Keywords: Neural Networks
Abstract: This presentation introduces an approach that leverages the known properties of isolated nonlinearities—referred to as quadratic abstractions—to analyze the closed-loop behavior of dynamical systems, including stability, performance, and robustness. Different ways to reduce the conservatism inherent in traditional quadratic abstraction methods are also proposed. This framework is particularly effective for analyzing activation functions in neural network architectures, such as multilayer perceptrons (MLPs), when used to control dynamical systems, offering a robust tool for closed-loop analysis.

The proposed methodology relies on Lyapunov functions, which can be either standard quadratic or sign-indefinite quadratic forms. The latter incorporates an extended quadratic structure to further mitigate conservatism, enhancing the accuracy and applicability of the analysis. By incorporating sign-indefinite quadratic Lyapunov functions with extended quadratic structures, our methodology not only mitigates conservatism but also enhances the accuracy and applicability of the analysis, paving the way for more reliable neural network-controlled systems.

Keywords: Optimal Control, Linear Systems, Machine Learning and Control
Abstract: We introduce a model-free receding-horizon algorithm for the discrete-time Linear Quadratic Regulator problem with infinite-horizon cost and unknown dynamics. Inspired by REINFORCE, our approach uses a gradient estimation technique that avoids the impractical assumptions of commonly used two-point methods, while maintaining the same order of sample complexity. In particular, these methods require access to zero-order evaluations for different policies driven by identical randomness, an assumption that is completely avoided in our work. Moreover, the receding-horizon structure of the algorithm removes the need for prior knowledge of an initial stabilizing policy, a ubiquitous requirement in existing literature. Beyond these improvements, we provide a refined analysis of error propagation by exploiting the contraction of the Riccati operator under the Riemannian distance, leading to better sample complexity rates and convergence guarantees.

Keywords: Linear Systems, Machine Learning and Control
Abstract: This extended abstract presents a negative result for the direct data-driven parametrization used for linear quadratic regulator (LQR) problem and the corresponding semi-definite program (SDP). While this SDP is shown to lead to correct LQR gains when the input-state data from the system is noise free, we show that it has a trivial solution with probability one whenever the system is subject to process or measurement noise. We also discuss why certain types of regularization do not mitigate this problem.

Keywords: Operator Theoretic Methods in Systems Theory, Nonlinear Systems and Control, Nonlinear Filtering and Estimation
Abstract: In this extended abstract, we present results on a unified operator-theoretic framework for both emph{nonlinear optimal control} and emph{nonlinear state estimation}. We show that the solution to both these problems can be reduced to the solution of a Hamilton--Jacobi (HJ) equation, and that both problems admit an efficient emph{quadratic parameterization} in emph{Koopman eigenfunction coordinates}. The results presented in this extended abstract are reported from cite{vaidya_KoopmanspectrumTAC}cite{vaidya_Koopmanestimat ion}. The main idea is to (i) construct a low-dimensional Koopman coordinate map using principal eigenfunctions of the (open-loop) dynamics, (ii) parameterize the HJ value function quadratically in these Koopman coordinates, and (iii) compute the quadratic parameters through Riccati-type differential equations. The Koopman eigenfunctions are computed independently from the open-loop dynamics using a path-integral (Monte Carlo) procedure, which leads to a separation principle not only between estimation and control, but also at the level of value-function construction: the Riccati equations for the quadratic parameters can be solved separately from the Koopman eigenfunctions, which are reusable across multiple objectives.

Keywords: System Identification, Nonlinear Systems and Control
Abstract: A semigroup characterization, equivalently, a characterization via the generator, is a classical framework for describing continuous-time nonlinear dynamical systems. In a datadriven setting, learning an unknown nonlinear system amounts to estimating the generator of the semigroup of its Koopman operators from discrete-time observations and establishing convergence to the true generator in an appropriate sense. Existing methods either rely on accurate time-derivative estimation and therefore face limitations under restricted observation rates, or bypass derivative estimation by exploiting the logarithm of a Koopman operator, which is valid only on restrictive function spaces and depends on prior knowledge of spectral properties. In this extended abstract, we summarize the recent advances in Meng et al. (2026), which propose a resolvent-type generator learning method that relaxes observation-frequency requirements and constraints on the choice of observable functions.

