Guaranteed Control of Sampled Switched Systems using Semi-Lagrangian Schemes and One-Sided Lipschitz Constants

In this paper, we propose a new method for ensuring formally that a controlled trajectory stay inside a given safety set S for a given duration T. Using a finite gridding X of S, we first synthesize, for a subset of initial nodes x of X , an admissible control for which the Euler-based approximate trajectories lie in S at t $\in$ [0,T]. We then give sufficient conditions which ensure that the exact trajectories, under the same control, also lie in S for t $\in$ [0,T], when starting at initial points 'close' to nodes x. The statement of such conditions relies on results giving estimates of the deviation of Euler-based approximate trajectories, using one-sided Lipschitz constants. We illustrate the interest of the method on several examples, including a stochastic one

Model Reduction of Linear Switched Systems by Restricting Discrete Dynamics

We present a procedure for reducing the number of continuous states of discrete-time linear switched systems, such that the reduced system has the same behavior as the original system for a subset of switching sequences. The proposed method is expected to be useful for abstraction based control synthesis methods for hybrid systems

Reachability analysis of linear hybrid systems via block decomposition

Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous and discrete post operators to compute states reachable according to continuous and discrete dynamics, respectively. In this paper, we enhance both of these operators and make sure that most of the involved computations are performed in low-dimensional state space. In particular, we improve the continuous-post operator by performing computations in high-dimensional state space only for time intervals relevant for the subsequent application of the discrete-post operator. Furthermore, the new discrete-post operator performs low-dimensional computations by leveraging the structure of the guard and assignment of a considered transition. We illustrate the potential of our approach on a number of challenging benchmarks.Comment: Accepted at EMSOFT 202