Min-max Lyapunov control for a class of hyperbolic PDE with application to parabolic solar collector

In this contribution we present a new practice to deal with the output tracking problem of the process governed by hyperbolic partial differential equation (PDE) model. The principal obstacle in the achievement of our aim, consists in the complexity of the PDE model. To avoid this latter the spacial discretization is adopted to provide an equivalent uncertain state space which describes accurately the original PDE systems. Sub-sequently, based on the uncertain model the min-max Lyapunov controller is synthesized. The proposed controller allows us to achieve the desired performances with comprehensive and simple convergence analysis. Thus, it is abl to handle effectively and in optimal way the system uncertainty (caused by the truncation error). Finally, an assessment of the final control scheme is carried out through simulation to keep the outlet temperature of Parabolic Solar Collector in a wanted referene.