A predictive control method for nonlinear parabolic PDE systems

Abstract

The problem of receding horizon control for a class of nonlinear distributed processes is investigated. The main focus of the manuscript lies in the development of a computationally efficient method to identify the optimal control action with respect to predefined performance criteria. An optimal control problem is formulated and is solved using standard, gradient-based, search algorithms. Employing nonlinear transformations and assuming piece-wise constant control action, the dynamic optimization problem is reformulated as a nonlinear optimization one with analytically computed sensitivities. The proposed method lies at the interface between collocation and shooting methods, since the distributed states are discretized explicitly in space and time and their sensitivity to the control action is analytically computed, reminiscent of collocation methods, while the states now enter the optimization problem explicitly as a nonlinear function of the control action and are eliminated from the equality constraints, thus reducing the number variables, evocative of shooting methods.