Shape Optimization of Actuators over Banach Spaces for Nonlinear Systems

TL;DR

This paper develops optimal actuator shape conditions for nonlinear parabolic systems within Banach spaces, applying the theory to a railway track model to enhance control design.

Contribution

It extends the optimal actuator shape theory to Banach spaces for nonlinear systems and demonstrates its application to a railway track model.

Findings

Existence of optimal actuator shapes established.

Optimality conditions derived for Banach space settings.

Application demonstrated on railway track model.

Abstract

In this paper, optimal actuator shape for nonlinear parabolic systems is discussed. The system under study is an abstract differential equation with a locally Lipschitz nonlinear part. A quadratic cost on the state and input of the system is considered. The existence of an optimal actuator shape has been established in the literature. This paper focuses on driving the optimality conditions for actuator shapes belonging to a Banach space. The application of the theory to the optimal actuator shape design for railway track model is considered.