Optimal Actuator Design for Semi-linear Systems

TL;DR

This paper investigates the optimal placement and design of actuators in semi-linear systems, establishing existence and deriving optimality conditions, with applications to railway and wave models.

Contribution

It introduces a framework for optimal actuator and control design in semi-linear PDE systems, including existence proofs and necessary conditions.

Findings

Existence of optimal control and actuator under certain conditions

Derivation of first-order necessary optimality conditions

Application to railway track and wave models

Abstract

Actuator location and design are important choices in controller design for distributed parameter systems. Semi-linear partial differential equations model a wide spectrum of physical systems with distributed parameters. It is shown that under certain conditions on the nonlinearity and the cost function, an optimal control input together with an optimal actuator choice exists. First-order necessary optimality conditions are derived. The results are applied to optimal actuator and controller design in a nonlinear railway track model as well as semi-linear wave models.