Time-Constrained Temporal Logic Control of Multi-Affine Systems

TL;DR

This paper presents a control method for multi-affine systems to satisfy temporal logic specifications within a time limit, using time bounds estimation and optimal reachability algorithms.

Contribution

It introduces a novel algorithm combining time bounds estimation with a time optimal reachability approach for multi-affine systems under temporal logic constraints.

Findings

Successfully enforces temporal logic specifications within time constraints.

Utilizes a random optimization algorithm for solution improvement.

Applicable to systems with rectangular state space regions.

Abstract

In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically co-safe linear temporal logic formulas over rectangular regions in the state space. The proposed algorithm is based on the estimation of time bounds for facet reachability problems and solving a time optimal reachability problem on the product between a weighted transition system and an automaton that enforces the satisfaction of the specification. A random optimization algorithm is used to iteratively improve the solution.