Robust State Estimation for a Linear Reaction-Convection-Diffusion Equation Under Unknown Disturbances

We propose a robust state estimation approach for a linear reaction-convection-diffusion equation under bounded unknown disturbances. Inspired by sliding mode theory, an adequate discontinuous input function is designed to compensate for the effect of the unknown disturbances. Based on Filippov's solutions theorem, we report the existence of generalized solutions to the estimation error system subject to the discontinuous input. Based on a Lyapunov stability analysis, we show the asymptotic convergence of the estimation error. The observer is then designed under more relaxed and realistic assumptions by replacing the discontinuous input by a continuous approximation and by using adaptive techniques to compensate for the upper bound on the bounded disturbances which are rather assumed to be unknown. Numerical simulations are performed to illustrate the effectiveness of the proposed robust estimation approach.

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