which does not require any model of the plant nor large datasets. Passivity is achieved via constrained optimization. iFIRs are more expressive than proportional-integral-derivative (PID) controllers but retain their features and simplicity of use. The approach is illustrated with a compliant mechanical system.

Keywords: Linear Systems, Feedback Control Systems, Discrete Event Systems
Abstract: We consider a classical problem of decoupling the output of a linear time-invariant system from the disturbances. It is well known that if certain decoupling conditions are met, there exists a linear state-feedback control that decouples the output from the disturbance. However, the control law obtained for disturbance decoupling in continuous time is usually implemented digitally leading to ineffective decoupling. Typically, one redesigns the decoupling control considering a discrete-time linear system obtained by using a sample and hold mechanism for control with uniform sampling. In contrast, here, we develop a self-triggered control strategy that ensures that the norm of the output of the system under the disturbance input remains bounded within a specified tolerance for all time. Furthermore, a heuristic procedure is provided to increase the time between successive triggers, thus reducing the number of triggers.

Keywords: Model Predictive Control, Adaptive Control, Feedback Control Systems
Abstract: The novel model-based controller funnel MPC allows for output tracking of smooth reference signals within prescribed error bounds for nonlinear multi-input multi-output systems with stable internal dynamics. Recently, a combination of this MPC algorithm with the model-free high-gain adaptive funnel control was proposed to make the former robust against disturbances, uncertainties, and structural model-plant mismatches. In this work we propose a generalization of this robust funnel MPC scheme to higher order systems that may encompass nonlinear time delays and potentially infinite dimensional internal dynamics.

Keywords: Adaptive Control, Feedback Control Systems, Nonlinear Systems and Control
Abstract: A feedback controller is proposed to perform output reference tracking with prescribed performance for nonlinear continuous-time systems of relative degree two. The controller is of sampled-data type, i.e., measurements are available only at sampling times - a typical situation in real systems when sensors are involved. Furthermore, only output information is available, i.e., neither the full state nor derivatives can be used for feedback. A sufficient uniform sampling rate is derived and the control consists of piecewise constant signals on the sampling intervals, i.e., zero-order hold. Feasibility of the controller and satisfaction of the control objective are rigorously proven. The controller is illustrated by a numerical example.

Keywords: Optimal Control, Control of Distributed Parameter Systems, Infinite Dimensional Systems Theory
Abstract: Linear-Quadratic (LQ) optimal controls are computed for a class of linear infinite-dimensional hyperbolic partial differential equations (PDEs), with inputs and outputs at the boundary of the spatial domain. After converting the continuous-time system into an equivalent discrete-time system, the optimal control problem is solved in discrete-time and its solution is then interpreted in continuous-time.

Keywords: Optimal Control, Large Scale Systems
Abstract: We present an explicit solution to the discrete-time Bellman equation for minimax optimal control of positive systems under unconstrained disturbances. The primary contribution of our result relies on deducing a bound for the disturbance penalty, which characterizes the existence of a finite solution to the problem class. Moreover, this constraint on the disturbance penalty reveals that, in scenarios where a solution is feasible, the problem converges to its equivalent minimization problem in the absence of disturbances.

Keywords: Optimal Control, Model Predictive Control, Optimization : Theory and Algorithms
Abstract: In this paper, we propose a novel method for addressing Optimal Control Problems (OCPs) with input-affine dynamics and cost functions. This approach adopts a Model Predictive Control (MPC) strategy, wherein a controller is synthesized to handle an approximated OCP within a finite time horizon. Upon reaching this horizon, the controller is re-calibrated to tackle another approximation of the OCP, with the approximation updated based on the final state and time information. To tackle each OCP instance, all non-polynomial terms are Taylor-expanded about the current time and state and the resulting Hamilton-Jacobi-Bellman (HJB) PDE is solved via Sum-of-Squares (SOS) programming, providing us with an approximate polynomial value function that can be used to synthesize a bang-bang controller.

Keywords: Optimal Control, Nonlinear Systems and Control, Feedback Control Systems
Abstract: The design and implementation of optimal robust controllers to optimize inter-sample tracking in nonlinear sampled-data control systems is considered. Optimal robust controllers that minimize inter-sample tracking errors are shown to exist for a very broad family of nonlinear systems that includes most systems of practical interest. A relatively simple technique for the design and implementation of such controllers is presented. Results apply to most nonlinear systems of practical interest.

