Pontryagin's Minimum Principle for output-feedback systems: A compact overview

Abstract

Pontryagin's Maximum Principle is one of two famous results towards characterization of solutions of optimal control problems. Due to a shift in the desire from maximizing gain or profit to minimizing costs it is nowadays more often and henceforth in this publication referred to as Minimum Principle. The theory behind it utilizes variational calculus and provides necessary conditions. Many versions of the minimum principle exist. Among them variations exist that consider constraints, sufficient conditions, whereas other realize time-discrete formulations of the problem. Nevertheless, so far a generalization towards output-feedback systems is not found in the literature. The goal of this publication is to extend the existing theory via including an output function and variables. Additionally, general equality and inequality constraints as well as terminal constraints and sufficient conditions will be incorporated. The original Pontryagin's Minimum Principle can then be seen as a special case of the derived criteria.