Keywords: Nonlinear Systems and Control, Stability
Abstract: Invariant sets are essential for ensuring safety, i.e. constraint adherence, of dynamical systems. With the increasing availability of sampled data from complex (and often unmodeled) systems, it is advantageous to leverage these data sets for control invariant set synthesis. This work will discuss the use of data to directly evaluate geometric conditions of invariance and synthesize positive and control invariant sets, without the benefit of a dynamical model. Beyond a data set and Lipschitz continuity, no additional information about the system is needed. A tree data structure partitioning the space is the crucial ingredient, enabling efficient set operations and construction of the invariant sets, while Lipschitz continuity is used to provide deterministic guarantees of invariance.

Keywords: Large Scale Systems, Optimal Control, Computations in Systems Theory
Abstract: We classify a family of matrices of shift operators that can be factorised in a computationally tractable manner with the Cholesky algorithm. Such matrices arise in the linear quadratic regulator problem, and related areas. We use the factorisation to uncover intrinsic sparsity properties in the control laws for transportation problems with an underlying tree structure. This reveals that the optimal control can be applied in a distributed manner that is obscured by standard solution methods

Keywords: Linear Systems, Optimal Control, Stability
Abstract: This abstract shows that positive linear systems can be stabilized using positive Luenberger-type observers. This is achieved by structuring the observer as monotonically converging upper and lower bounds on the state. Analysis of the closed-loop properties under linear observer feedback gives conditions that cover a larger class than previous observer designs. The results are applied to nonpositive systems by enforcing positivity of the dynamics using feedback from the upper bound observer. The setting is expanded to include stochastic noise, giving conditions for convergence in expectation using feedback from positive observers.

Keywords: Linear Systems, Stability
Abstract: This paper announces an equivalent condition for the notion of stabilizability on a cone, namely the solution to a conic inequality. This equivalence can be viewed as a generalization of a well-known stability result for unforced cone-preserving systems, and it collapses to a standard statement about stabilizing linear feedback in the case of the positive semidefinite cone. Of particular interest is the cone itself, which is constructed intuitively by stacking slices of a lower-dimensional cone: stabilizability then corresponds to stable closed-loop dynamics on these layers by means of linear feedback manifesting as an embedding of the latter cone into the former. This result along with its associated definitions is part of an ongoing effort to home in on and better understand certain cone analogs to some standard concepts and results in linear-quadratic theory.

Keywords: Operator Theoretic Methods in Systems Theory, Infinite Dimensional Systems Theory, Stability
Abstract: We investigate the exponential dichotomy of retarded-perturbed boundary control systems with dynamic boundary conditions. The perturbation consists of a delayed interior feedback term Lx_t and a coupling term Hx from the state to the boundary dynamics. Using the feedback theory of infinite-dimensional regular linear systems, we establish well-posedness of the system and prove that the associated semigroup is hyperbolic under suitable spectral conditions. Moreover, we study the robustness of exponential dichotomy under these perturbations. The theoretical findings are illustrated by a coupled ODE-transport PDE system.

Keywords: Infinite Dimensional Systems Theory, Linear Systems, Control of Distributed Parameter Systems
Abstract: For linear infinite-dimensional systems, exponential detectability is known to be stronger than exponential zero-detectability, and both these concepts are hard to extend to the nonlinear setting. In this work, we show that there is a broad hierarchy of detectability notions between these two concepts, centered around the concept of exponential output-to-state stability (eOSS). We study eOSS for linear infinite-dimensional systems with bounded output operators. It is shown that exponential detectability guarantees the existence of a coercive eOSS Lyapunov function and therefore eOSS. Several counterexamples demonstrate the fundamental differences between the detectability concepts employed in this work. However, if the system has only finitely many unstable eigenvalues, then all the concepts coincide. The results are illustrated with an example.

Keywords: Operator Theoretic Methods in Systems Theory, Control of Distributed Parameter Systems, Port-Hamiltonian Systems
Abstract: We establish well-posedness of a passive boundary control system associated with Maxwell’s equations. The analysis is based on trace spaces for curl-conforming vector fields, i.e., vector fields with square-integrable curl, together with operator-theoretic methods.

