Minimally Constrained Stable Switched Systems and Application to Co-simulation

We propose an algorithm to restrict the switching signals of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching signals. Our work is motivated by applications to (co-)simulation, where numerical stability is a hard constraint, but should be attained by restricting as little as possible the allowed behaviours of the simulators. We apply our results to certify the stability of an adaptive co-simulation orchestration algorithm, which selects the optimal switching signal at run-time, as a function of (varying) performance and accuracy requirements.Comment: Technical report complementing the following conference publication: Gomes, Cl\'audio, Beno\^it Legat, Rapha\"el Jungers, and Hans Vangheluwe. "Minimally Constrained Stable Switched Systems and Application to Co-Simulation." In IEEE Conference on Decision and Control. Miami Beach, FL, USA, 201

Strong exponential stability of switched impulsive systems with mode-constrained switching

Strong stability, defined by bounds that decay not only over time but also with the number of impulses, has been established as a requirement to ensure robustness properties for impulsive systems with respect to inputs or disturbances. Most existing results, however, only consider weak stability. In this paper, we provide a method for calculating the maximum overshoot and the decay rate for strong (and weak) global uniform exponential stability bounds for non-linear switched impulsive systems. We consider the scenario of mode-constrained switching where not all transitions between subsystems are allowed, and where subsystems may exhibit unstable dynamics in the flow and jump maps. Based on direct and reverse mode-dependent average dwell-time and activation-time constraints, we derive stability bounds that can be improved by considering longer switching sequences for computation. We provide numerical examples that illustrate the weak and strong exponential stability bounds and also how the results can be employed to ensure the stability robustness of nonlinear systems that admit a global state weak linearization.Comment: 23 pages, 4 figure

Quantifying impact on safety from cyber-attacks on cyber-physical systems

We propose a novel framework for modelling attack scenarios in cyber-physical control systems: we represent a cyber-physical system as a constrained switching system, where a single model embeds the dynamics of the physical process, the attack patterns, and the attack detection schemes. We show that this is compatible with established results in the analysis of hybrid automata, and, specifically, constrained switching systems. Moreover, we use the developed models to compute the impact of cyber attacks on the safety properties of the system. In particular, we characterise system safety as an asymptotic property, by calculating the maximal safe set. The resulting new impact metrics intuitively quantify the degradation of safety under attack. We showcase our results via illustrative examples.Comment: 8 pages, 5 figures, submitted for presentation to IFAC World Congress 2023, Yokohama, JAPA

Asynchronous Networks and Event Driven Dynamics

Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a theoretical and conceptual framework for the study of network dynamics where nodes can evolve independently of one another, be constrained, stop, and later restart, and where the interaction between different components of the network may depend on time, state, and stochastic effects. This framework is sufficiently general to encompass a wide range of applications ranging from engineering to neuroscience. Typically, dynamics is piecewise smooth and there are relationships with Filippov systems. In the first part of the paper, we give examples of asynchronous networks, and describe the basic formalism and structure. In the second part, we make the notion of a functional asynchronous network rigorous, discuss the phenomenon of dynamical locks, and present a foundational result on the spatiotemporal factorization of the dynamics for a large class of functional asynchronous networks