A Second Order Cone Formulation of Min-Max MPC With Zone Control for LPV Systems

Abstract

This paper proposes a Second Order Cone Formulation of min-max MPC with zone control for LPV Systems. The min-max strategy in model predictive control (MPC) allows computing the optimal control actions where the worst-case performance to the system uncertainties is assumed. Zone control is used instead of a reference trajectory, as the MPC performance for several complex systems with uncertainty improves with a control range rather than a reference path. Unfortunately, min-max formulations of predictive controllers often produce intractable optimization problems as the number of states, inputs, and outputs of the system increase. Hence, in this paper uncertainty is treated in such a way that the min-max optimization problem can be solved through a second-order cone programming problem. This equivalent solution has a polynomial complexity for the min-max solution, a fact that constitutes the most remarkable feature of the proposed formulation. Performance of the method is verified in simulation through the application on a stirred tank reactor (CSTR) system.