Least-violating symbolic controller synthesis for safety, reachability and attractivity specifications

Specifications considered in symbolic control are often interpreted qualitatively and controllers usually classified as correct if they enforce the specification or incorrect do not. In practice, a given ideal might be impossible to meet. that case, it is interesting for system designer able quantify distance between achievable behaviors specification, synthesize least-violating controller enforcing closed-loop behavior closest one. this paper, we develop such an approach three types of specifications: safety, uniform reachability attractivity. We define controllability measures associated these properties. For finite transition systems, present dynamic programming algorithms computation controllers. discuss how results can used infinite systems via techniques. To demonstrate relevance our approach, show application adaptive cruise control.