Published 31 Mar 2020 •  vol 13  •  no 3  • 



Farouk Zouari, Unité de recherche LARA automatique, Ecole Nationale d'Ingénieurs de Tunis (ENIT), BP. 37, le Belvédère, 1002 Tunis, Tunisia



We study the complexity of global adaptive stabilization for feedback nonlinear complex multivariable systems with nonlinear parameterization. The global adaptive stabilization systems may be performed by switching nonlinear controllers. In this paper, we present also that the global adaptive stabilization can also be obtained by switching linear controllers. From the study of the implemented, the linear regulator exhibits clear advantages. Two steps are needed to realize our global adaptive stabilizer. First, we construct a linear stabilizer with unknown gains. Second, we determine a set of coherent switching updating online gains in a switching configuration. The proposed control has two advantages. The first advantage is that all closed-loop states are bounded regardless of the initial conditions. The second advantage is that the asymptotic regulation is realized.



Multivariable Complex Nonlinear Systems, Linear Stabilizer, Linear Controllers, Nonlinear Controllers, Adaptive Control, Global Adaptive Stabilizer



[1] Kanellakopoulos I, Kokotovic P. V, Morse A. S, Systematic design of adaptive controllers for feedback linearizable systems, Automatic Control, IEEE Transactions on , Vol. 36, No. 11, 1991, pp. 1241 - 1253.
[2] Kanellakopoulos, I., Kokotovic, P. V., Morse, A. S. , Systematic Design of Adaptive Controllers Feedback Linearizable Systems , American Control Conference, 1991, pp. 649 - 654.
[3] Haojian Xu, Petros A. Ioannou, Robust adaptive control of linearizable nonlinear single input systems with guaranteed error bounds, Automatica, Vol. 40, No. 11, 2004, pp. 1905-1911.
[4] M. Krstic, I. Kanellakopoulos and P.V. Kokotovic, Adaptive nonlinear control without overparametrization, Systems & Control Letters, Vol. 19, 1992, pp. 177–185.
[5] M. Krstic, I. Kanellakopoulos, P.V. Kokotovic, Nonlinear and Adaptive Control Design, Wiley, New York, 1995.
[6] A. Boulkroune, M. M'saad, On the design of observer-based fuzzy adaptive controller for nonlinear systems with unknown control gain sign, Fuzzy Sets and Systems, Vol. 201, 2012, pp. 71-85.
[7] Fang SHANG, Yun-Gang LIU, Adaptive Output-feedback Stabilization for a Class of Uncertain Nonlinear Systems, Acta Automatica Sinica, Vol. 36, No. 1, 2010, pp. 92-100.
[8] Weisheng Chen, Zhengqiang Zhang, Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign, Fuzzy Sets and Systems, Vol. 161, No. 6, 2010, pp. 821-836.
[9] A. Boulkroune, M. Tadjine, M. M’Saad, M. Farza, Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction, Fuzzy Sets and Systems, Vol. 161, No. 6, 2010, pp. 797-820.
[10] Khoshnam Shojaei, Alireza Mohammad Shahri, Ahmadreza Tarakameh, Adaptive feedback linearizing control of nonholonomic wheeled mobile robots in presence of parametric and nonparametric uncertainties, Robotics and Computer-Integrated Manufacturing, Vol. 27, No. 1, 2011, pp. 194-204.
[11] Ghazal Montaseri, Mohammad Javad Yazdanpanah, Adaptive control of uncertain nonlinear systems using mixed backstepping and Lyapunov redesign techniques, Communications in Nonlinear Science and Numerical Simulation, Vol. 17, No. 8, 2012, pp. 3367-3380.
[12] Khalil, H.K., Adaptive output feedback control of nonlinear systems represented by input-output models, Automatic Control, IEEE Transactions on, Vol. 41, No. 2, 1996, pp. 177 - 188.
[13] Mustapha Ait Rami, Solvability of static output-feedback stabilization for LTI positive systems, Systems & Control Letters, Vol. 60, No. 9, 2011, pp. 704-708.
[14] Jorge Diaz-Salgado, Jesus Alvarez, Alexander Schaum, Jaime A. Moreno, Feedforward output-feedback control for continuous exothermic reactors with isotonic kinetics, Journal of Process Control, Vol. 22, No. 1, 2012, pp. 303-320.
[15] Fangzheng Gao, Fushun Yuan, Hejun Yao, Xiaowu Mu, Adaptive stabilization of high order nonholonomic systems with strong nonlinear drifts, Applied Mathematical Modelling, Vol. 35, No. 9, 2011, pp. 4222-4233.
