Adaptive neural control and learning of affine nonlinear systems

This paper presents deterministic learning from adaptive neural network control of affine nonlinear systems with completely unknown system dynamics. Thanks to the learning capability of radial basis function, neural network (NN), stable adaptive NN controller is designed for the unknown affine nonlinear systems. The designed adaptive NN controller is rigorously shown that learning of the unknown closed-loop system dynamics can be achieved during the stable control process because partial persistent excitation condition of some internal signals in the closed-loop system is satisfied. Subsequently, neural learning controller using the knowledge obtained from deterministic learning is constructed to achieve closed-loop stability and improve control performance. Numerical simulation is provided to show the effectiveness of the proposed control scheme.

[1]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[2]  Cong Wang,et al.  Identification and Learning Control of Ocean Surface Ship Using Neural Networks , 2012, IEEE Transactions on Industrial Informatics.

[3]  Laxmidhar Behera,et al.  Direct adaptive neural control for affine nonlinear systems , 2009, Appl. Soft Comput..

[4]  Frank L. Lewis,et al.  Control of Robot Manipulators , 1993 .

[5]  Cong Wang,et al.  Learning from neural control of nonlinear systems in normal form , 2009, Syst. Control. Lett..

[6]  Kok Kiong Tan,et al.  Adaptive backstepping control for a class of nonlinear systems using neural network approximations , 2004 .

[7]  D. Mayne.  Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[8]  Cong Wang,et al.  Learning from neural control , 2006, IEEE Transactions on Neural Networks.

[9]  Tianping Chen,et al.  Global exponential stability of delayed Hopfield neural networks , 2001, Neural Networks.

[10]  David J. Hill,et al.  Deterministic Learning Theory , 2009 .

[11]  Wang Cong.  Learning from output feedback adaptive neural control of robot , 2012 .

[12]  Kao-Shing Hwang,et al.  Reinforcement learning to adaptive control of nonlinear systems , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[13]  Jun Wang,et al.  Noise-Induced Stabilization of the Recurrent Neural Networks With Mixed Time-Varying Delays and Markovian-Switching Parameters , 2007, IEEE Transactions on Neural Networks.

[14]  Dimitry M. Gorinevsky,et al.  On the persistency of excitation in radial basis function network identification of nonlinear systems , 1995, IEEE Trans. Neural Networks.

[15]  Tao Zhang,et al.  Stable Adaptive Neural Network Control , 2001, The Springer International Series on Asian Studies in Computer and Information Science.

[16]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

[17]  Cong Wang,et al.  Rapid Detection of Small Oscillation Faults via Deterministic Learning , 2011, IEEE Transactions on Neural Networks.

[18]  Shiuh-Jer Huang,et al.  A stable self-organizing fuzzy controller for robotic motion control , 2000, IEEE Trans. Ind. Electron..

[19]  Antonio Loría,et al.  Uniform exponential stability of linear time-varying systems: revisited , 2002, Syst. Control. Lett..

[20]  Wei Zeng,et al.  Human gait recognition via deterministic learning , 2012, Neural Networks.

[21]  Shuzhi Sam Ge,et al.  A direct method for robust adaptive nonlinear control with guaranteed transient performance , 1999 .

[22]  Zhidong Teng,et al.  Exponential stabilization and synchronization of neural networks with time-varying delays via periodically intermittent control , 2010 .

[23]  Guodong Zhang,et al.  Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays , 2013, Neural Networks.

[24]  A. Tesi,et al.  New conditions for global stability of neural networks with application to linear and quadratic programming problems , 1995 .

[25]  F. J. Narcowich,et al.  Persistency of Excitation in Identification Using Radial Basis Function Approximants , 1995 .

[26]  Jun Wang,et al.  Almost Sure Exponential Stability of Recurrent Neural Networks With Markovian Switching , 2009, IEEE Transactions on Neural Networks.

[27]  M. Polycarpou,et al.  Stable adaptive tracking of uncertain systems using nonlinearly parametrized on-line approximators , 1998 .