Keywords: Optimal Control, Optimization : Theory and Algorithms, Systems on Graphs
Abstract: Distributed optimisation algorithms are used in a wide variety of problems where the goal is for a set of agents in a network to solve a network-wide optimisation problem via decentralised update rules. Here, we use inverse optimal control to show that a broad class of augmented primal-dual distributed optimisation algorithms can be viewed as the optimal solution to a network-wide optimal control problem, thus providing a performance metric for such methods.

Keywords: Optimal Control, Stochastic Control and Estimation, Nonlinear Systems and Control
Abstract: We consider an indefinite optimal regulator problem for a class of nonlinear stochastic systems with a square-root nonlinearity, random and possibly unbounded coefficients, and the quadratic-linear criterion with weight matrices being indefinite in general. This represents a certain nonlinear generalisation of the indefinite stochastic linear-quadratic control with random coefficients. All solutions to this problem are obtained in an explicit closed-form as an affine state-feedback control the coefficients of which are determined by the solution pairs of certain backward stochastic differential equations with algebraic equality and inequality constraints.

Keywords: Port-Hamiltonian Systems, Computations in Systems Theory, Linear Systems
Abstract: We discuss a new framework for structure-preserving model reduction of port-Hamiltonian systems based on optimization. Using frequency response samples, that can either be obtained from transfer function evaluations or measurements, we define an objective functional that measures the error between the given data and corresponding data that is generated by a reduced-order model with a prescribed structure. This functional can be minimized by gradient-based optimization to find a port-Hamiltonian model of prescribed order that explains the given data best and typically leads to small H-infinity errors due to its construction. We will also discuss extensions of the framework, e.g., to model reduction of descriptor systems or H-infinity control and to systems with other structures.

Keywords: Port-Hamiltonian Systems, Nonlinear Systems and Control
Abstract: In this work, we consider a scalable lumped-parameter model of the flexible structure in the port-Hamiltonian framework. We then propose a structure-preserving model reduction approach in the contraction framework. The contraction framework facilitates performing model reduction not around an equilibrium point, but rather along a trajectory of the system. As the interconnection matrix and the dissipation matrix are constant for the discretized model, the variational system provides the flexibility to preserve the port-Hamiltonian structure for the reduced-order model along a trajectory.

Keywords: Port-Hamiltonian Systems, Optimal Control, Linear Systems
Abstract: We discuss a calibration approach for port-Hamiltonian systems that was recently introduced in Guenther, Jacob, Totzeck (2023). The method exploits that the defining matrices of linear port-Hamiltonian systems are elements of manifolds embedded in respective Euclidean vector spaces. The matrix structure, for example positive definiteness or skew-symmetry, is preserved in each step of the gradient-based algorithm. Numerical results illustrate the feasibility and robustness of the approach.

Keywords: Port-Hamiltonian Systems, Stability, Stochastic Modeling and Stochastic Systems Theory
Abstract: This study revisits a recently proposed symmetric port-Hamiltonian single-file model in one dimension. The uniform streaming solutions are stable in the deterministic model. However, the introduction of white noise into the dynamics causes the model to exhibit divergence. In response, we add a relaxation term that draws the agents' speed to a desired constant speed and plays the role of the input in the port-Hamiltonian framework. Our results show that this relaxation term effectively stabilises the dynamics even in the presence of stochastic noise.

Keywords: Port-Hamiltonian Systems
Abstract: In general model order reduction techniques may lead to unstable reduced-order models, even if the corresponding full-order model is stable. One possibility for ensuring stability preservation is given by the preservation of a port-Hamiltonian structure which often implies stability. While there are many structure-preserving techniques in the context of linear subspace techniques, in this talk we focus on approaches involving nonlinear manifolds and demonstrate how to achieve structure preservation. To this end, we consider two classes of nonlinear manifolds and present corresponding structure-preserving model reduction techniques. At the end of the talk, we illustrate both approaches by means of a transport-dominated numerical test case.

Keywords: Stability, System Identification, Nonlinear Systems and Control
Abstract: This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability is a fundamental attribute of dynamical systems, yet it is not always assured in models derived through inference. Our main objective is to develop a method that facilitates the inference of quadratic control dynamical systems with inherent stability guarantees. To this aim, we investigate the stability characteristics of control systems with energy-preserving nonlinearities, thereby identifying conditions under which such systems are bounded-input bounded-state stable. These insights are subsequently applied to the learning process, yielding inferred models that are inherently stable by design. The efficacy of our proposed framework is demonstrated through a couple of numerical examples.

