Model predictive control for LPV models with maximal stabilizable model range

• Published in: Asian journal of control Vol. 22; no. 5; pp. 1940 - 1950
• Main Authors: Yang, Yuanqing, Ding, Baocang
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc 01.09.2020
• Subjects: Complexity; Computational geometry; Control stability; Control theory; convex optimization; Convexity; homogeneous polynomial; Liapunov functions; model predictive control; Optimization; Predictive control; robust control; Robustness (mathematics); stabilizable model range
• ISSN: 1561-8625; 1934-6093
• DOI: 10.1002/asjc.2070

This paper characterizes model predictive control (MPC) for linear parameter varying (LPV) models subject to state and input constraints, which is based on the homogeneous polynomially parameterized (HPP) Lyapunov function and HPP control law with tunable complexity degrees. The controller guarantees the closed‐loop asymptotic stability and finds the control move through the convex optimization. While it is known that this technique can improve the control performance and reduce conservatism, we suggest that it also enlarges, and maximizes with the sufficiently large complexity degrees, the stabilizable LPV model range. The computational burden becomes heavier when the complexity degrees increase. However, the main contributions of this paper are more on theory than on practice. It explores to what extent robust MPC can be applied for stabilization of LPV models. Numerical examples are provided to illustrate the effectiveness of the proposed technique.