Data Driven Stability Analysis of Black-box Switched Linear Systems

Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of observations, one can give probabilistic stability guarantees. The probabilistic nature of these guarantees implies a trade-off between their quality and the desired level of confidence. We provide an explicit way of computing the best stability-like guarantee, as a function of both the number of observations and the required level of confidence. Our proof techniques rely on geometrical analysis, chance-constrained optimization, and stability analysis tools for switched systems, including the joint spectral radius

Data Driven Stability Analysis of Black-box Switched Linear Systems.

Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of observations, one can give probabilistic stability guarantees. The probabilistic nature of these guarantees implies a trade-off between their quality and the desired level of confidence. We provide an explicit way of computing the best stability-like guarantee, as a function of both the number of observations and the required level of confidence. Our proof techniques rely on geometrical analysis, chance-constrained optimization, and stability analysis tools for switched systems, including the joint spectral radiu

Data Driven Stability Analysis of Black-box Switched Linear Systems

Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of observations, one can give probabilistic stability guarantees. The probabilistic nature of these guarantees implies a trade-off between their quality and the desired level of confidence. We provide an explicit way of computing the best stability-like guarantee, as a function of both the number of observations and the required level of confidence. Our proof techniques rely on geometrical analysis, chance-constrained optimization, and stability analysis tools for switched systems, including the joint spectral radius

Deciding Stability of a Switched System Without Identifying It

We address the problem of deciding stability of a “black-box” dynamical system (i.e., a system whose model is not known) from a set of observations. The only assumption we make on the black-box system is that it can be described by a switched linear system. We show that, for a given (randomly generated) set of observations, one can give a stability guarantee, for some level of confidence, with a trade-off between the quality of the guarantee and the level of confidence. We provide an explicit way of computing the best stability guarantee, as a function of both the number of observations and the required level of confidence. Our results rely on geometrical analysis and combine chance-constrained optimization theory with stability analysis techniques for switched systems 1

Safety Guarantees for Hybrid Systems

Hybrid systems describe processes that typically need to satisfy a set of strict physical, computation, and communication constraints. Mission-critical and time-critical cyber-physical systems are a prime example where these constraints play a key role in analysis, controller synthesis, and implementation. On top of classical notions such as stability, safety plays a major role in the control design of hybrid systems. There is a long history of methods related to the safety analysis and safety enforcement for dynamical systems, with the ones concerning linear systems being more mature than the others. Due to the importance and complexity of the underlying problem, several different techniques have been developed for hybrid systems. This entry summarizes the most important approaches and tools, together with references for further reading