Auditor Product and Controller Synthesis for Nondeterministic Transition Systems With Practical LTL Specifications

Abstract

Controller design for continuous systems with linear temporal logic (LTL) specifications is a computationally intensive task. Abstracting a discrete transition system from a real-world continuous-state system often results in a state machine with a large number of states and nondeterministic transitions. This makes controller synthesis for LTL specifications difficult specially when the design specification is lengthy. To reduce the complexity, we consider the specifications that are in the conjunctive form of practical LTL patterns. We use auditor product to incrementally restrict the system to satisfy the safety part of each subspecification. The control strategy, that satisfies the liveness part is then calculated by solving a generalized Buchi game on the result of the auditor product of the discrete transition system with all subspecifications. This approach has the same worst case computational complexity as $\text{GR}(1)$ synthesis, but avoids some of the fundamental limitations involved with $Assumption \Rightarrow Guarantee$ formulation of the problem.