Data-Driven Control of Unknown Switched Linear Systems Using Scenario Optimization

We tackle uniform state feedback control of switched linear systems under arbitrary switching using scenario optimization. We propose a data-driven control framework, in which scenario programs are formulated to compute stabilizing state feedback control relying on a finite set of observations of trajectories with quadratic and sum of squares (SOS) Lyapunov functions. We do not require the exact dynamical model or the switching signal, and as a consequence, we aim at solving uniform stabilization problems, in which the feedback is stabilizing for all possible switching sequences. In order to generalize the solution obtained from trajectories to the actual system, probabilistic guarantees on the obtained quadratic or SOS Lyapunov function are derived in the spirit of scenario optimization. For the quadratic Lyapunov technique, the generalization relies on a geometric analysis argument, while, for the SOS Lyapunov technique, we follow a sensitivity analysis argument. In order to deal with high-dimensional systems, we also develop a parallelized scheme for the proposed approach. We show that, with some modifications, the data-driven quadratic Lyapunov technique can be extended to linear quadratic regulator (LQR) control design. Finally, the proposed data-driven control framework is demonstrated on several numerical examples.