Keywords: Mechanical Systems, Mathematical Theory of Networks and Circuits
Abstract: This paper explores concepts to construct rotary fluid inerters, i.e. passive mechanical one-port (two terminal) devices such that the equal and opposite torque applied is proportional to the relative angular acceleration between them. Embodiments with unlimited and limited travel will be described. Their potential as robust integrated devices, and the use of parallel cavities to enhance their performance will also be considered.

Keywords: Multidimensional Systems, Hybrid Systems, Mechanical Systems
Abstract: In nature, different species of smaller animals produce ultra-fast movements to aid in their locomotion or protect themselves against predators. These ultra-fast impulsive motions are possible, as often times, there exist a small latch in the organism that could hold the potential energy in the system, and once released, generate an impulsive motion. These type of systems are classified as Latch Mediated Spring Actuated (LaMSA) systems, a multi-dimensional, multi-mode hybrid system that switches between a latched and an unlatched state. The LaMSA mechanism has been studied extensively in the field of biology and is observed in a wide range of animal species, such as the mantis shrimp, grasshoppers, and trap-jaw ants. In recent years, research has been done in mathematically modeling the LaMSA behavior with physical implementations of the mechanism. A significant focus is given to mimicking the physiological behavior of the species and following an end-to-end trajectory of impulsive motion. This paper introduces a foundational analysis of the theoretical dynamics of the contact latch-based LaMSA mechanism. The authors answer the question on what makes these small-scale systems impulsive, with a focus on the intrinsic properties of the system using bifurcations. Necessary and sufficient conditions are derived for the existence of the saddle fixed points. The authors propose a mathematical explanation for mediating the latch when a saddle node exists, and the impulsive behavior after the bifurcation happens.

Keywords: Networked Control Systems, Mathematical Theory of Networks and Circuits, Mechanical Systems
Abstract: This paper proposes two-port network representations for the inerter. The inerter is a genuine mechanical two-port element analogous to the capacitor in electrical networks in the force-current analogy. Its prominent advantages and unique mechanical characteristics have garnered widespread attention. This paper proposes two-port network representations of the inerter. For example, considering the rack-pinion inerter, we derive its corresponding block diagrams and two-port networks. Finally, we apply linear fractional transformations to derive their equivalent inertances.

Keywords: Optimal Control, Mechanical Systems, Large Scale Systems
Abstract: In this paper we provide optimal H2 and H-infinity controllers for an interesting class of mass-spring systems under no damping and uniform damping. The H2 optimal controller for the undamped and uniformly damped system are themselves passive damped mass-spring systems. This means that the controllers can be built from physical components and without an energy source. The H-infinity optimal control of the undamped mass-spring system is decentralized linear feedback. The types of systems that are investigated have an interesting interpretation in the AC frequency control of electrical power systems.

Keywords: System Identification, Mathematical Theory of Networks and Circuits, Mechanical Systems
Abstract: Passive vibration absorbers are employed in a wide range of engineering applications. Modern absorbers often incorporate physical components from various domains, including mechanical, hydraulic, pneumatic, and electrical. Research has shown that these multidomain absorbers offer broader functionalities compared to those limited to a single domain. Traditional design approaches for vibration absorbers typically involve making specific modifications to existing designs. While these approaches can enhance performance, they are limited in scope, addressing only a narrow range of design variation around the conventional device. Consequently, numerous absorber design possibilities remain unexplored, leaving their potentials locked.

Network synthesis, originally developed for electrical engineering problems, offers the opportunity to identify optimal absorber properties in network representation. Such properties are represented using a mechanical network configuration consisting of stiffness, damping and inertance elements. By employing network synthesis techniques, alternative absorber properties can be obtained which theoretically outperform traditional designs. However, such properties have not yet been translated into practical application due to two unresolved questions: 1) What is the network configuration of the conventional absorber? The existing network-synthesis design approach constructs network possibilities without considering any links to the existing absorber design. Therefore, there is no guarantee that the identified optimal network configuration can be physically realised. 2) How can the optimal network configuration be realised considering physical components from multiple domains? The existing network-synthesis approach focuses on a single-domain (i.e., mechanical) representation. This means the diversified functionalities of components from other domains cannot be systematically exploited.

This paper addresses these two key questions by developing a novel bi-directional multidomain synthesis technique. Using this technique, a vibration-absorber design methodology is proposed, which can construct an optimal vibration absorber considering physical components from multiple domains.

