Optimal synthesis control for evolution equations subject to nonlocal inputs

TL;DR

This paper develops a comprehensive optimal control framework for infinite-dimensional evolution equations with nonlocal inputs, providing a closed-loop Riccati solution that extends previous work on integro-differential equations.

Contribution

It introduces a novel Riccati-based solution for LQ control of evolution equations with distributed nonlocal inputs, expanding the scope of optimal control in infinite dimensions.

Findings

Provides a closed-loop Riccati solution for the control problem.

Extends previous integro-differential control methods to broader evolution equations.

Offers theoretical foundations for optimal control with nonlocal inputs.

Abstract

We consider the linear quadratic (LQ) optimal control problem for a class of evolution equations in infinite dimensions, in the presence of distributed and nonlocal inputs. Following the perspective taken in our previous research work on the LQ problem for integro-differential equations, where the memory term -- here involving the control actions -- is seen as a component of the state, we offer a full (closed-loop, Riccati-like) solution to the optimization problem.