Keywords: Lyapunov Methods, Hybrid Nonlinear Systems, Switching Control
Abstract: Recently a novel method was presented to compute convex Lyapunov functions for discrete-time, switched linear systems. The method uses linear programming to parameterize continuous, cone-wise linear, convex Lyapunov functions. We prove that for two-dimensional systems the method is always able to generate a Lyapunov function, whenever the origin is exponentially stable, given that the triangulation used by the algorithm is sufficiently dense.

Keywords: Optimization and Scheduling, Computational Efficiency, Hybrid Nonlinear Control Systems
Abstract: Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to decomposition techniques, does not require relaxing the integrality constraints. Based on the discretize-then-optimize approach, our scheme addresses mixed-integer nonlinear problems under mild assumptions. The proposed numerical algorithm builds upon the augmented Lagrangian framework, whose subproblems are handled using successive mixed-integer linearizations with trust regions. We validate the performance of the numerical routine with extensive investigations using hybrid optimal control problems from different fields of application. Promising preliminary results are presented for a motion planning task with hysteresis and a Lotka-Volterra fishing problem with total variation.

Keywords: Input-To-State Stability, Lyapunov Methods, Hybrid Nonlinear Systems
Abstract: In this work we provide a Lyapunov type characterization of the input-to-state stability property for dynamical systems on time scales subjected to external disturbances. We consider time scales with bounded graininess as a special case. First a concept of dwell- time conditions on time scales will be introduced to investigate some uniformity properties. Under these conditions a sufficiency result for input-to-state stability will be formulated using exponential Lyapunov functions. Lastly we briefly give some results on the interaction between the discrete and continuous dynamics of a time scale system.

Keywords: Stabilization, Lyapunov Stability Methods, Hybrid Nonlinear Control Systems
Abstract: Safe obstacle avoidance and target set stabilization for nonlinear systems using reactive feedback control is under consideration. Based only on local information and by considering virtual dynamics, a safe path is generated online. The control law for the virtual dynamics is combined with a feedback controller for the dynamics of interest, where Lyapunov arguments and forward invariance are used to ensure that the state of the system remains in a vicinity of the path. To allow for discrete decisions in the avoidance controller design, the closed-loop dynamics are formulated using the hybrid systems framework. The results are illustrated by a numerical example for unicycle dynamics.

Keywords: Hybrid Nonlinear Control Systems, Switching Control, Optimal Control
Abstract: Mean field games and controls involve guiding the behavior of large populations of interacting agents, where each individual’s influence on the group is negligible but collectively impacts overall dynamics. Hybrid systems integrate continuous dynamics with discrete transitions, effectively modeling the complex interplay between continuous flows and instantaneous jumps in a unified framework. This paper formulates mean field game and control strategies for switching hybrid systems and proposes computational methods to solve the resulting integro-partial differential equation. This approach enables scalable, decentralized decision-making in large-scale switching systems, which is illustrated through numerical examples in an emergency evacuation scenario with sudden changes in the surrounding environment.

Keywords: Observability and Observer Design, Hybrid Nonlinear Systems, Switching Control
Abstract: This paper presents a distributed state estimation problem by a group of networked observer agents for a jointly observable linear time-invariant (LTI) system, where agents communicate sporadically at discrete instants over a communication network that is dynamically changing. In this setting, no single agent can independently estimate the system state using only its own measurements. A distributed hybrid estimation protocol is developed to achieve asymptotically converging state estimates under intermittently arriving measurements and asynchronous inter-agent interactions. By employing Lyapunov-based stability analysis for hybrid systems, sufficient conditions are derived for global exponential stability of the zero estimation error set.

Keywords: Optimal Control, Feasibility and Stability Issues, Lyapunov Methods
Abstract: We analyze the stability of general nonlinear discrete-time stochastic systems controlled by optimal inputs that minimize an infinite-horizon discounted cost. Under a novel stochastic formulation of cost-controllability and detectability assumptions inspired by the related literature on deterministic systems, we prove that uniform semi-global practical recurrence holds for the closed-loop system, where the adjustable parameter is the discount factor. Under additional continuity assumptions, we further prove that this property is robust.

Keywords: Biological and Biomedical Systems, Model Based Control, Optimal Control
Abstract: Synthetic biology applies engineering principles to design and construct novel cellular functions. Cybergenetics is an emerging field of research that applies control theory to the synthetic regulation of living cells. A major challenge in cybergenetics lies in the inherent stochasticity of gene expression and biomolecular interactions governing gene regulation.

To overcome the challenge of controlling stochastic gene regulatory networks, we use here an efficient approximation of the Chemical Master Equation using a system of Partial Integro-Differential Equations (PIDEs). This approach offers a novel path for controlling synthetic biocircuits by transforming the inherently stochastic dynamics of biochemical systems into a deterministic framework, thereby making control more tractable.

We demonstrate the effectiveness of PIDE-model based control through three case studies of relevance in synthetic biology: stabilizing a stochastic toggle switch, optimizing control in a gene regulatory circuit, and regulating a stochastic genetic oscillator.

Keywords: Optimal Control, Necessary Conditions
Abstract: This paper derives a Hamilton-Jacobi-Bellman equation for nonlinear optimal control problems that minimize cost functions with fractional discounted costs, based on Bellman's principle of optimality. The exponential function is used as the discounted cost in conventional optimal control problems. The fractional discounted cost is described by the Mittag-Leffler function, which can be considered a generalized exponential function and is used in the solutions of fractional dynamical systems. The Mittag-Leffler function can describe gradual changes in the weights of cost functions with respect to time evolution, compared to exponential functions.

