Sampled-data in Space Control of Scalar Semilinear Parabolic and Hyperbolic Systems

TL;DR

This paper introduces a novel sampled-data in space control method for scalar semilinear parabolic and hyperbolic systems, achieving reduced control costs and robustness against disturbances through LMI-based stability analysis.

Contribution

The paper presents a new spatial sampled-data control approach for scalar semilinear systems, with a specific function choice that improves control efficiency and robustness.

Findings

Exponential stability of the closed-loop system is established.

The proposed control law reduces control costs compared to existing methods.

Simulations confirm the theoretical robustness and efficiency of the approach.

Abstract

The paper describes a novel method of sampled-data in space (spatial variable) control of scalar semilinear systems of parabolic and hyperbolic type with unknown parameters and distributed disturbances. A finite set of sampled-data in the spatial variable measurements is available. The control law depends on the function which depends on the spatial variable and on a finite set of state measurements. A special choice of this function can affect on some properties of the closed-loop system. In particular, the paper describes the examples of this function that provides reduced control costs in comparison with some other control methods. The exponential stability of the closed-loop system and robustness with respect to unknown parameters and disturbances is proposed in terms of linear matrix inequalities (LMIs). The simulations confirm theoretical results and show the efficiency of the proposed control law compared with some existing ones.