Efficient and Safe Learning-based Control of Piecewise Affine Systems Using Optimization-Free Safety Filters*

Control of piecewise affine (PWA) systems under complex constraints faces challenges in guaranteeing both safety and online computational efficiency. Learning-based methods can rapidly generate control signals with good performance, but rarely provide safety guarantees. A safety filter is a modular method to improve safety for any controller. When applied to PWA systems, a traditional safety filter usually need to solve a mixed-integer convex program, which reduces the computational benefit of learning-based controllers. We propose a novel optimization-free safety filter designed to handle state constraints that involve a combination of polyhedra and ellipsoids. The proposed safety filter only utilizes algebraic and min-max operations to determine safe control inputs. This offers a notable advantage compared with traditional safety filters by allowing for significantly more efficient computation of control signals. The proposed safety filter can be integrated into various function approximators, such as neural networks, enabling safe learning throughout the learning process. Simulation results on a bicycle model with PWA approximation validate the proposed method regarding constraint satisfaction, CPU time, and the preservation of sub-optimality.