# American Institute of Mathematical Sciences

2015, 5(3): 275-288. doi: 10.3934/naco.2015.5.275

## Output regulation for discrete-time nonlinear stochastic optimal control problems with model-reality differences

 1 Department of Mathematics, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Malaysia 2 Department of Mathematics, Universiti Teknologi Malaysia, 81310 UTM, Skudai, Malaysia

Received  May 2014 Revised  March 2015 Published  August 2015

In this paper, we propose an output regulation approach, which is based on principle of model-reality differences, to obtain the optimal output measurement of a discrete-time nonlinear stochastic optimal control problem. In our approach, a model-based optimal control problem with adding the adjustable parameters is considered. We aim to regulate the optimal output trajectory of the model used as closely as possible to the output measurement of the original optimal control problem. In doing so, an expanded optimal control problem is introduced, where system optimization and parameter estimation are integrated. During the computation procedure, the differences between the real plant and the model used are measured repeatedly. In such a way, the optimal solution of the model is updated. At the end of iteration, the converged solution approaches closely to the true optimal solution of the original optimal control problem in spite of model-reality differences. It is important to notice that the resulting algorithm could give the output residual that is superior to those obtained from Kalman filtering theory. The accuracy of the output regulation is therefore highly recommended. For illustration, a continuous stirred-tank reactor problem is studied. The results obtained show the efficiency of the approach proposed.
Citation: Sie Long Kek, Mohd Ismail Abd Aziz. Output regulation for discrete-time nonlinear stochastic optimal control problems with model-reality differences. Numerical Algebra, Control & Optimization, 2015, 5 (3) : 275-288. doi: 10.3934/naco.2015.5.275
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