Neuro-adaptive backstepping control of SISO non-affine systems with unknown gain sign.

This paper presents two neuro-adaptive controllers for a class of uncertain single-input, single-output (SISO) nonlinear non-affine systems with unknown gain sign. The first approach is state feedback controller, so that a neuro-adaptive state-feedback controller is constructed based on the backstepping technique. The second approach is an observer-based controller and K-filters are designed to estimate the system states. The proposed method relaxes a priori knowledge of control gain sign and therefore by utilizing the Nussbaum-type functions this problem is addressed. In these methods, neural networks are employed to approximate the unknown nonlinear functions. The proposed adaptive control schemes guarantee that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB). Finally, the theoretical results are numerically verified through simulation examples. Simulation results show the effectiveness of the proposed methods.

[1]  Yongming Li,et al.  Adaptive fuzzy backstepping robust control for uncertain nonlinear systems based on small-gain approach , 2010, Fuzzy Sets Syst..

[2]  Bing Chen,et al.  Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems , 2008, Fuzzy Sets Syst..

[3]  Petros A. Ioannou,et al.  Necessary and sufficient conditions for strictly positive real matrices , 1990 .

[4]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Tracking Control of MIMO Stochastic Nonlinear Systems With Unknown Control Directions and Unknown Dead Zones , 2015, IEEE Transactions on Fuzzy Systems.

[5]  H. F. Ho,et al.  Adaptive fuzzy approach for a class of uncertain nonlinear systems in strict-feedback form. , 2008, ISA transactions.

[6]  Wei Li,et al.  Backstepping control for periodically time-varying systems using high-order neural network and Fourier series expansion. , 2010, ISA transactions.

[7]  Xiaochuan Chen,et al.  NN-based output feedback adaptive variable structure control for a class of non-affine nonlinear systems: A nonseparation principle design , 2009, Neurocomputing.

[8]  Salim Labiod,et al.  Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems , 2007, Fuzzy Sets Syst..

[9]  Jing Wang,et al.  Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems , 2002, IEEE Trans. Neural Networks.

[10]  Hamid Reza Karimi,et al.  Adaptive Neural Stabilizing Controller for a Class of Mismatched Uncertain Nonlinear Systems by State and Output Feedback , 2015, IEEE Transactions on Cybernetics.

[11]  Shaocheng Tong,et al.  Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systems , 2010, Int. J. Appl. Math. Comput. Sci..

[12]  Mohammad Mehdi Arefi,et al.  Observer‐based adaptive neural control of uncertain MIMO nonlinear systems with unknown control direction , 2013 .

[13]  R. Nussbaum.  Some remarks on a conjecture in parameter adaptive control , 1983 .

[14]  Gang Feng,et al.  A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[15]  Shaocheng Tong,et al.  Adaptive Fuzzy Output Feedback Dynamic Surface Control of Interconnected Nonlinear Pure-Feedback Systems , 2015, IEEE Transactions on Cybernetics.

[16]  Shaocheng Tong,et al.  Adaptive Fuzzy Output Feedback Control for Switched Nonstrict-Feedback Nonlinear Systems With Input Nonlinearities , 2016, IEEE Transactions on Fuzzy Systems.

[17]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

[18]  Shaocheng Tong,et al.  Command-Filtered-Based Fuzzy Adaptive Control Design for MIMO-Switched Nonstrict-Feedback Nonlinear Systems , 2017, IEEE Transactions on Fuzzy Systems.

[19]  Petar V. Kokotovic,et al.  Systematic design of adaptive controllers for feedback linearizable systems , 1991 .

[20]  Weisheng Chen,et al.  Globally stable adaptive backstepping fuzzy control for output-feedback systems with unknown high-frequency gain sign , 2010, Fuzzy Sets Syst..

[21]  Mohammad R. Jahed-Motlagh,et al.  Observer-based adaptive robust control of nonlinear nonaffine systems with unknown gain sign , 2014 .

[22]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[23]  Mohammad Mehdi Arefi,et al.  Adaptive robust synchronization of Rossler systems in the presence of unknown matched time-varying parameters , 2010 .

[24]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Backstepping Output Feedback Control of Uncertain MIMO Pure-Feedback Nonlinear Systems , 2012, IEEE Transactions on Fuzzy Systems.

[25]  Xiaoping Liu,et al.  Direct adaptive fuzzy control of nonlinear strict-feedback systems , 2009, Autom..

[26]  M. Jahed-Motlagh,et al.  Observer-Based Adaptive Neural Control for a Class of Nonlinear Non-affine Systems with Unknown Gain Sign , 2011 .

[27]  Licheng Jiao,et al.  Adaptive Backstepping Fuzzy Control for Nonlinearly Parameterized Systems With Periodic Disturbances , 2010, IEEE Transactions on Fuzzy Systems.

[28]  Yangmin Li,et al.  Adaptive nonlinear output-feedback dynamic surface control with unknown high-frequency gain sign , 2013, Int. J. Control.

[29]  A. Isidori,et al.  Adaptive control of linearizable systems , 1989 .

[30]  Hamid Reza Karimi,et al.  Adaptive output feedback neural network control of uncertain non-affine systems with unknown control direction , 2014, J. Frankl. Inst..