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Dynamic H∞ Feedback Boundary Control for a Class of Parabolic Systems with a Spatially Varying Diffusivity

Yanjiu Zhou*, Baotong Cui, and Xuyang Lou
International Journal of Control, Automation, and Systems, vol. 19, no. 2, pp.999-1012, 2021

Abstract : The dynamic H∞ feedback boundary control for a class of parabolic distributed parameter systems with a non-constant (spatially varying) diffusion rate is addressed in this paper. The observer-based controller is designed to deal with non-collocated sensors and actuators, and the H∞ performance index is employed to tackle the influence of the external disturbance and measurement noise. The resulting closed-loop system is formed by the boundary actuation with the H∞ control strategy, and the output feedback is designed from the domain-averaged and boundary valued measurement, respectively. With the sufficient conditions of the linear matrix inequality that infer the stability of the system, the corresponding gains of observer and controller are solved. Numerical simulations are given to show the validity of the main results.

Keyword : Boundary dynamic feedback control, H∞ performance index, linear matrix inequality, non-constant diffusion rate, parabolic system

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