[16] Liang LIU, Na DUAN, Xue-Jun XIE, Output-feedback Stabilization for Stochastic High-order Nonlinear Systems with a Ratio of Odd Integers Power, Acta Automatica Sinica, Vol. 36, No. 6, 2010, pp. 858-864.
[17] Bo-Jun MA, Yong-Chun FANG, Xiao XIAO, Switching Logic-based Adaptive Robust Control of Nonlinearly Parameterized Uncertain Systems, Acta Automatica Sinica, Vol. 33, No. 6, 2007, pp. 668-672.
[18] Claudio De Persis, Robust stabilization of nonlinear systems by quantized and ternary control, Systems & Control Letters, Vol. 58, No. 8, 2009, pp. 602-608.
[19] Xudong Ye, Switching adaptive output-feedback control of nonlinearly parametrized systems, Automatica, Vol. 41, No. 6, 2005, pp. 983-989.
[20] Aleksandar Kojić, Anuradha M. Annaswamy, Adaptive control of nonlinearly parameterized systems with a triangular structure, Automatica, Vol. 38, No. 1, 2002, pp. 115-123.
[21] Liang Liu, Xue-Jun Xie, Decentralized adaptive stabilization for interconnected systems with dynamic input–output and nonlinear interactions, Automatica, Vol. 46, No. 6, 2010, pp. 1060-1067.
[22] Min Wang, Jun Zhao, Quadratic stabilization of a class of switched nonlinear systems via single Lyapunov function, Nonlinear Analysis: Hybrid Systems, Vol. 4, No. 1, 2010, pp. 44-53.
[23] Xudong Ye , Global adaptive control of nonlinearly parametrized systems, Automatic Control, IEEE Transactions on, Vol. 48, No. 1, 2003, pp. 169 - 173.
[24] Minyue Fu , Adaptive stabilization of linear systems via switching control, Automatic Control, IEEE Transactions on , Vol. 31, No. 12, 1986, pp. 1097 - 1103.
[25] S. Alonso-Quesada and M. De la Sen, Robust Adaptive Stabilization of Linear Time-Invariant Dynamic Systems by Using Fractional-Order Holds and Multirate Sampling Controls, Discrete Dynamics in Nature and Society, Article ID 620546, 27 pages.
[26] M. de la Sen, Adaptive stabilization of continuous-time systems guaranteeing the controllability of a modified estimation model, Mathematical Problems in Engineering, Vol. 7, No. 1, 2001, pp. 29-54.
[27] Cong-Ran Zhao, Xue-Jun Xie, and Na Duan, Adaptive State-Feedback Stabilization for High-Order Stochastic Nonlinear Systems Driven by Noise of Unknown Covariance, Mathematical Problems in Engineering, Volume 2012 (2012), Article ID 246579, 13 pages.
[28] Miller, D.E., An adaptive controller which provides an arbitrarily good transient and steady-state response, Automatic Control, IEEE Transactions on, Vol. 36, No. 1, 1991, pp. 68 - 81.
[29] Shlomi Dolev, Ted Herman, Parallel composition for time-to-fault adaptive stabilization, Distributed Computing, Vol. 20, No. 1, 2007, pp. 29-38.
[30] A.S. Morse, Control using logic-based switching, in: A. Isidori (Ed.), Trends in Control, Springer-Verlag, New York, 1995.
[31] Leonid B. Freidovich, Hassan K. Khalil, Logic-based switching for robust control of minimum-phase nonlinear systems, Systems & Control Letters, Vol. 54, No.8, 2005, pp. 713-727.
[32] Fotis N. Koumboulis, Robert E. King, Anna Stathaki, Logic-based switching controllers – A stepwise safe switching approach, Information Sciences, Vol. 177, No.13, 2007, pp. 2736-2755.
[33] João P. Hespanha, A.Stephen Morse, Switching between stabilizing controllers, Automatica, Vol. 38, No.11, 2002, pp. 1905-1917.
[34] Ye Xudong, Logic-based switching adaptive stabilization of feedforward nonlinear systems, Automatic Control, IEEE Transactions on, Vol. 44, No.11, 1999, pp. 2174 - 2178.



Zouari, F. (2020). Adaptive Control for a Class of Multivariable Complex Nonlinear Systems by Switching Linear Controllers. International Journal of Control and Automation (IJCA), ISSN: 2005-4297 (Print); 2207-6387 (Online), NADIA, 13(3), 35-50. doi: 10.33832/ijca.2020.13.3.04.

Zouari, Farouk, “Adaptive Control for a Class of Multivariable Complex Nonlinear Systems by Switching Linear Controllers.” International Journal of Control and Automation, ISSN: 2005-4297 (Print); 2207-6387 (Online), NADIA, vol. 13, no. 3, 2020, pp. 35-50. IJCA,

[1] F. Zouari, "Adaptive Control for a Class of Multivariable Complex Nonlinear Systems by Switching Linear Controllers." International Journal of Control and Automation (IJCA), ISSN: 2005-4297 (Print); 2207-6387 (Online), NADIA, vol. 13, no. 3, pp. 35-50, Mar 2020.