An ILC-Based Adaptive Control for General Stochastic Systems With Strictly Decreasing Entropy

In this paper, a new method for adaptive control of general nonlinear and non-Gaussian unknown stochastic systems has been proposed. The method applies the minimum entropy control scheme to decrease the closed-loop randomness of the output under an iterative learning control (ILC) basis. Both modeling and control of the plant are performed using dynamic neural networks. For this purpose, the whole control horizon is divided into a certain number of time domain subintervals called batches and a pseudo-D-type ILC law is employed to train the plant model and controller parameters so that the entropy of the closed-loop tracking error is made to decrease batch by batch. The method has the advantage of decreasing the output uncertainty versus the advances of batches along the time horizon. The analysis on the proposed ILC convergence is made and a set of demonstrable experiment results is also provided to show the effectiveness of the obtained control algorithm, where encouraging results have been obtained.

[1]  B. Silverman,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[2]  K. Cai,et al.  Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  N. M. Filatov,et al.  Adaptive predictive control policy for nonlinear stochastic systems , 1995, IEEE Trans. Autom. Control..

[4]  Hong Wang.  Minimum entropy control of non-Gaussian dynamic stochastic systems , 2002, IEEE Trans. Autom. Control..

[5]  K. Glover,et al.  Minimum entropy H ∞ control , 1990 .

[6]  Ian R. Petersen,et al.  Minimax optimal control of stochastic uncertain systems with relative entropy constraints , 2000, IEEE Trans. Autom. Control..

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

[8]  V. Solo.  Stochastic adaptive control and Martingale limit theory , 1990 .

[9]  Suguru Arimoto,et al.  Bettering operation of Robots by learning , 1984, J. Field Robotics.

[10]  Hong Wang,et al.  Radial Basis Function based Iterative Learning Control for stochastic distribution systems , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[11]  K. Loparo,et al.  Active probing for information in control systems with quantized state measurements: a minimum entropy approach , 1997, IEEE Trans. Autom. Control..

[12]  Hai-Bo Ji,et al.  Adaptive output-feedback tracking of stochastic nonlinear systems , 2006, IEEE Trans. Autom. Control..

[13]  David H. Owens,et al.  Iterative learning control - An optimization paradigm , 2015, Annu. Rev. Control..

[14]  Henry L. Weidemann.  Entropy Analysis of Feedback Control Systems1 1The research for this paper was supported in part by funds from the United States Air Force Office of Scientific Research under AFOSR Grant 699-67. , 1969 .

[15]  Zeungnam Bien,et al.  Higher-order iterative learning control algorithm , 1989 .

[16]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[17]  Sankar K. Pal,et al.  Entropy: a new definition and its applications , 1991, IEEE Trans. Syst. Man Cybern..

[18]  J.F. Zhang,et al.  Periodic learning of B-spline models for output PDF control: application to MWD control , 2005, Proceedings of the 2005, American Control Conference, 2005..

[19]  Hong Wang,et al.  Minimum entropy control of closed-loop tracking errors for dynamic stochastic systems , 2003, IEEE Trans. Autom. Control..

[20]  Jinglin Zhou,et al.  Minimum entropy of B-spline PDF systems with mean constraint , 2006, Autom..

[21]  H. Wang,et al.  Minimising entropy and mean tracking control for affine nonlinear and non-Gaussian dynamic stochastic systems , 2004 .

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

[23]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[24]  Hong Wang,et al.  ILC-based Generalised PI Control for Output PDF of Stochastic Systems Using LMI and RBF Neural Networks , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[25]  G. Saridis.  Entropy formulation of optimal and adaptive control , 1988 .

[26]  D. H. Owens,et al.  Iterative learning control — 2D control systems from theory to application , 2004 .

[27]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .