Explicit MPC of Constrained Nonlinear Systems with Quantized Inputs

Abstract

This chapter presents an approximate multi-parametric Nonlinear Integer Programming (mp-NIP) approach to design explicit MPC controllers for constrained nonlinear systems with quantized control inputs. It is organized as follows. In Section 5.2, general regulation and reference tracking quantized NMPC problems are formulated and represented as an mp-NIP problem. Then, in Section 5.3, an approximate mp-NIP approach to explicit quantized NMPC is described. The idea of the approach is to construct a piecewise constant (PWC) approximation to the optimal solution of the mp-NIP problem on a hyper-rectangle of interest by imposing an orthogonal state space partition. In Section 5.4, an explicit quantized NMPC controller for the electropneumatic clutch actuator (described in Section 4.5) is designed and its performance is compared to that of the explicit NMPC with continuous control input. In Section 5.5, the approximate mp-NIP approach is applied to design an explicit quantized NMPC controller for optimal regulation of a continuous stirred tank reactor.