Learning-Aided Safe Controller Synthesis with Formal Guarantees via Vector Barrier Certificates

The design of controllers for safety-critical systems is an important research issue. Especially, the generation of controllers with formal safety guarantees is a challenging problem. Recently, for safety objectives of various system control tasks, machine learning technologies have been used to achieve ideal training and simulation performance, but formal guarantees are still lacking. This paper takes advantages of learning technology to assist safe controller synthesis with formal guarantees. On the one hand, the generation of verifiable safe controllers is aided by reinforcement learning; on the other hand, a set of barrier certificates (BC), i.e. a vector BC, is synthesized with the aid of deep learning to certify the safety of synthesized controllers. Vector BCs are more expressive than the conventional single BCs for safety verification. Compared with the existing work on vector BC generation, our method has two advantages: first, our method verifies a learned candidate vector BC, rather than directly generating a verified one, and thus has low computational complexity; second, the existing method has made relaxations to the non-convex vector BC constraints, which reduced the feasible region of solutions, while our method can deal with the original constraints. Furthermore, experiments fully demonstrate the effectiveness of our method on a series of benchmarks.