Linear Model Predictive Control

Abstract

In the most basic and common linear model predictive control (LMPC) formulation, a deterministic linear model is used for a prediction of the system states along with a quadratic cost function and linear constraints. This chapter presents an overview of various aspects of LMPC. First, the unconstrained LMPC will be explained, including the solution of the optimization problem and the resulting control structure. Based on these results, the extension of the optimization problem by constraints is investigated. The constraints can apply for the actuated values or the system states, for instance. Two different ways to formulate the optimization problem are shown, namely the sparse and the dense formulations. It is shown that a quadratic program (QP) results for a constrained LMPC, which can be solved very efficiently. Additionally, the MPC scheme for linear time-variant (LTV) systems, called LTV MPC, is investigated. For the LTV MPC, a QP has to be solved in each time step. This is of particular interest, because with LTV MPC already appropriate control results can be achieved for slightly nonlinear systems. To show applications of the methods presented, the chapter concludes with numerical examples.