Necessary condition for sparse optimal control problem with intermediate constraints

TL;DR

This paper develops a new Pontryagin maximum principle for sparse optimal control problems with intermediate constraints and introduces a numerical algorithm to compute optimal trajectories efficiently.

Contribution

It presents a novel maximum principle for intermediate-constraint sparse control problems and a practical algorithm for computing optimal solutions.

Findings

New necessary conditions for optimality in constrained sparse control problems

A computational algorithm for trajectory optimization under intermediate constraints

Illustrative examples demonstrating the effectiveness of the approach

Abstract

This article treats optimal sparse control problems with multiple constraints defined at intermediate points of the time domain. For such problems with intermediate constraints, we first establish a new Pontryagin maximum principle that provides first order necessary conditions for optimality in such problems. Then we announce and employ a new numerical algorithm to arrive at, in a computationally tractable fashion, optimal state-action trajectories from the necessary conditions given by our maximum principle. Several detailed illustrative examples are included.