The Pontryagin Maximum Principle for Optimal Multiprocesses with Continuous States

TL;DR

This paper introduces a novel approach to optimal multiprocesses with continuous states by incorporating switching strategies as classical controls, leading to new necessary conditions for optimality demonstrated through examples.

Contribution

It presents a new method to handle switching strategies in multiprocesses, overcoming previous restrictions and deriving Pontryagin maximum principle conditions.

Findings

Switching strategies are modeled as classical controls.

Necessary conditions for optimality are established.

Illustrative examples demonstrate the approach.

Abstract

In this paper we give a new approach to introduce switching strategies in a special class of optimal multiprocesses. Defined as the set of partitions of the time interval, switching strategies become the character of a classical control. With this approach we overcome the restrictive comparison of multiprocesses with the same switching strategy. The necessary conditions for strong local optimizer in form of the Pontryagin maximum principle are demonstrated in illustrative examples.