Keywords: Infinite Dimensional Systems Theory, Operator Theoretic Methods in Systems Theory
Abstract: This work aims at providing a unified analysis of the exponential stabilization of some abstract infinite dimensional systems undergoing an event-triggering mechanism that samples the control input. The partial differential equation is supposed to be defined by a skew-adjoint operator and controlled and observed through bounded operators. The continuously controlled closed loop system is assumed to be exponentially stable and the goal is to prove that a well- designed event-triggering mechanism to rule the time updates of the sampled control will allow to keep such a stability property. The key of the proof relies on the existence of an adequate Lyapunov functional. Existence and regularity of the solution to the closed-loop event-triggered system are also proven, along with the avoidance of Zeno behavior.

Keywords: Signal Processing, Nonlinear Filtering and Estimation, Large Scale Systems
Abstract: We propose a tensor-based generalized likelihood ratio test (GLRT) for target detection in massive MIMO radar systems. Unlike conventional methods that vectorize multi-dimensional data and destroy the spatial-temporal-range structure, our approach operates directly on tensor-valued observations, exploiting their low-rank nature via canonical polyadic decomposition. The resulting detector achieves dramatic complexity reduction while retaining the optimality of conventional GLRT, enabling real-time processing for arrays with over one thousand antennas. Simulations confirm performance comparable to the optimal detector with orders-of-magnitude computational savings.

keywords: MIMO radar, tensor decomposition, GLRT, adaptive detection, massive arrays, canonical polyadic decomposition

Keywords: Stochastic Control and Estimation, Optimal Control, Physical Systems Theory
Abstract: A diffusion-based representation for the Maslov dequantization of the time-dependent Schrodinger equation is obtained, where the wave function corresponds to the statical value function of a complex-valued stochastic control problem. Whereas previous efforts along this line were restricted to holomorphic potentials, we here use an additional controller specifically constructed to generate the Coulomb potential via staticization. The solution to the Schrodinger equation is obtained from requantization of the representations. A demonstrative numerical example is included at the end.

Keywords: System Identification, Large Scale Systems, Nonlinear Filtering and Estimation
Abstract: The Expectation-Maximization algorithm is fundamental for parameter estimation in state space models but becomes computationally intractable for high-dimensional systems due to cubic-complexity matrix operations. We develop a scalable variant that replaces direct linear solves with iterative Krylov subspace methods, achieving quadratic complexity per iteration. We establish convergence to stationary points under summable tolerance conditions, extending classical EM theory to accommodate controlled approximation errors. An adaptive tolerance schedule automatically adjusts solver precision as convergence progresses, requiring no problem-specific tuning. Warm-starting from previous iterates yields substantial computational savings. Experiments on high-dimensional tracking problems demonstrate order-of-magnitude speedups while preserving solution accuracy to machine precision.

Keywords: Nonlinear Filtering and Estimation, Applications of Algebraic and Differential Geometry in Systems Theory, Robotics
Abstract: We apply a continuous discrete geometric approximate minimum energy filter design to the problem of estimating the pose (position and orientation) of a mobile robot moving in 3D space. The robot measures bearings to known landmarks in the environment and its own linear and angular velocities. We show that, surprisingly, the robustness of the resulting nonlinear deterministic filtering algorithm to different levels of initialization error heavily depends on the choice of Riemannian metric employed in the filter design. The obtained result is unintuitive since it turns out that endowing SE(3) with a direct product metric outperforms the a priori more natural choice of an invariant metric, pointing to an intriguing open question on quadratic approximation in-the-large of value functions defined on smooth manifolds.

Keywords: Nonlinear Systems and Control
Abstract: Classical contraction theory is a well-established framework for analyzing nonlinear dynamics, with numerous applications in control theory. However, its strict requirements can often limit its practical applicability. This semi-plenary explores two relaxations of the contraction definition. First, we examine the transition from Incremental Global Exponential Stability to Incremental Global Asymptotic Stability. While relaxing the exponential bound provides theoretical flexibility, recent topological insights indicate that these two notions often coincide globally. Consequently, this relaxation, although analytically rigorous, results in a relatively minor shift in practical system behavior. Next, we explore the concept of k-contraction, which generalizes standard distance convergence to the shrinkage of k-dimensional volumes. We will briefly review existing analysis results before presenting recent developments in k-contraction theory. Specifically, we will show how to derive sufficient conditions that avoid the use of compound matrices, thereby enabling the systematic design of k-contractive controllers.

