Controller synthesis against omega‐regular specifications: A funnel‐based control approach

Abstract The paper focuses on the problem of formal synthesis of controllers for control‐affine nonlinear systems against complex properties. Our goal is to design a closed‐form control policy that guarantees the satisfaction of complex properties that are expressed using ()‐regular languages and equivalently recognized by nondeterministic Büchi automata (NBA). We propose leveraging a funnel‐based control approach to provide a closed‐form solution to the problem. Our approach decomposes the specification represented by NBA into a sequence of reachability problems, which we solve using a funnel‐based control approach. Controllers associated with each reachability problem are then combined to design a hybrid control policy enforcing the desired ()‐regular property. We demonstrate the effectiveness of the proposed results on room temperature control and mobile robot motion control case studies.