Keywords: System Identification, Mathematical Theory of Networks and Circuits, Mechanical Systems
Abstract: Network synthesis offers a systematic way for identifying optimal passive vibration suppression systems (VSSs). The conventional approach uses linear element properties to synthesize optimised impedances. However, the elements’ parasitic effects can cause discrepancies between the ideal and actual behaviours of a network, potentially leading to oversight of the true optimal network configuration. To address this issue, this paper introduces a physics-informed approach for VSS design that considers parasitic effects early in the optimal network identification stage. The approach’s efficacy is demonstrated through a case study, applying it to determine the optimal configuration of a hydraulic shock absorber for passenger cars.

Keywords: Adaptive Control, Nonlinear Systems and Control, Delay Systems
Abstract: We propose a new funnel control algorithm for output tracking with prescribed performance of the tracking error for a class of nonlinear multi-input, multi-output systems in the presence of input and state measurement delays. The controller does not require a precise knowledge of the system parameters and is of low complexity. The approach presented here fixes an error in the control design presented in a recent work on the same topic.

Keywords: Delay Systems, Hybrid Systems, Linear Systems
Abstract: From an input-output perspective, an asynchronous sampled-data link is an uncertain time-varying saw-tooth delay. It is well-known that the L2 gain of the corresponding integrator weighted perturbation of the ideal unity gain link is bounded by the maximum delay. A new parametrization of this uncertain perturbation is proposed in terms of the minimum delay increase between zero-order hold output updates, in addition to the maximum delay parameter. It is shown that a perturbation gain bound smaller than the maximum delay is possible over a narrow region of the parameter space; specifically, where the minimum delay increase is a sufficiently large fraction of the maximum delay. Outside this narrow region the maximum delay bound is less conservative.

Keywords: Delay Systems, Infinite Dimensional Systems Theory
Abstract: A continuous affine semiflow is introduced describing linear control systems with delays in the state and control and with bounded control range. The state of the semiflow includes the control function. It is proved that there exists a unique chain control set which corresponds to the chain recurrent set of the semiflow. The semiflow can be lifted to a linear semiflow on an infinite dimensional vector bundle with chain transitive base flow. A decomposition into exponentially separated subbundles is provided by a recent generalization of Selgrade's theorem.

Keywords: Delay Systems, Nonlinear Systems and Control, Stability
Abstract: In this paper, we are concerned with the regional exponential stabilization of a 1-D Burgers' equation under Neumann actuation via a modal decomposition method and dynamic extension. We consider a sampled-data finite-dimensional boundary control, which is implemented via a generalized hold device. We use Wirtinger-based piecewise continuous-time Lyapunov functional to compensate sampling of the finite-dimensional state, and provide the H^1-stability analysis for the full-order closed-loop system. Given a decay rate, we provide the efficient linear matrix inequality (LMI) conditions for finding the controller dimension and gain, as well as a bound on the domain of attraction. We prove that for some fixed upper bounds on the initial value and sampling intervals, the feasibility of LMIs for some N (dimension of the controller) implies their feasibility for N+1. Numerical example illustrates the efficiency of the proposed method.

Keywords: Delay Systems, Stability, Nonlinear Systems and Control
Abstract: For nonlinear time-delay systems, characterizations of input-to-state stability (ISS) are investigated. While general ISS superposition theorems for infinite-dimensional systems can be applied in this context, the criteria provided by such theorems are unnecessarily demanding. It is shown that for time-delay systems relaxed characterizations can be obtained. While recovering some ISS characterizations known for ordinary differential equations, we also highlight specific obstructions posed by time-delay systems. In particular, the boundedness of finite-time reachability sets becomes a central property in this context. As it turns out this assumption cannot be relaxed in a meaningful sense. With this assumption, however, several uniformity properties may be derived for time-delay systems.

Keywords: Delay Systems, Infinite Dimensional Systems Theory, Control of Distributed Parameter Systems
Abstract: For feedback control systems where the closed-loop system description is governed by linear delay-differential equations of neutral type, the achieved stability may be fragile, in the sense of being sensitive to infinitesimal perturbations to parameters in the system model or arbitrarily small errors in the implementation of the controller. A natural approach to resolve this problem of ill-posedness and to break down the underlying instability mechanisms, rooted in characteristic roots moving from the left plane to the right one via the point at infinity, consists of including a low-pass filter in the control loop, provided its inclusion is stability preserving. The addition of a low-pass filter essentially boils down to a ``regularization'' of delay-difference equations and delay equations of neutral type in terms of parametrized delay equations of retarded type, where the parameter corresponds to the filter's cut-off frequency. In my talk, the stability properties of these parametrized delay equations are analyzed in a general, multi-delay setting, with focus on the transition to the original delay-difference or neutral equation. It is illustrated that the spectral abscissa may be discontinuous at the transition. Conditions for preservation of stability in terms of a novel robustified stability indicator called filtered spectral abscissa are presented, for which mathematical characterizations and a computationally tractable expression are provided. The potential of the results in the controller design of systems described by hyperbolic PDEs, relying on integral transformations, is also discussed.

