Set-based control for disturbed piecewise affine systems with state and actuation constraints

We address the finite horizon control of a discrete time piecewise affine (PWA) system, which is affected by an additive bounded disturbance. The goal is to robustly drive the state of the system to some target region, while satisfying state and actuation constraints. This problem is challenging due to the mixed discrete and continuous dynamics, requiring the exploration of many mode sequences. We address this problem by proposing a two-step approach which is based on designing a reference trajectory followed by a feedback controller that tries to make all solutions adhere to the reference mode sequence. As a result, the number of considered mode sequences can be drastically reduced. Termination is guaranteed since the time horizon and the number of modes are finite. Key to the computational efficiency of this procedure is the choice of the reference trajectory, which should be designed to avoid the branching of mode sequences from the reference sequence. The resulting set-based feedback control law is simple and easy to implement. Due to the use of reachability analysis, our results are formally correct. A quadruple-tank benchmark example shows the effectiveness of our approach.