Keywords: Control of Distributed Parameter Systems
Abstract: In biomechanics, local phenomena, such as tissue perfusion, are strictly related to the global features of the surrounding blood circulation. We propose a heterogeneous model where a local, accurate, 3D description of fluid flows through deformable porous media by means of poroelastic systems is coupled with a systemic 0D lumped model of the remainder of the circulation. This represents a multiscale strategy, which couples an initial boundary value problem to be used in a specific region with an initial value problem for the rest of the circulatory system. We present new results on wellposedness analysis, optimal control and solution methods for this nonlinear multiscale interface coupling of PDEs and ODEs. Our results have applications in biomedicine and bioengineering, including tissue perfusion, fluid flow inside cartilages and bones, and design of bioartificial organs.

Keywords: Nonlinear Filtering and Estimation, Neural Networks, Machine Learning and Control
Abstract: Kazantzis-Kravaris/Luenberger (KKL) observers estimate the state of a nonlinear system by constructing an injective map that embeds the system state into a higher-dimensional observer state with linear, exponentially stable error dynamics. The corresponding inverse map then recovers the state estimate in the original coordinates. In practice, identifying a suitable transformation and its inverse remains a challenge. Recent work addresses this difficulty by approximating the forward map with a physics-informed neural network (PINN) and the inverse map with a conventional neural network. Although generalization bounds for these approximations have been derived, they depend on non-computable terms, and therefore do not yield concrete robustness guarantees. In this paper, we develop a computable estimation error certificate for learning-based KKL observers with the use of the neural network verification tool alpha beta-CROWN.

Keywords: Robotics, Machine Learning and Control
Abstract: Control Barrier Functions (CBFs) are a popular method to guarantee safety of autonomous systems, however, their safety guarantees can be invalidated by sensor faults that prevent the system from obtaining an accurate state estimate. In this paper, we introduce a sensor fault detection and mitigation algorithm to ensure safe operation of autonomous systems. Our approach is based on constructing a sequence of nested sets of state space, each with a corresponding CBF constraint, and proving that each set is invariant under a particular fault mode. Faults can then be detected and diagnosed by observing which invariance constraints are violated, effectively utilizing the CBFs as fault detectors. We present a loss-function construction for synthesizing data-driven fault-tolerant Neural CBFs and verify our results on unicycle obstacle avoidance.

Keywords: Neural Networks, Machine Learning and Control
Abstract: We present a novel framework for embedding guaranteed constraint satisfaction into neural network (NN) architectures, specifically feedforward neural networks and transformers, with input-dependent affine constraints of arbitrary cardinality. Traditional constraint enforcement approaches either rely on penalty-based soft constraints, which offer no guarantee of satisfaction, or on post-processing methods that enforce constraints after the NN is trained, which may lead to suboptimality. We introduce a trainable constraint-affine (CAffine) layer into NNs, yielding CAffNet, which goes beyond enforcing affine constraints via fixed orthogonal or parallel projections and enables joint optimization with network parameters. Moreover, we impose no restrictions on the constraint space dimensions and establish that our construction preserves the universal approximation properties of NNs, while providing provable guarantees on constraint adherence for all inputs. Various simulations demonstrate guaranteed constraint satisfaction, including for enforcing control barrier function constraints for dynamical systems.