Keywords: Hybrid Systems, Systems on Graphs
Abstract: In this paper, we consider the decentralized control design problem for a particular case of networked switched affine systems. The considered network consists of interconnected (identical) linear systems with the controlled input switching among a finite set of values. We address a challenging case where the network can be only locally stabilized. Scalable Lyapunov based conditions are proposed for designing such decentralized controllers. The derived conditions (theoretical and linear matrix inequalities) do not depend on the number of subsystems. Ellipsoidal estimates of the domain of attraction are given.

Keywords: Hybrid Systems, Networked Control Systems, Dissipativity
Abstract: We consider robust controller synthesis for switched systems with graph-constrained switching with respect to quadratic performance criteria. The presented methods are based on dissipativity arguments and can be used to handle switched systems affected by a broad range of uncertainties and switching input-/output-dimension. Moreover, we show how the results can be applied to weakly hard real-time control systems – a system class naturally appearing in networked and real-time control.

Keywords: Hybrid Systems, Stability, Networked Control Systems
Abstract: To analyze the stability of a network of agents described by nonlinear oscillators which only exchange information about their position with some of its neighbors from time to time, we consider a theoretical framework of singularly perturbed hybrid systems. We describe such systems as an interconnection of two hybrid subsystems, a timer which triggers the jumps, and some discrete variables to determine the index of the jump maps. The flow equations of these variables are singularly perturbed differential equations, and in particular, smaller value of the singular perturbation parameter leads to increase in the frequency of the jump instants. For the limiting value of this parameter, we consider a decomposition which comprises a quasi-steady-state system modeled by a differential equation without any jumps, and a boundary-layer system described by purely discrete dynamics. Under appropriate stability assumptions on the quasi-steady-state system and the boundary-layer system, we derive results showing practical stability of a compact attractor when the information exchange between the agents occurs frequently often.

Keywords: Control of Distributed Parameter Systems, Hybrid Systems, Stability
Abstract: We consider here the uniform exponential stability analysis of linear time-invariant infinite dimensional impulsive systems defined on a Hilbert space X. Such systems have been the subject of previous works such as [1]. We combine ideas from hybrid systems theory [2,3] and infinite-dimensional systems [4–6] to produce operator-based stability conditions, which can be analytically or numerically checked using off- the-shelf tools. We extend the general results to address the stability of such systems subject to periodic impulse sequences and sequences satisfying a minimum dwell-time condition.

Keywords: Stability, Hybrid Systems
Abstract: This note investigates input-to-state stability (ISS) of nonlinear impulsive systems with hybrid impulses. Such systems contain a time-dependent jump map that can generate both stabilizing and destabilizing impulsive jumps. To cope with the two-fold effect of impulses within a single impulse time sequence, we use the concept of average impulsive gain. We provide novel sufficient conditions for ISS in terms of exponential ISS-Lyapunov function equipped with average impulsive gain and appropriate dwell-time condition. Contrary to the existing results we do not impose severe restrictions on impulsive gains, like periodicity or a finite number of different gains. Finally, we demonstrate effectiveness of our results by concluding ISS for a system whose ISS property cannot be verified by any other result available in the literature.

Keywords: Adaptive Control, Hybrid Systems, Numerical and Symbolic Computations
Abstract: This paper considers hybrid ODE solvers for process dynamics constructed by combining standard numerical schemes with standard observers. Specifically, we combine the first order Euler scheme with a Luenberger observer. The key ideas are to take advantage of available process output information and to switch from the numerical scheme to the process output-driven observer when the numerical scheme alone would produce inadequate results. Within this setup, two tasks emerge: How do we choose the observer gain? How do you choose the step size in the numerical scheme? Underpinning our approach is a λ tracking-based sampled-data observer that invokes a λ dead zone. This λ tracking observer adaptively determines the observer gain and the numerical step size. The resulting adaptive hybrid algorithm is a time-stepping numerical scheme. Using a sampled-data observer allows for process measurements to be only available at some discrete times, whilst adaptive tuning allows the gains and sampling times to adjust automatically to each other – rather than both being subject to design. Results are illustrated with examples of simulation.

