Linear and Nonlinear Distributed Economic Model Predictive Control

Abstract

Model predictive control (MPC), also called receding horizon control, is a control technique to determine control actions for systems by using mathematical optimization theory such as linear or nonlinear programming. It is widely adopted for industrial applications because of its capability of dealing with constraints. For implementation of MPC we solve an online optimization problem which minimizes the object function with respect to the given constraints. We commonly adopt convex cost function, which is minimum at the set-point, since by minimizing this cost over horizons we can obtain the convergence of states to the desired set-point. This thesis, however, considers MPC with economically defined objective functions, and implements it in decentralized manner. The key difference of the economic objectives, acquired from the actual value of plants to operate, is that they are not necessarily minimum at the best steady-state, which we decide as the set-point for the state for the operations. Distributed system usually refers to a large-scale system which consists of multiple subsystems interacting with each other. In cooperative MPC which we deal with throughout this thesis, all the subsystems share and optimize the common cost. The main difficulty of this control arises from the coupled inputs and states between subsystems, and the effect between them. While computing consideration on state estimation of other subsystems should be taken into account for the controller design, so large computational burden is unavoidable. We divide the computation into several small problems, and suggest the iterations between the subsystems for the improvement of performance. For linear systems the convex sum of the computation, or estimation, of each subsystem generates the feasible input sequence at any number of iteration. Furthermore, we define and investigate individual 0. Abstract 6 feasibility for nonlinear systems. For both cases we prove the iterates converge to the Nash equilibria under some assumptions including asymptotic average constraints. For application example, we investigate the consecutive-competitive reactions, whose resultant substance and byproduct compete to be produced more through the reactions, with numerical simulations.