Application of interval predictor model into robust model predictive control

Here we apply interval prediction model into robust model predictive control (MPC) strategy. After introducing the family of models and some basic information, we present the computational results for the construction of interval predictor model, whose regression parameters are included in a sphere parameter set. Given a size measure to scale the average amplitude of the predictor interval, one optimal model that minimises a size measure is efficiently computed by solving a linear programming problem. We apply the active set approach to solve the linear programming problem and based on these optimisation variables, the predictor interval of the considered model with sphere parameter set can be constructed. As for a fixed non-negative number from the size measure, we propose a better choice by using the optimality conditions. In order to apply interval prediction model into robust MPC, two strategies are proposed to analyse a min-max optimisation problem. After input and output variables are regarded as decision variables, a standard quadratic optimisation is obtained and its dual form is derived, then Gauss–Seidel algorithm is proposed to solve the dual problem and convergence of Gauss–Seidel algorithm is provided too. Finally two simulation examples confirm the theoretical results.