Optimal tracking control for a class of boundary controlled linear coupled hyperbolic PDE systems: Application to plug flow reactor with temperature output feedback

This work addresses an optimal linear quadratic (LQ) boundary output regulator design problem for the plug flow reactor described by hyperbolic partial differential equations (PDEs), with actuation applied only at the inlet of the reactor. By applying the weak variational approach, the necessary optimality conditions are provided and then an optimal state feedback controller is presented. In particular, the time-varying state feedback gain is determined by solving Riccati-type PDEs and this work extends the linear quadratic regulator design to the class of boundary controlled hyperbolic PDE systems. Along the line of the LQ design, an optimal boundary tracking regulator is designed such that the output of the considered reaction process tracks the desired reference signal generated by an exosystem. A simulation example is included to show performance of the proposed approach.