Distributed tracking control of an uncertain heat diffusion process

This paper addresses the design of a distributed non smooth tracking controller for a class of uncertain diffusive processes with homogeneous boundary conditions of Neumann type. Uncertainty in the diffusivity parameter, along with the presence of a sufficiently smooth distributed disturbance, characterize the considered class of processes. The paper considers a dynamical controller with a linear PI structure complemented by a certain non-smooth integral term which gives the algorithm its main robustness properties. A constructive Lyapunov-based stability analysis is illustrated which leads to simple tuning conditions for the controller parameters guaranteeing the asymptotic tracking in the space L2 of sufficiently smooth reference profiles. The main contribution of the present paper over recent related works (cfr. [19], [20]) is the relaxation of a quite restrictive assumption involving the external perturbation and, at the same time, the achievement of the control goal with milder information demand on the system's state. The good performance of the proposed control systems are verified by means of computer simulations.