Keywords: Control of Distributed Parameter Systems, Machine Learning and Control, Optimal Control
Abstract: Many control systems are designed under with control signals continuous in time and amplitude. In applications, however, actuators often operate through finitely many admissible configurations combined with switching mechanisms. Motivated by this, we introduced the concept of ``multilevel control'', that is, piecewise constant in time controls taking values in a prescribed finite set. This multilevel structure is not imposed as a hard constraint, but rather encoded indirectly through nonsmooth convex penalties in the cost functional, allowing finite-valued and switching controls to emerge naturally from optimality conditions. This approach preserves the variational nature of the control problem and avoids the combinatorial complexity proper of switching optimization. This multilevel framework reveals deep connections with learning dynamics, particularly in the context of Neural Ordinary Differential Equations (Neural ODEs), where learning is naturally interpreted as a simulatneous controllability problem in which a time-dependent function steers the system's state from input data to desired outputs. Our results showed that such simultaneous controllability problems admit solutions with a simple temporal structure: optimal controls are piecewise constant in time, with a finite number of switches. Moreover, explicit bounds on the number of switches can be derived in terms of the data's geometry and distribution. These findings suggest that switching complexity plays a role analogous to model capacity in learning theory, providing a quantitative measure of the expressive power required to fit a given dataset. In this talk, we will present the multilevel control framework and its duality-based characterization, emphasizing how switches arise as intrinsic features of optimal solutions, and discuss how controllability and expressivity in Neural ODEs can be naturally interpreted within this setting.

Keywords: Networked Control Systems, Neural Networks, Linear Systems
Abstract: Most existing neural network verification frameworks assume that network parameters are fixed and precisely known, and mainly focus on input uncertainty, such as adversarial perturbations. However, in real-world deployments, especially in cyber-physical systems, this assumption often does not hold. Neural network weights and biases can be uncertain due to quantization, hardware variability, and model updates, which may significantly alter closed-loop system behavior and compromise safety guarantees. To capture this, we model such networks as Interval Neural Networks (INNs), where parameter uncertainty is represented using interval-based perturbation sets. Accordingly, we study the problem of robust verification of INN-controlled dynamical systems. Our approach performs sequential reachability analysis of both the INN and the underlying dynamical system over a finite horizon of K iterations, and safety is verified by checking whether the computed reachable set intersects with a given unsafe set. We extend both Big-M and Starset-based techniques to compute reachable sets for INN-controlled dynamical systems and evaluate the approach on Adaptive Cruise Control (ACC) and Translational Oscillator with Rotational Actuator (TORA) benchmarks. Experimental results show that the Big-M-based method is faster than the Starset-based approach.

Keywords: Algebraic Systems Theory, Multidimensional Systems, Linear Systems
Abstract: Since the formulation of Data Informativity, which assesses whether a model consistent with given data possesses desirable system characteristics, numerous results concerning controllability, observability, and other fundamental properties crucial to model-based control have been reported. In this way, while data-driven control draws on the subjects and methods of analysis and design in model-based control to a greater or lesser extent, approaches that focus on constructing the theoretical framework itself―as discussed in model-based control―remain relatively few. This paper focuses on Informativity for observability from an algebraic viewpoint. Inspired by the Geometric Approach in model-based control,observability is revisited starting from the definition of the unobservable subspace. By explicitly characterizing the geometric and algebraic structure between models and data, we derive observability Informativity conditions that are independent of the data acquisition dimension.

Keywords: Algebraic Systems Theory, Nonlinear Systems and Control, Numerical and Symbolic Computations
Abstract: Successive re-centering of Chen-Fliess series (CFS) extends the domain of the series representation of systems beyond their finite execution horizon, which enables applications in receding horizon system analysis and control. However, each re-centering step introduces an approximation error due to truncation and re-centering coefficient deviations. {Systematically quantifying these stepwise errors is an essential first step toward understanding their behavior over successive re-centerings.} This paper develops a methodology for quantifying the error induced by the truncation and re-centering of a CFS. Explicit upper bounds are derived for truncation error, re-centering error, and their combined effect, in terms of the convergence properties of the associated CFS. Examples are provided to illustrate the results.

Keywords: Nonlinear Systems and Control, Applications of Algebraic and Differential Geometry in Systems Theory
Abstract: Identifying the dynamic precompensator that renders a nonlinear control system feedback linearizable is a challenging problem. Researchers have explored the problem --- dynamic feedback linearization --- and produced existence conditions and constructive procedures for the dynamic precompensator. These remain, in general, either computationally expensive or restrictive. Treating the challenge as intrinsic, this article views the problem as a search problem over a category. Dynamic programming applies and, upon restriction to a finite category, classic search algorithms find the minimal dynamic extension. Alternatively, a heuristic aiming towards feedback linearizable systems can be employed to select amongst the infinitely-many extensions. This framing provides a distinctive, birds-eye view of the search for the dynamic precompensator.

