Problem of optimal control for bilinear systems with endpoint constraint

TL;DR

This paper investigates optimal control strategies for bilinear systems with endpoint constraints, proposing approximation methods, identifying systems with feedback law solutions, and applying results to PDEs.

Contribution

It introduces a novel approach to characterize optimal control via unconstrained minimization and identifies classes with explicit feedback law solutions.

Findings

Optimal control characterized through unconstrained minimization problems

Identification of bilinear systems with explicit feedback control laws

Applications demonstrated on parabolic and hyperbolic PDEs

Abstract

In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former. Then a class of bilinear systems for which the optimal control can be expressed as a time-varying feedback law will be identified. Finally, applications to parabolic and hyperbolic partial differential equations are provided.