Adaptive robust stabilization of a class of uncertain non-linear systems with mismatched time-varying parameters

• Published in: Proceedings of the Institution of Mechanical Engineers. Part I, Journal of systems and control engineering Journal of systems and control engineering, 2012-02, Vol.226 (2), p.204-214
• Main Authors: Arefi, M M, Jahed-Motlagh, M R
• Format: Article
• Language: English
• Subjects: Adaptive systems; Algorithms; Asymptotic properties; Closed loop systems; Control systems; Control theory; Dynamical systems; Mathematical models; Mechanical engineering; Nonlinear systems; Robust stabilization; Simulation; Uncertainty
• ISSN: 0959-6518; 2041-3041
• DOI: 10.1177/0959651811415002

In this paper, an adaptive robust stabilization algorithm is presented for a class of non-linear systems with mismatched uncertainties. In this regard, a new controller based on the Lyapunov theory is proposed in order to overcome the problem of stabilizing non-linear time-varying systems with mismatched uncertainties. This method is such that the stability of the closed-loop system is guaranteed in the absence of the triangularity assumption. The proposed approach leads to asymptotic convergence of the states of the closed-loop system to zero for unknown but bounded uncertainties. Subsequently, this method is modified so that all the signals in the closed-loop system are uniformly ultimately bounded. Eventually, numerical simulations support the effectiveness of the given algorithm.