Keywords: Applications of Algebraic and Differential Geometry in Systems Theory, Nonlinear Systems and Control, Feedback Control Systems
Abstract: Despite ongoing research, testing the flatness of discrete-time systems remains a challenging problem. To date, only the property of forward-flatness - a special case of difference-flatness - can be checked in a computationally efficient manner. In this paper, we propose a systematic approach for testing backward-flatness, which is another special case of difference-flatness, and for deriving a corresponding backward-flat output. Additionally, we discuss the relationship between the Jacobian matrices associated with the flat parameterization of backward- and forward-flat systems and illustrate our results by an academic example.

Keywords: Algebraic Systems Theory, Nonlinear Systems and Control, Applications of Algebraic and Differential Geometry in Systems Theory
Abstract: This presentation aims to give an overview of some algebraic aspects of the author's joint research project with Michael Herty (RWTH Aachen University) in the area of particle dynamics, which was funded by the German Research Foundation DFG within the framework of the Collaborative Research Center "Sparsity and Singular Structures", from mid-2022 to mid-2026. Thanks to this support, we were able to hire PhD student Melanie Harms, who submitted and defended her thesis in 2025, and postdoc researcher Chiara Segala, who obtained a position at the University of Italian-speaking Switzerland in late 2024.

Keywords: Control of Distributed Parameter Systems, Large Scale Systems
Abstract: This extended abstract considers PDE continua as approximations of large-scale hyperbolic PDEs. The continuum approximation aspect is considered from the viewpoints of approximating both solutions to hyperbolic PDEs and solutions to backstepping kernel equations, which can be employed in stabilization of such systems. Finally, we provide discussion on alternative ways of constructing continuum approximations, as well as on potential alternative frameworks for PDE continua.

Keywords: Control of Distributed Parameter Systems, Feedback Control Systems, Nonlinear Systems and Control
Abstract: We study the control of a one-dimensional heat equation with two inputs and two outputs. Our main goal is to design a controller that makes the closed-loop system excitable in the sense of the system's sensitivity to external inputs exceeding a given threshold. We achieve this with a nonlinear dynamic feedback controller. We demonstrate the excitability properties of the controlled heat equation.

Keywords: Control of Distributed Parameter Systems, Linear Systems, Multidimensional Systems
Abstract: This work addresses the control of spatially multidimensional hyperbolic PDE models that frequently arise in transport–reaction processes in chemical engineering. The main contribution of this manuscript is a systematic analytical approach for obtaining the evolution of a multidimensional hyperbolic PDE system. In particular, the well-known Laplace transform is used in both space and time to obtain analytical expressions for the input-output mapping and the state evolution under arbitrary initial conditions. The stability analysis reveals the boundedness of the state evolution and provides insight into the system's minimum-time stability

Keywords: Infinite Dimensional Systems Theory, Control of Distributed Parameter Systems, Stochastic Control and Estimation
Abstract: This work addresses optimal constrained state and output estimation of distributed parameter systems under limited and noisy output measurements using moving horizon estimation (MHE). In particular, we consider the MHE design for the discrete-time infinite-dimensional system, which can be linked to the corresponding continuous-time infinite-dimensional system using the Cayley-Tustin time discretization method. To address the data scarcity issue in state and output estimation of the discrete-time infinite-dimensional system, we propose a new MHE framework to achieve a good balance between the feasibility of the algorithm execution and estimation performance. Furthermore, we show the stability analysis of the proposed MHE method and the relationship between the estimation error, MHE parameters, and the observability of the system. Finally, we provide numerical examples on a class of conservative distributed parameter systems (such as the Schrödinger equation) to demonstrate the effectiveness of the proposed MHE design.

