Discrete-time inverse optimal neural control for synchronous generators

This paper presents a robust inverse optimal neural control approach for stabilization of discrete-time uncertain nonlinear systems, which simultaneously minimizes a meaningful cost functional. A neural identifier scheme is used to model the uncertain system, and based on this neural model and an appropriate control Lyapunov function, then the robust inverse optimal neural controller is synthesized. Applicability of the proposed scheme is illustrated via simulation results for a synchronous generator model.

[1]  Alexander G. Loukianov,et al.  Discrete-Time Inverse Optimal Control for Nonlinear Systems , 2013 .

[2]  Kevin M. Passino,et al.  Swarm Stability and Optimization , 2011 .

[3]  Alexander S. Poznyak,et al.  Differential Neural Networks for Robust Nonlinear Control , 2004, IEEE Transactions on Neural Networks.

[4]  Alma Y. Alanis,et al.  Discrete-Time Reduced Order Neural Observers , 2009 .

[5]  L. Magni,et al.  Stability margins of nonlinear receding-horizon control via inverse optimality , 1997 .

[6]  E. Sánchez,et al.  Discrete-Time Robust Inverse Optimal Control for a Class of Nonlinear Systems , 2011 .

[7]  Reza Langari,et al.  Rollover Prediction and Control in Heavy Vehicles Via Recurrent High Order Neural Networks , 2011, Intell. Autom. Soft Comput..

[8]  Alexander G. Loukianov,et al.  Real-Time Discrete Neural Block Control Using Sliding Modes for Electric Induction Motors , 2010, IEEE Transactions on Control Systems Technology.

[9]  Keck Voon Ling,et al.  Inverse optimal adaptive control for attitude tracking of spacecraft , 2005, IEEE Trans. Autom. Control..

[10]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[11]  Iickho Song,et al.  Identification of Finite State Automata With a Class of Recurrent Neural Networks , 2010, IEEE Transactions on Neural Networks.

[12]  Richard Gourdeau,et al.  Object-oriented programming for robotic manipulator simulation , 1997, IEEE Robotics Autom. Mag..

[13]  Yong Huang,et al.  Convergence Study in Extended Kalman Filter-Based Training of Recurrent Neural Networks , 2011, IEEE Transactions on Neural Networks.

[14]  L. Dugard,et al.  Discrete-time nonlinear control scheme for synchronous generator , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[15]  R. Freeman,et al.  Robust Nonlinear Control Design: State-Space and Lyapunov Techniques , 1996 .

[16]  Carlos E. Castañeda,et al.  Decentralized neural identifier and control for nonlinear systems based on extended Kalman filter , 2012, Neural Networks.

[17]  J. Willems,et al.  Inverse optimal control problem for linear discrete-time systems , 1977 .

[18]  Edgar N. Sánchez,et al.  Output tracking with constrained inputs via inverse optimal adaptive recurrent neural control , 2008, Eng. Appl. Artif. Intell..

[19]  Frank L. Lewis,et al.  Discrete-Time Nonlinear HJB Solution Using Approximate Dynamic Programming: Convergence Proof , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Stefano Di Gennaro,et al.  Discrete time sliding mode control with application to induction motors , 2008, Autom..

[21]  Miroslav Krstic,et al.  Lyapunov tools for predictor feedbacks for delay systems: Inverse optimality and robustness to delay mismatch , 2008, 2008 American Control Conference.

[22]  S. Haykin.  Kalman Filtering and Neural Networks , 2001 .

[23]  Alexander L. Fradkov,et al.  Introduction to Control of Oscillations and Chaos , 1998 .

[24]  J. Grizzle,et al.  The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systems , 1992, 1992 American Control Conference.

[25]  Miroslav Krstic,et al.  Stabilization of Nonlinear Uncertain Systems , 1998 .

[26]  Danil V. Prokhorov,et al.  Simple and conditioned adaptive behavior from Kalman filter trained recurrent networks , 2003, Neural Networks.

[27]  Guanrong Chen,et al.  Introduction to random signals and applied Kalman filtering, 2nd edn. Robert Grover Brown and Patrick Y. C. Hwang, Wiley, New York, 1992. ISBN 0‐471‐52573‐1, 512 pp., $62.95. , 1992 .

[28]  T. Kishore Kumar,et al.  Swarm Intelligence Based Tuning of Unscented Kalman Filter for Bearings Only Tracking , 2009 .

[29]  Jacques L. Willems,et al.  The return difference for discrete-time optimal feedback systems , 1978, Autom..

[30]  Nikolay I. Nikolaev,et al.  Nonlinear maximum likelihood estimation of electricity spot prices using recurrent neural networks , 2011, Neural Computing and Applications.

[31]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[32]  J. P. Lasalle.  The stability and control of discrete processes , 1986 .

[33]  Victor M. Becerra,et al.  Optimal control , 2008, Scholarpedia.

[34]  Alexander G. Loukianov,et al.  Discrete-Time Backstepping Synchronous Generator Stabilization using a Neural Observer , 2008 .

[35]  F. Mazenc,et al.  Disturbance attenuation for discrete-time feedforward nonlinear systems , 1999 .

[36]  Andrew Chi-Sing Leung,et al.  Dual extended Kalman filtering in recurrent neural networks , 2003, Neural Networks.

[37]  Eduardo Bayro-Corrochano,et al.  Decentralized neural identification and control for uncertain nonlinear systems: Application to planar robot , 2010, J. Frankl. Inst..

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

[39]  Mrdjan J. Jankovic,et al.  Constructive Nonlinear Control , 2011 .

[40]  Sharad Singhal,et al.  Training Multilayer Perceptrons with the Extende Kalman Algorithm , 1988, NIPS.

[41]  Gerardo Espinosa-Pérez,et al.  Validity testing of third-order nonlinear models for synchronous generators , 2009 .

[42]  Manolis A. Christodoulou,et al.  Adaptive Control with Recurrent High-order Neural Networks , 2000, Advances in Industrial Control.

[43]  D. Normand-Cyrot,et al.  Control Lyapunov stabilization of affine discrete-time systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[44]  C. Byrnes,et al.  Design of discrete-time nonlinear control systems via smooth feedback , 1994, IEEE Trans. Autom. Control..

[45]  Ronald J. Williams,et al.  A Learning Algorithm for Continually Running Fully Recurrent Neural Networks , 1989, Neural Computation.

[46]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[47]  P. Kokotovic,et al.  Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations , 1999 .

[48]  J. Grizzle,et al.  The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systemsy , 1995 .

[49]  R. Langari,et al.  Rollover prediction and control in heavy vehicles via recurrent neural networks , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[50]  Edgar N. Sánchez,et al.  Inverse optimal neural control of blood glucose level for type 1 diabetes mellitus patients , 2012, J. Frankl. Inst..

[51]  R. E. Kalman,et al.  When Is a Linear Control System Optimal , 1964 .

[52]  Alexander G. Loukianov,et al.  Real-time inverse optimal control for a planar robot , 2010, 2010 IEEE International Symposium on Intelligent Control.

[53]  R.A. Freeman,et al.  Optimal nonlinear controllers for feedback linearizable systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[54]  B. Anderson,et al.  Nonlinear regulator theory and an inverse optimal control problem , 1973 .

[55]  Alexander G. Loukianov,et al.  Speed-gradient inverse optimal control for discrete-time nonlinear systems , 2011, IEEE Conference on Decision and Control and European Control Conference.