Approximately Optimal Controllers for Quantitative Two-Phase Reach-Avoid Problems on Nonlinear Systems

TL;DR

This paper develops a method to synthesize approximately optimal controllers for two-phase reach-avoid problems on nonlinear systems, improving over naive approaches by solving specialized subproblems, with practical validation on delivery and aircraft routing tasks.

Contribution

It introduces a novel approach for optimal control in two-phase reach-avoid problems using symbolic methods, surpassing naive subdivision strategies.

Findings

The proposed method produces near-optimal controllers for nonlinear systems.

Experimental validation confirms the method's effectiveness on real-world tasks.

The approach outperforms naive strategies in achieving optimality.

Abstract

The present work deals with quantitative two-phase reach-avoid problems on nonlinear control systems. This class of optimal control problem requires the plant's state to visit two (rather than one) target sets in succession while minimizing a prescribed cost functional. As we illustrate, the naive approach, which subdivides the problem into the two evident classical reach-avoid tasks, usually does not result in an optimal solution. In contrast, we prove that an optimal controller is obtained by consecutively solving two special quantitative reach-avoid problems. In addition, we present a fully-automated method based on Symbolic Optimal Control to practically synthesize for the considered problem class approximately optimal controllers for sampled-data nonlinear plants. Experimental results on parcel delivery and on an aircraft routing mission confirm the practicality of our method.