Keywords: Infinite Dimensional Systems Theory, Optimal Control, Systems Biology
Abstract: Fluid flow in deformable porous media appears in many applications, from geomechanics to biomechanics, and is commonly modeled by coupled partial differential equations describing the interaction between fluid transport and mechanical deformation. A standard framework is Biot’s theory of poroelasticity which, under quasi-static assumptions, yields a coupled parabolic–elliptic system that can be viewed as an implicit, degenerate evolution equation. While well-posedness and regularity are well-understood, optimal control problems constrained by such poroelastic dynamics, especially in biomedical settings where pressure and displacement must be regulated, remain relatively unexplored and mathematically challenging due to degeneracy and implicit coupling. In this work, we reformulate the flow–deformation model as an implicit dynamical system on Hilbert spaces and analyze it using E-radiality theory, a generalization of the Hille–Yosida framework for non-explicit evolution equations. This approach yields new well-posedness insights and provides a unified framework for linear control problems governed by degenerate evolution dynamics.

Keywords: Nonlinear Systems and Control, Stability, Hybrid Systems
Abstract: We present sufficient conditions for the semi-global exponential stability of nonlinear systems whose dynamics have both slow and fast time variations. Unlike most existing results, the fast variation is non-periodic, thereby allowing a wider class of systems, especially switched systems with fast (non-periodic) switching and those with quasi-periodic variations; we therefore rely on general averaging to construct an average system. It is assumed that the average system admits a time-invariant equilibrium that is globally exponentially stable when the slow variation is frozen, i.e., remaining at a fixed value. This slow variation is allowed to be discontinuous in time, provided its total variation (flows and jumps) is bounded. The main result is illustrated using a nonlinear switched system with slow-fast non-periodic switching.

Keywords: Nonlinear Systems and Control, Stability
Abstract: This paper is concerned with local stabilization of discrete-time bilinear systems through the combination of a stabilizing nonlinear state feedback control law and a bilinear state observer, leading to an observer-based controller and an observer-incorporated closed-loop system. More specifically, we assume that a state feedback control law with state and input constraints satisfied is designed through a quadratic Lyapunov function. We further assume that an observer is designed in such a way that a quadratic Lyapunov function ensures the associated estimation error dynamics to be stable robustly regardless of the sequence of the plant input, as long as it satisfies, via saturation treatment, the constraint that has been taken into account in the design of the nonlinear state feedback control law. With the knowledge by the preceding studies by the authors that such design procedures are indeed available, we are naturally interested in whether or not a separation principle holds for the combination of these procedures. This paper establishes a positive answer to this question by showing that the origin of the observer-incorporated closed-loop system is locally exponentially stable. In addition, the arguments are extended to accommodate the case without explicit control input constraints, and an implication of the established separation principle on the use of integral compensation is further discussed.

Keywords: Nonlinear Systems and Control, Stability, Systems Biology
Abstract: We propose a two-dimensional nonlinear ODE model for the coupled dynamics of depression symptoms and resilience in response to adverse external stimuli. The model is monotone with respect to a natural partial order and exhibits bistability: a locally stable healthy equilibrium and a locally stable severe-depression equilibrium, separated by an unstable saddle that depends on the stimulus intensity. We characterize all equilibria, their stability properties, and domains of attraction using linearization, Lyapunov functions, and monotonicity arguments. The resulting trajectories qualitatively reproduce established resilience trajectory typologies (chronic, delayed, recovery, resilient).

Keywords: Nonlinear Systems and Control, Stability
Abstract: Enlarging the region of attraction (RoA) near the current state is an effective technique to improve robustness against disturbances. Existing methods for enlarging the RoA are typically conservative, limited to specialized settings such as polynomial systems, and attempt to expand the RoA in all directions rather than near the current state, thereby sacrificing improved robustness near the current state for additional robustness in distant regions of state space. This work develops a computationally efficient method for numerically varying parameter values to maximize the distance from the current state to the RoA boundary. Local convergence guarantees are provided for the method for a large class of general nonlinear systems. The algorithm is demonstrated successfully on a quadcopter simulation, where it improves the robustness to an unknown disturbance.

Keywords: Stability, Nonlinear Systems and Control
Abstract: In this paper, we review several generalized notions of contraction mappings and related fixed point theorems. We first present a new characterization of Rakotch contractions on geodesic metric spaces. We then show that a Rakotch contraction is almost the same as a Banach contraction in terms of the speed of convergence. On the other hand, we provide a generalization of Weissinger's theorem and discuss its relationship with stability concepts in the literature. Finally, we revisit incremental stability properties of dynamical systems through the lens of contraction mappings.