Quantised MPC for LPV systems by using new Lyapunov–Krasovskii functional

• Published in: IET control theory & applications Vol. 11; no. 3; pp. 439 - 445
• Main Authors: Lee, Sangmoon, Kwon, Ohmin
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 03.02.2017
• Subjects: closed loop systems; closed‐loop system; Constants; Construction costs; continuous time systems; continuous‐time impulsive dynamic model; control input quantisation; control nonlinearities; Control systems; Dynamic models; Dynamical systems; infinite horizon; infinite horizon cost function; linear parameter varying systems; LPV systems; Lyapunov‐Krasovskii functional; Mathematical models; Nonlinear dynamics; Parameters; piecewise constant sampled‐data; predictive control; quantised MPC; Research Article; sampled data systems; sampled‐data model predictive control; sector nonlinearity; upper bound minimisation; sampled-data model predictive control; control input quantisation; closed loop systems; infinite horizon cost function; sampled data systems; upper bound minimisation; sector nonlinearity; linear parameter varying systems; control nonlinearities; Lyapunov-Krasovskii functional; continuous-time impulsive dynamic model; LPV systems; continuous time systems; predictive control; quantised MPC; closed-loop system; piecewise constant sampled-data; infinite horizon
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2016.0597

This study deals with the problem of sampled-data model predictive control (MPC) for linear parameter varying (LPV) systems with input quantisation. The LPV systems under consideration depend on a set of parameters that are bounded and available online. To deal with a piecewise constant sampled-data and quantisation of the control input, the closed-loop system is modelled as a continuous-time impulsive dynamic model with sector non-linearity. The control problem is formulated as a minimisation of the upper bound of infinite horizon cost function subject to a sufficient condition for stability. The stability of the proposed MPC is guaranteed by constructing new Lyapunov–Krasovskii functional. Finally, a numerical example is provided to illustrate the effectiveness and benefits of the proposed theoretical results.