Multi-objective minimum entropy controller design for stochastic processes

Minimum variance control is an established method in control of systems corrupted by noise. In these cases, as it is not possible to directly control the actual value of the system variables, one aims to reduce the variations instead. However, when the system noises are non-Gaussian, this approach fails because non-Gaussian noise cannot be characterised by simple measures such as variance. In these cases, the Entropy is proposed as a generalisation of the variance measure and the control objective becomes that of minimising the Entropy. Previously a limited form of this problem has been solved using first order Newtonian methods. In this paper, the control objective is first expanded to also include an error term related to the closed loop tracking performance, and the combined problem is then solved using a fast global optimisation search algorithm. The effectiveness of the approach is demonstrated through a case study based on a first principle model of a nonlinear heat exchanger.

[1]  B. Babu,et al.  A DIFFERENTIAL EVOLUTION APPROACH FOR GLOBAL OPTIMIZATION OF MINLP PROBLEMS , 2002 .

[2]  M. F. Cardoso,et al.  A simulated annealing approach to the solution of minlp problems , 1997 .

[3]  Ivan Zelinka,et al.  ON STAGNATION OF THE DIFFERENTIAL EVOLUTION ALGORITHM , 2000 .

[4]  Francesco Carlo Morabito.  Advances in intelligent systems , 1997 .

[5]  M. Chidambaram,et al.  Non-linear controllers for a heat exchanger , 1992 .

[6]  Hong Wang,et al.  An ILC-based Minimum Entropy PI Controller for Unknown and Non-Gaussian Stochastic Systems , 2008 .

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

[8]  Thomas F. Edgar,et al.  Nonlinear Heat Exchanger Control through the Use of Partially Linearized Control Variables , 1986 .

[9]  Hong Wang,et al.  Minimum entropy control of non-Gaussian dynamic stochastic systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[10]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[11]  H. Kushner.  Introduction to Stochastic Control Theory (Karl J. Astrom) , 1972 .

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

[13]  Hong Wang,et al.  ILC-Based Fixed-Structure Controller Design for Output PDF Shaping in Stochastic Systems Using LMI Techniques , 2009, IEEE Transactions on Automatic Control.

[14]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[15]  Jouni Lampinen,et al.  MIXED VARIABLE NON-LINEAR OPTIMIZATION BY DIFFERENTIAL EVOLUTION , 1999 .

[16]  Amin Nobakhti,et al.  A simple self-adaptive Differential Evolution algorithm with application on the ALSTOM gasifier , 2008, Appl. Soft Comput..

[17]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

[18]  Hong Wang,et al.  ILC-based adaptive minimum entropy control for general stochastic systems using neural networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[19]  Tianyou Chai,et al.  An ILC-Based Adaptive Control for General Stochastic Systems With Strictly Decreasing Entropy , 2009, IEEE Transactions on Neural Networks.

[20]  Mohammad Bagher Menhaj,et al.  Artificial neural networks for stochastic control of nonliner state space systems , 2008, 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence).

[21]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

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

[23]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

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