Optimal control of Goursat-Volterra systems

TL;DR

This paper develops extremal principles similar to Pontryagin's maximum principle for optimal control problems involving two-variable Volterra integral systems, generalizing hyperbolic and ordinary Volterra control problems.

Contribution

It introduces a new extremal principle framework for Goursat-Volterra systems, extending control theory to systems with two independent variables.

Findings

Established extremal principles for Goursat-Volterra systems

Unified control approaches for hyperbolic and Volterra systems

Extended Pontryagin's maximum principle to two-variable integral systems

Abstract

We analyze an optimal control problem for systems of integral equations of Volterra type with two independent variables. These systems generalize both, the hyperbolic control problems for systems of Goursat-Darboux type, and the optimal control of ordinary (i.e. with one independent variable) Volterra integral equations. We prove extremal principles akin to Pontryagin's maximum principle.