MPC with No Model Uncertainty

Abstract

This section provides a review of some of the key concepts and techniques in classical MPC. Here the term “classical MPC” refers to a class of control problems involving linear time invariant (LTI) systems whose dynamics are described by a discrete time model that is not subject to any uncertainty, either in the form of unknown additive disturbances or imprecise knowledge of the system parameters.In the first instance the assumption will be made that the system dynamics can be described in terms of the LTI state-space model xk+1= Axk+ Buk yk= Cxk where xk∈Rnx, uk∈Rnu, yk∈Rny are, respectively, the system state, the control input and the system output, and k is the discrete time index. If the system to be controlled is described by a model with continuous time dynamics (such as an ordinary differential equation), then the implicit assumption is made here that the controller can be implemented as a sampled data system and that (2.1a) defines the discrete time dynamics relating the samples of the system state to those of its control inputs.