Adaptive NN control of uncertain nonlinear pure-feedback systems
Automatica 38 (2002) 671–682
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Adaptive NN control of uncertain nonlinear pure-feedback systems S.S. Ge ∗ , C. Wang1 Department of Electrical & Computer Engineering, National University of Singapore, Singapore 117576, Singapore Received 22 September 2000; received in revised form 2 April 2001; accepted 8 October 2001
Abstract This paper is concerned with the control of nonlinear pure-feedback systems with unknown nonlinear functions. This problem is considered di/cult to be dealt with in the control literature, mainly because that the triangular structure of pure-feedback systems has no a/ne appearance of the variables to be used as virtual controls. To overcome this di/culty, implicit function theorem is 0rstly exploited to assert the existence of the continuous desired virtual controls. NN approximators are then used to approximate the continuous desired virtual controls and desired practical control. With mild assumptions on the partial derivatives of the unknown functions, the developed adaptive NN control schemes achieve semi-global uniform ultimate boundedness of all the signals in the closed-loop. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Adaptive neural control; Uncertain pure-feedback system; Backstepping
1. Introduction In the past decade, interest in adaptive control of nonlinear systems has been ever increasing, and many signi0cant developments have been achieved. As a breakthrough in nonlinear control area, adaptive backstepping was introduced to achieve global stability and asymptotic tracking for a large class of nonlinear systems in the parametric strict-feedback form by Kanellakopoulos, Kokotovic, and Morse (1991). Later, the overparametrization problem was successfully eliminated in Krsti;c, Kanellakopoulos, and Kokotovic (1992) through the tuning function method. In an e
www.elsevier.com/locate/automatica
Adaptive NN control of uncertain nonlinear pure-feedback systems S.S. Ge ∗ , C. Wang1 Department of Electrical & Computer Engineering, National University of Singapore, Singapore 117576, Singapore Received 22 September 2000; received in revised form 2 April 2001; accepted 8 October 2001
Abstract This paper is concerned with the control of nonlinear pure-feedback systems with unknown nonlinear functions. This problem is considered di/cult to be dealt with in the control literature, mainly because that the triangular structure of pure-feedback systems has no a/ne appearance of the variables to be used as virtual controls. To overcome this di/culty, implicit function theorem is 0rstly exploited to assert the existence of the continuous desired virtual controls. NN approximators are then used to approximate the continuous desired virtual controls and desired practical control. With mild assumptions on the partial derivatives of the unknown functions, the developed adaptive NN control schemes achieve semi-global uniform ultimate boundedness of all the signals in the closed-loop. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Adaptive neural control; Uncertain pure-feedback system; Backstepping
1. Introduction In the past decade, interest in adaptive control of nonlinear systems has been ever increasing, and many signi0cant developments have been achieved. As a breakthrough in nonlinear control area, adaptive backstepping was introduced to achieve global stability and asymptotic tracking for a large class of nonlinear systems in the parametric strict-feedback form by Kanellakopoulos, Kokotovic, and Morse (1991). Later, the overparametrization problem was successfully eliminated in Krsti;c, Kanellakopoulos, and Kokotovic (1992) through the tuning function method. In an e
