A Survey on Explicit Model Predictive Control.

Explicit model predictive control (MPC) addresses the problem of removing one of the main drawbacks of MPC, namely the need to solve a mathematical program on line to compute the control action. This computation prevents the application of MPC in several contexts, either because the computer technology needed to solve the optimization problem within the sampling time is too expensive or simply infeasible, or because the computer code implementing the numerical solver causes software certification concerns,especially in safety critical applications. Explicit MPC allows one to solve the optimization problem off-line for a given range of operating conditions of interest. By exploiting multiparametric programming techniques, explicit MPC computes the optimal control action off line as an ˵explicit″ function of the state and reference vectors, so that on-line operations reduce to a simple function evaluation. Such a function is piecewise affine in most cases, so that the MPC controller maps into a lookup table of linear gains. In this paper we survey the main contributions on explicit MPC appeared in the scientific literature. After recalling the basic concepts and problem formulations of MPC, we review the main approaches to solve explicit MPC problems, including a novel and simple suboptimal practical approach to reduce the complexity of the explicit form. The paper concludes with some comments on future research directions. [ABSTRACT FROM AUTHOR]