Statistic information tracking of Non-Gaussian systems: A data-driven control framework based on adaptive NN modeling

A new type of data-driven control framework for Non-Gaussian stochastic systems is established in this paper. Different from the traditional feedback style, the driven information for tracking problem is the statistic information set (SIS) of the output rather than the output value. The set of statistical information (including the moments and the entropy) or probability density functions (PDFs) of the output are the measured information and the controlled objective. Under this framework, a mixed two-step adaptive neural network (NN) modeling is established with combining a static NN for description of the statistic information or PDFs and a dynamic one for identification of the relationship between input and output weight vectors. An adaptive PI tracking controller based on the proposed dynamic NNs is designed so as to track a target stochastic distribution. Finally, simulation results on a model in paper-making processes are given to demonstrate the effectiveness.

[1]  John F. Forbes,et al.  Regulatory control design for stochastic processes: shaping the probability density function , 2003, Proceedings of the 2003 American Control Conference, 2003..

[2]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[3]  Thia Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software , 2001 .

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

[5]  Lei Guo,et al.  Statistic Tracking Control: A Multi-objective Optimization Algorithm , 2006, ISNN.

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

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

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

[9]  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.

[10]  Hong Wang,et al.  Applying observer based FDI techniques to detect faults in dynamic and bounded stochastic distributions , 2000 .

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

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

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

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

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

[16]  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.

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

[18]  Jian-Qiao Sun,et al.  Nonlinear stochastic control via stationary probability density functions , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[19]  Hong Wang,et al.  Optimal probability density function control for NARMAX stochastic systems , 2008, Autom..

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

[21]  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).

[22]  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..

[23]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[24]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.