Constraint Algorithm for Extremals in Optimal Control Problems

TL;DR

This paper introduces a geometric presymplectic constraint algorithm to classify extremals in optimal control, including abnormal extremals, enhancing the understanding of optimal control solutions.

Contribution

It presents a general presymplectic constraint algorithm for extremal classification in optimal control, including a method to identify strict abnormal extremals.

Findings

The algorithm effectively characterizes different extremal types.

It provides a way to distinguish strict abnormal extremals.

An example illustrates the identification of a strict abnormal extremal.

Abstract

A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum Principle. Apart from the design of this general algorithm useful for any optimal control problem, it is showed how it works to split the set of extremals and, in particular, to characterize the strict abnormality. An example of strict abnormal extremal for a particular control-affine system is also given.