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In this work, the boundary control of a distributed parameter system (DPS) modeled by parabolic partial differential equations with spatially varying coefficients is studied. An infinite dimensional state space setting is formulated and an exact transformation of the boundary actuation is realized to obtain an evolutionary model. The evolutionary model is used for subsequent linear quadratic regulator synthesis which incorporates the spatially varying coefficients of the underlying set of the PDEs. The formulated LQR controller is applied to the nonlinear model of the system and its performance is studied.

In this work a model predictive control methodology is applied to a set of hyperbolic partial differential equations (PDEs) which models a chemical fixed-bed reactor. Initially, the model of the fixed-bed reactor is linearized and by the method of characteristics is transformed into the set of ODEs which is explored within the model predictive controller synthesis. We consider uncertainties present in the reactor model which are taken into account by the construction of the polytopic family of plants and subsequent robust model predictive controller synthesis which ensures input and state constraints satisfaction. The proposed robust control problem formulation and the performance of the controller have been evaluated by simulations.