Zonotope-based Controller Synthesis for LTL Specifications

TL;DR

This paper introduces a zonotope-based method for synthesizing controllers that ensure Linear Temporal Logic (LTL) specifications are satisfied in dynamic systems, combining state space partitioning, verification, and abstraction techniques.

Contribution

It presents a novel abstraction construction and control synthesis approach using constrained zonotopes for LTL specifications, enhancing existing methods.

Findings

Successfully verified LTL specifications using zonotope techniques.

Designed finite local controllers to satisfy LTL in numerical examples.

Demonstrated the approach on autonomous robot systems.

Abstract

This paper studies the controller synthesis problem for Linear Temporal Logic (LTL) specifications using (constrained) zonotope techniques. First, we implement (constrained) zonotope techniques to partition the state space and further to verify whether the LTL specification can be satisfied. Once the LTL specification can be satisfied, the next step is to design a controller to guarantee the satisfaction of the LTL specification for dynamic systems. Based on the verification of the LTL specification, an abstraction-based control design approach is proposed in this paper: a novel abstraction construction is developed first, then finite local abstract controllers are designed to achieve the LTL specification, and finally the designed abstract controllers are combined and refined as the controller for the original system. The proposed control strategy is illustrated via a numerical example from autonomous robots.