A Specification-Guided Framework for Temporal Logic Control of Nonlinear Systems

TL;DR

This paper introduces a new specification-guided control framework for nonlinear systems with linear temporal logic, directly characterizing winning sets in the continuous state space without full system abstraction.

Contribution

It presents a novel approach that avoids abstraction, using a monotonic operator and adaptive subdivision to efficiently synthesize control strategies for complex temporal logic specifications.

Findings

The method is sound for full LTL specifications.

It is robustly complete for DBA-recognizable specifications with bounded disturbances.

Demonstrated effectiveness on jet engine control and robot motion planning.

Abstract

This paper proposes a specification-guided framework for control of nonlinear systems with linear temporal logic (LTL) specifications. In contrast with well-known abstraction-based methods, the proposed framework directly characterizes the winning set, i.e., the set of initial conditions from which a given LTL formula can be realized, over the continuous state space of the system via a monotonic operator. Following this characterization, an algorithm is proposed to practically approximate the operator via an adaptive interval subdivision scheme, which yields a finite-memory control strategy. We show that the proposed algorithm is sound for full LTL specifications, and robustly complete for specifications recognizable by deterministic B\"uchi automata (DBA), the latter in the sense that control strategies can be found whenever the given specification can be satisfied with additional bounded disturbances. Without having to compute and store the abstraction and the resulting product system with the DBA, the proposed method is more memory efficient, which is demonstrated by complexity analysis and performance tests. A pre-processing stage is also devised to reduce computational cost via a decomposition of the specification. We show that the proposed method can effectively solve real-world control problems such as jet engine compressor control and motion planning for manipulators and mobile robots.