Abstract

This paper addresses the robust explicit model predictive control scheme for linear systems with input and output constraint in the presence of disturbances and noise. Conditions for disturbance rejection are established by incorporating full state and disturbance observer. The separation principle is applied to design an optimal observer in the unconstrained problem. Then, an efficient algorithm is developed to explicitly design observer gain for the constrained problem by minimizing a quadratic performance criterion. It is shown that the solution includes a set of regions with piecewise affine functions of state and reference vectors and a set of regions with optimal observers. In the proposed method, two sets of partitions associated with, the control law and observer are obtained. Therefore, the online computation includes finding the active regions of both observer and control law partitions in which the current state is located. The proposed technique is particularly attractive for a wide range of practical problems where the exact model of the actual system is not available.