Observer-based robust model predictive control of switched nonlinear systems with time delay and parametric uncertainties

• Published in: Journal of vibration and control 2021-09, Vol.27 (17-18), p.1939-1955
• Main Authors: Taghieh, Amin, Shafiei, Mohammad Hossein
• Format: Article
• Language: English
• Subjects: Control systems; Cost function; Linear matrix inequalities; Mathematical models; Nonlinear control; Nonlinear systems; Optimization; Parameter uncertainty; Predictive control; Robust control; State observers; Subsystems; Time lag; Upper bounds
• ISSN: 1077-5463; 1741-2986
• DOI: 10.1177/1077546320950523

In this study, an observer-based robust model predictive control scheme is proposed to control a class of switched nonlinear systems in the presence of time delay and parametric uncertainties under arbitrary switching. Constructing an appropriate Lyapunov–Krasovskii functional in conjunction with an infinite horizon cost function, sufficient conditions are obtained to guarantee the asymptotic stability of the closed-loop switched system in terms of linear matrix inequalities depending on the time delay, the upper bounds of uncertain parameters, and the Lipschitz constant of subsystems. To model the uncertainty of the system, the parametric uncertainty is used to reduce the computational burden and the conservatism of the method. In the proposed method, a predictive state observer and an observer-based controller are synthesized via an online optimization problem to minimize the upper bound of the cost function, while handling the constraints. Finally, the obtained results are validated using practical and numerical simulations.