1. A Robust Nonlinear Model Reference Adaptive Control for Disturbed Linear Systems: An LMI Approach
- Author
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Roberto Franco, Alejandra Ferreira de Loza, Denis Efimov, Hector Rios, Tecnológico Nacional de México (TecNM), Instituto Politecnico Nacional [Mexico] (IPN), Consejo Nacional de Ciencia y Tecnología [Mexico] (CONACYT), Finite-time control and estimation for distributed systems (VALSE), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), National Research University of Information Technologies, Mechanics and Optics [St. Petersburg] (ITMO), Roberto Franco, Héctor Ríos and Alejandra Ferreira de Loza thank the financial support from CONACYT CVU 772057, Cátedras CONACYT CVU 270504 project 922, and Cátedras CONACYT CVU 166403 project 1537, respectively, and and from TecNM projects.
- Subjects
0209 industrial biotechnology ,Adaptive control ,Computer science ,Linear system ,MathematicsofComputing_NUMERICALANALYSIS ,02 engineering and technology ,Nonlinear control ,Model Reference Adaptive Control ,[SPI.AUTO]Engineering Sciences [physics]/Automatic ,Computer Science Applications ,Tracking error ,Nonlinear system ,020901 industrial engineering & automation ,Rate of convergence ,Control and Systems Engineering ,Control theory ,Uncertain Linear Systems ,Electrical and Electronic Engineering ,Robust control ,Robust Control ,Nonlinear Control - Abstract
International audience; In this paper a robust nonlinear Model Reference Adaptive Control (MRAC) is proposed for disturbed linear systems, i.e., linear systems with parameter uncertainties, and external time-dependent perturbations or nonlinear unmodeled dynamics matched with the control input. The proposed nonlinear control law is composed of two nonlinear adaptive gains. Such adaptive gains allow the control to counteract the effects of some perturbations and nonlinear unmodeled dynamics ensuring asymptotic convergence of the tracking error to zero, and the boundedness of the adaptive gains. The nonlinear controller synthesis is given by a constructive method based on the solution of Linear Matrix Inequalities (LMIs). Besides, the simulation results show that, due to the nonlinearities, the rate of convergence of the proposed algorithm is faster than the provided by a classic MRAC.
- Published
- 2022