Generalization of Euler-Lagrange Equations to Find Min-max Optimal Solution of Uncertain Systems

TL;DR

This paper extends calculus of variation methods to derive Euler-Lagrange conditions for finding min-max optimal solutions in uncertain dynamical systems, providing necessary conditions and verifying effectiveness through examples.

Contribution

It introduces a new form of Euler-Lagrange conditions tailored for uncertain systems and establishes necessary conditions for min-max optimal solutions.

Findings

New Euler-Lagrange conditions for uncertain systems

Necessary conditions for min-max optimality

Validation through example cases

Abstract

In this paper, calculus of variation methods are generalized to find min-max optimal solution of uncertain dynamical systems with uncertain or certain cost. First, a new form of Euler-Lagrange conditions for uncertain systems is presented. Then several cases are indicated where final condition can be specified or free. Also necessary conditions are introduced to existence of min-max optimal solution of the uncertain systems. Finally, efficiency of the proposed method is verified through some examples.