Optimal control of differential inclusions with endpoint and state constraints and duality

TL;DR

This paper develops optimal control theory for higher order differential inclusions with constraints, deriving conditions for optimality, establishing duality relations, and analyzing specific higher order cases.

Contribution

It introduces a unified approach to optimal control of higher order differential inclusions, including duality theorems and explicit conditions for optimality.

Findings

Euler-Lagrange type inclusion derived for higher order DFIs

Adjoint inclusion for first order DFIs matches classical Euler-Lagrange inclusion

Duality theorem links Euler-Lagrange inclusions to dual problems

Abstract

The paper studies optimal control problem described by higher order evolution differential inclusions (DFIs) with endpoint and state constraints. In the term of Euler-Lagrange type inclusion is derived sufficient condition of optimality for higher order DFIs. It is shown that the adjoint inclusion for the first order DFIs, defined in terms of locally adjoint mapping, coincides with the classical Euler-Lagrange inclusion. Then a duality theorem is proved, which shows that Euler-Lagrange inclusions are "duality relations" for both problems. At the end of the paper duality problems for third order linear and fourth order polyhedral DFIs are considered.