Adaptive Statistic Tracking Control Based on Two-Step Neural Networks With Time Delays

This paper presents a new type of control framework for dynamical stochastic systems, called statistic tracking control (STC). The system considered is general and non-Gaussian and the tracking objective is the statistical information of a given target probability density function (pdf), rather than a deterministic signal. The control aims at making the statistical information of the output pdfs to follow those of a target pdf. For such a control framework, a variable structure adaptive tracking control strategy is first established using two-step neural network models. Following the B-spline neural network approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. The dynamic neural network (DNN) is employed to identify the unknown nonlinear dynamics between the control input and the weights related to the integrated function. To achieve the required control objective, an adaptive controller based on the proposed DNN is developed so as to track a reference trajectory. Stability analysis for both the identification and tracking errors is developed via the use of Lyapunov stability criterion. Simulations are given to demonstrate the efficiency of the proposed approach.

[1]  Chih-Min Lin,et al.  Recurrent-neural-network-based adaptive-backstepping control for induction servomotors , 2005, IEEE Transactions on Industrial Electronics.

[2]  Wen Yu,et al.  Stability Analysis of Nonlinear System Identification via Delayed Neural Networks , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Shuzhi Sam Ge,et al.  Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs , 2007, Autom..

[4]  Tian-Ping Zhang,et al.  Stable direct adaptive fuzzy control for a class of MIMO non-linear systems , 2003, Int. J. Syst. Sci..

[5]  Lei Guo,et al.  PID controller design for output PDFs of stochastic systems using linear matrix inequalities , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  J. F. Forbes,et al.  Control design for first-order processes: shaping the probability density of the process state , 2004 .

[7]  Hong Wang,et al.  Bounded Dynamic Stochastic Systems: Modelling and Control , 2000 .

[8]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[9]  Peter J. Gawthrop,et al.  Neural networks for control systems - A survey , 1992, Autom..

[10]  Ling Hong,et al.  On the feedback control of stochastic systems tracking prespecified probability density functions , 2005 .

[11]  Marios M. Polycarpou,et al.  High-order neural network structures for identification of dynamical systems , 1995, IEEE Trans. Neural Networks.

[12]  Miroslav Kárný,et al.  Towards fully probabilistic control design , 1996, Autom..

[13]  Xiaoou Li,et al.  Some new results on system identification with dynamic neural networks , 2001, IEEE Trans. Neural Networks.

[14]  Huaguang Zhang,et al.  Global Asymptotic Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[15]  Subhash Challa,et al.  Nonlinear filter design using Fokker-Planck-Kolmogorov probability density evolutions , 2000, IEEE Trans. Aerosp. Electron. Syst..

[16]  Li-Xin Wang.  Stable adaptive fuzzy control of nonlinear systems , 1993, IEEE Trans. Fuzzy Syst..

[17]  George A. Rovithakis.  Robust neural adaptive stabilization of unknown systems with measurement noise , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[18]  Alexander S. Poznyak,et al.  Nonlinear adaptive trajectory tracking using dynamic neural networks , 1999, IEEE Trans. Neural Networks.

[19]  Jian-Qiao Sun,et al.  Non-linear stochastic control via stationary response design , 2003 .

[20]  Richard D. Braatz,et al.  On the "Identification and control of dynamical systems using neural networks" , 1997, IEEE Trans. Neural Networks.

[21]  Hong Wang,et al.  Robust control of the output probability density functions for multivariable stochastic systems with guaranteed stability , 1999, IEEE Trans. Autom. Control..

[22]  Chih-Min Lin,et al.  RCMAC Hybrid Control for MIMO Uncertain Nonlinear Systems Using Sliding-Mode Technology , 2007, IEEE Transactions on Neural Networks.

[23]  Thiagalingam Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation , 2001 .

[24]  Hong Wang,et al.  Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonlinear filters , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[25]  Naira Hovakimyan,et al.  Neural Network Adaptive Control for a Class of Nonlinear Uncertain Dynamical Systems With Asymptotic Stability Guarantees , 2008, IEEE Transactions on Neural Networks.

[26]  Lei Guo,et al.  Generalized discrete-time PI control of output PDFs using square root B-spline expansion , 2005, Autom..

[27]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[28]  Guanrong Chen,et al.  Reproducing chaos by variable structure recurrent neural networks , 2004, IEEE Transactions on Neural Networks.

[29]  Gordon Lightbody,et al.  Local Model Network Identification With Gaussian Processes , 2007, IEEE Transactions on Neural Networks.

[30]  Xuemei Ren,et al.  Identification of Nonlinear Systems With Unknown Time Delay Based on Time-Delay Neural Networks , 2007, IEEE Transactions on Neural Networks.

[31]  Lennart Ljung,et al.  On-line identification and adaptive trajectory tracking for nonlinear stochastic continuous time systems using differential neural networks , 2001, Autom..

[32]  Chih-Chiang Cheng,et al.  A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems , 2003, IEEE Trans. Autom. Control..

[33]  Hong Wang,et al.  Bounded Dynamic Stochastic Systems , 2012 .

[34]  Ahmad B. Rad,et al.  Identification and control of continuous-time nonlinear systems via dynamic neural networks , 2003, IEEE Trans. Ind. Electron..