Sliding-mode boundary control of uncertain reaction-diffusion processes with spatially varying parameters

The primary concern of the present paper is the stabilization problem of a one-dimensional uncertain reaction-diffusion process powered with a Dirichlet type actuator from one of the boundaries. The heat flux at the controlled boundary is the only measured signal, the uncertain diffusion and reaction parameters are admitted to be spatially varying, and the system is also affected by a sufficiently smooth boundary disturbance, which is not available for measurements and can be also unbounded in magnitude. The proposed robust synthesis is based on a dynamic input extension, and it is formed by the relay control algorithm and a linear term, suitably combined. A continuous stabilizing boundary control law is suggested to achieve exponential stability under some restrictions on the uncertain parameters spatial profiles characteristics. A Lyapunov-based functional analysis is invoked to establish the global exponential stability in the Sobolev space W^{1, 2}(0, 1). The proof is accompanied by a set of simple tuning rules for the controller parameters. The effectiveness of the developed control scheme is supported by simulation results.