No abstract

This paper develops the sliding mode control (SMC) design for N-coupled reaction-diffusion parabolic PDEs with boundary input disturbances. In order to reject the disturbances, the backstepping-based boundary SMC law is constructed to steer the system trajectory to a suitable sliding surface and then maintain sliding motion on the surface thereafter, resulting in the exponential convergence to the zero equilibrium state. The well-posedness of the closed-loop system is established based on a detailed spectral analysis and Riesz basis generation. Finally, a simulation example is provided to illustrate the effectiveness of the SMC design.

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This study is concerned with the output regulation of an anti-stable system of coupled wave equations with external disturbances. A state-feedback regulator is designed to force the output of the coupled wave equations to track the reference signal, which is generated by an exosystem. Moreover, the tracking error decays exponentially at a prescribed rate. The design is based on backstepping approach and relies on solving the regulator equations. The solvability condition of the regulator equations is characterised by the transfer matrix of the coupled wave equations and eigenvalues of the exosystem. An outputfeedback regulator is then constructed by developing an observer. Finally, the numerical simulations are demonstrated for the effectiveness of the theoretical results.