Keywords: Stochastic Modeling and Stochastic Systems Theory, Stochastic Control and Estimation, Robust and H-Infinity Control
Abstract: This paper addresses the limitations of standard uncertainty models, i.e., robust (norm-bounded) and stochastic (one fixed distribution, e.g., Gaussian), and proposes to model uncertainty via Optimal Transport (OT) ambiguity sets. These constitute a very rich uncertainty model, which enjoys many desirable geometrical, statistical, and computational properties, and which: (1) naturally generalizes both robust and stochastic models, and (2) captures many additional real-world uncertainty phenomena (e.g., black swan events). Our contributions show that OT ambiguity sets are also analytically tractable: they propagate easily and intuitively through linear (possibly corrupted by additive or multiplicative stochastic noise) maps, and the result of the propagation is again an OT ambiguity set or can be tightly upper bounded by one. In the context of dynamical systems, our results allow us to consider multiple sources of uncertainty (e.g., initial condition, additive noise, multiplicative noise) and to capture in closed-form, via an OT ambiguity set, the resulting uncertainty in the state at any future time.

Keywords: Machine Learning and Control, Adaptive Control, Feedback Control Systems
Abstract: We propose a two-component data-driven controller to safely perform docking maneuvers for satellites. Reinforcement Learning is used to deduce an optimal control policy based on measurement data. To safeguard the learning phase, an additional feedback law is implemented in the control unit, which guarantees the evolution of the system within predefined performance bounds. We define safe and safety-critical areas to train the feedback controller based on actual measurements. To avoid chattering, a dwell-time activation scheme is implemented. We provide numerical evidence for the performance of the proposed controller for a satellite docking maneuver with collision avoidance.

Keywords: Machine Learning and Control, Artificial Intelligence, Linear Systems
Abstract: This talk shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated lin- ear state-space representations of generic observations of an invertible dynamical system carry in their wake an embedding of the phase space dynamics into the chosen Euclidean state space. This embedding coincides with a natural generalized synchronization that arises in this setup and that yields a topological conjugacy between the state-space dynamics driven by the generic observations of the dynamical system and the dynamical system itself. This result provides additional tools for the representation, learning, and analysis of chaotic attractors and sheds additional light on the reservoir computing phenomenon in the context of recurrent neural networks.

Keywords: Machine Learning and Control, Neural Networks, Stochastic Control and Estimation

Keywords: Nonlinear Filtering and Estimation, Stochastic Control and Estimation, Stability
Abstract: For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly sampled. We propose a continuous-discrete McKean--Vlasov type diffusion process with additive Gaussian noise in observation model, which is used to describe the evolution of the individual particles in the ensemble. These particles are coupled through the empirical covariance and require less computations for implementation than the optimal ones based on solving Riccati differential equations. Using appropriate analysis tools, we show that the empirical mean and the sample covariance of the ensemble filter converges to the mean and covariance of the optimal filter if the mean sampling rate of the observation process is sufficiently large and as the number of particles tends to infinity.

Keywords: Stochastic Control and Estimation, Multidimensional Systems, Information Theory
Abstract: We discuss importance sampling of exit problems that involve unbounded stopping times; examples are mean first passage times, transition rates or committor probabilities in molecular dynamics. The naive application of variance minimization techniques can lead to pathologies here, including proposal measures that are not absolutely continuous to the reference measure or importance sampling estimators that formally have zero variance, but that produce infinitely long trajectories. We illustrate these issues with simple examples and discuss a possible solution that is based on a risk-sensitive optimal control framework of importance sampling.

Keywords: Robust and H-Infinity Control, Systems Biology, Systems on Graphs
Abstract: The presentation will overview a most remarkable path in Science and Engineering by Allen Tannenbaum, a towering figure in the field of Mathematical Systems Theory, Robust Control, Image Processing, Optimal Mass Transport and Biomedical Applications, who departed on December 28, 2023. We will highlight some of his most important contributions that underscore the broad spectrum and impact of his work, from the structure of systems to robust control, analytic function theory, partial differential equations and group invariance for applications in image analysis, optimal mass transport on continuous/discrete spaces and on the non-commutative/quantum setting, on the structure of networks focusing on gene regulatory networks, and on a wide range of biomedical applications targeting cancer.

Speakers: 1. Tryphon Georgiou (UC Irvine) 2. Yongxin Chen (Georgia Tech) 3. Hitay Özbay (Bilkent) 4. Yutaka Yamamoto (Kyoto)