Incremental Synthesis of Safe Controller Guided by Learning-Enabled Barrier Certificates with Efficient LP Verification

Abstract Safe controller synthesis with formal guarantees is widely employed in safety-critical systems. However, existing controller synthesis methods are subject to significant limitations in scalability and efficiency. This paper presents a novel controller incremental synthesis framework guided by barrier certificates (BCs), thereby generating a safe controller with BC verification. To enhance verification efficiency, we construct a learning-enabled polynomial BC combined with efficient post-verification, which is transformed into smaller-scale linear Programming (LP) subproblems for feasibility determination. Furthermore, we have implemented a tool called ISafeC and evaluated its performance over a set of benchmark examples. The comparative experimental results demonstrate the effectiveness and efficiency of our approach.