A novel approximation technique for online and multi-parametric model predictive control

Multi-parametric model predictive control has been widely recognized in the control literature. The objective of explicit MPC is to solve the constrained optimal control problem and derive the control variables as explicit functions of the states. Explicit MPC is particularly relevant for systems in which classical real time MPC implementation is impractical; In effect, the computations to derive the optimal control moves are performed offline. A framework for the development of such multiparametric/explicit controllers has been presented in [1]. The framework emphasizes the need for model approximation as a key challenge for a wider use of multiparametric/explicit MPC. We propose an approach that uses an interpolation method employed in a receding horizon fashion as a transient system identification technique to derive linear explicit algebraic expressions of the dynamics of the system under the form of linear expressions in the state parameter and controls. A major advantage of the approach is the availability of an a priori global error bound for the model mismatch due to the approximation. Linear dependency on the state parameters and controls enables to recast nonlinear and non convex MPC problems, into mp-QP optimization problems. The approach is demonstrated on a nonlinear benchmark model example of a 30 stages distillation column.