Keywords: Optimal Control, Numerical Methods
Abstract: We extend Al'brekht's method for finding the Taylor polynomials of the optimal cost and optimal feedback of a stationary, infinite horizon optimal contol problem to time varying, finite horizon problems in both finite and infinite dmensions.

Keywords: Optimal Control
Abstract: This is a short note about an optimal control problem having a non-smooth cost function and nonlinear constraints. The mathematical problem under consideration is motivated by the minimization of the energy consumed by a car-like vehicle or robot along a path having a flat profile. The constraints are given by means of a simple model of the longitudinal dynamics that takes into account both rolling resistance and aerodynamic drag. It is shown that the optimal trajectories consist of bang, inactivated, and singular arcs.

Keywords: Aerospace, Biological and Biomedical Systems, Optimal Control
Abstract: The problem of hovering in flapping insects/hummingbirds, and potential bio-mimicry by micro aerial vehicles (MAVs), have been studied for decades by scientists and engineers. Said communities often study hovering in flapping systems as either an open-loop or closed-loop system to analyze stability and/or propose control designs. Recently, a fundamentally novel result has been achieved in the literature of the hovering problem. That is, hovering in flapping insects/hummingbirds can be characterized/mimicked as a stable, model- free, real-time extremum seeking control (ESC) feedback system. In this paper we aim at two contributions: (i) provide a novel open-loop, optimal control characterization of hovering; and (ii) compare the performance of closed-loop, real-time ESC in hovering vs. the provided open-loop, non-real-time optimal control in hovering.

Keywords: State Estimation and Applications, Filter Design, Adaptive Filters
Abstract: To solve the problem of mismatch between the system model and the actual model in the state estimation process, this paper proposes an adaptive UKF algorithm based on LSTM and credibility. First, the LSTM neural network is used to model the nonlinear transfer function dynamically to solve the problem of inaccuracy of nonlinear transfer function. Second, the measurement error covariance of the UKF algorithm is analyzed in the framework of credibility, and a correction method for the measurement error covariance is proposed in combination with credibility to solve the problem of mismatch of noise covariance in the filtering process. Finally, the UKF algorithm is combined with the nonlinear transfer function and the adjusted set of measurement error covariance to estimate the target state and evaluate the credibility. The results of simulation experiments show that the algorithm can effectively improve the filtering prediction and tracking performance.

Keywords: Observability and Observer Design, Lyapunov Methods, State Estimation and Applications
Abstract: This paper addresses the design of robust nonlinear observers by leveraging the concept of incremental Exponential Input Output-to-State Stability (i-EIOSS). The key approach is to demonstrate that, under certain additional conditions, a system exhibiting the i-EIOSS property also satisfies the incremental Exponential Input-to-State Stability (i-EISS) property. Based on this result, novel linear matrix inequality (LMI) conditions for nonlinear observer design are proposed. The convergence analysis relies on Lyapunov methods combined with advanced stability analysis techniques.

Keywords: State Estimation and Applications, Observability and Observer Design, Sensor Network
Abstract: This paper proposes a distributed high-gain (HG) observer that combines a known communication network with a local HG observer for Lipschitz triangular nonlinear systems. By artificially decomposing the error system's nonlinearity, each nonlinear component can be confined to a smaller region compared to the standard HG observer. The HG parameter is reduced compared to a standard HG observer, leveraging the LMI-based observer technique to increase the practicality of distributed HG observer. Finally, the application to a vehicle platoon demonstrates the effectiveness of the distributed HG/LMI observer.

Keywords: Observability and Observer Design, Observer and Filter Design By Observer Error Linearization, State Estimation and Applications
Abstract: This paper proposes a novel approach for designing functional observers for nonlinear systems, with linear error dynamics and assignable poles. Sufficient conditions for functional observability are first derived, leading to functional relationships between the Lie derivatives of the output to be estimated and the ones of the measured output. These are directly used in the proposed design of the functional observer. The functional observer is defined in differential input-output form, satisfying an appropriate invariance condition that emerges from the state-space invariance conditions of the literature. A concept of functional observer index is also proposed, to characterize the lowest feasible order of functional observer with pole assignment.

Keywords: State Estimation and Applications, Optimal Control, Robotics
Abstract: Designing active prosthetic legs that effectively address the requirements of precision, energy efficiency, and user comfort remains a pivotal challenge in assistive technology. This paper introduces a novel approach that combines State-Dependent Riccati Equation based nonlinear control and estimation with Iterative Learning Control for prosthetic legs to meet these demands. Through simulations, we show that the approach provides excellent state estimation, even in the presence of significant process and measurement noises, and external disturbances such as ground reaction forces. Additionally, it achieves substantial energy savings, a critical factor for prolonged use. The approach also successfully handles large initial errors and reduced sensor configurations. This work pushes forward the development of next-generation prosthetic legs, offering a clear path to smarter, more efficient, and user-friendly solutions.

Keywords: Stability, State Estimation and Applications, Control of Mechanical, Electrical and Process Systems
Abstract: High-frequency signal injection in sensorless control results in a current oscillation. Therefore, sensorless control is considered within this contribution as stabilization problem of a periodic orbit. This new perspective simplifies the so far barely answered question about the stability of low-speed sensorless control. A specific sensorless control structure is considered and completely described in the time domain. The closed-loop system is linearized about the periodic orbit, and Floquet’s theorem is used for local stability analysis. The results are discussed by considering a numerical example.