Aperiodic sampled-data MPC strategy for LPV systems. Issue 2 (January 2022)

• Record Type: Journal Article
• Authors: Palmeira, Alessandra H. K.; Gomes da Silva Jr, João M.; Flores, Jeferson V.; Seuret, Alexandre
• Is Part Of: Journal of the Franklin Institute. Volume 359:Issue 2(2022)
• Page Start: 786
• Page End: 815
• Publication Date: 2022-01
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2021.03.031
• Languages: English
• ISSNs: 0016-0032

Abstract

Highlights: Aperiodic sampled-data MPC control for LPV systems. Modeling of the mismatch between continuous varying plant parameter and its sampled value. Use of Parameter dependent Lyapunov functions. Guaranteed cost sampled-data control under saturating inputs. Feasibility and stability guarantees with a given estimate of the region of attraction. Abstract: This paper addresses the design of a sampled-data model predictive control (MPC) strategy for linear parameter-varying (LPV) systems. A continuous-time prediction model, which takes into account that the samples are not necessarily periodic and that plant parameters vary continuously with time, is considered. Moreover, it is explicitly assumed that the value of the parameters used to compute the optimal control sequence is measured only at the sampling instants. The MPC approach proposed by Kothare et al. [1], where the basic idea consists in solving an infinite horizon guaranteed cost control problem at each sampling time using linear matrix inequalities (LMI) based formulations, is adopted. In this context, conditions for computing a sampled-data stabilizing LPV control law that provides a guaranteed cost for a quadratic performance criterion under input saturation are derived. These conditions are obtained from a parameter-dependent looped-functional and a parameter-dependent generalized sector condition. A strategy that consists in solving convex optimization problems in a receding horizon policy is therefore proposed. It is shown that the proposed strategy guarantees the feasibility of the optimization problem at each step and leads to the asymptotic stability of the origin. The conservatism reduction provided by the proposed results, with respect to similar ones in the literature, is illustrated through numerical examples.