Zonotope-based Symbolic Controller Synthesis for Linear Temporal Logic Specifications

TL;DR

This paper introduces a zonotope-based approach for synthesizing controllers that satisfy linear temporal logic specifications in nonlinear control systems, combining state space partitioning, graph verification, and local abstraction techniques.

Contribution

It presents a novel local-to-global control synthesis framework using zonotope partitioning and abstraction for LTL specifications, which is a new approach in this context.

Findings

Effective zonotope-based state space partitioning for LTL control synthesis

Graph-based verification of accepting paths for LTL formulas

Successful application to mobile robot path planning

Abstract

This paper studies the controller synthesis problem for nonlinear control systems under linear temporal logic (LTL) specifications using zonotope techniques. A local-to-global control strategy is proposed for the desired specification expressed as an LTL formula. First, a novel approach is developed to divide the state space into finite zonotopes and constrained zonotopes, which are called cells and allowed to intersect with the neighbor cells. Second, from the intersection relation, a graph among all cells is generated to verify the realization of the accepting path for the LTL formula. The realization verification determines if there is a need for the control design, and also results in finite local LTL formulas. Third, once the accepting path is realized, a novel abstraction-based method is derived for the controller design. In particular, we only focus on the cells from the realization verification and approximate each cell thanks to properties of zonotopes. Based on local symbolic models and local LTL formulas, an iterative synthesis algorithm is proposed to design all local abstract controllers, whose existence and combination establish the global controller for the LTL formula. Finally, the proposed framework is illustrated via a path planning problem of mobile robots.