Filtering solution of nonlinear stochastic optimal control problem in discrete-time with model-reality differences

Sie Long Kek; Kok Lay Teo; Mohd Ismail Abd Aziz

doi:10.3934/naco.2012.2.207

Article Contents

2012, Volume 2, Issue 1: 207-222. Doi: 10.3934/naco.2012.2.207

This issue Previous Article A filter successive linear programming method for nonlinear semidefinite programming problems Next Article

Filtering solution of nonlinear stochastic optimal control problem in discrete-time with model-reality differences

1.
Department of Mathematics, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja
2.
Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845
3.
Department of Mathematics, Universiti Teknologi Malaysia, 81310 UTM, Skudai

Received: March 2011

Revised: July 2011

Published: March 2012

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Abstract

In this paper, we propose an efficient algorithm for solving a nonlinear stochastic optimal control problem in discrete-time, where the true filtered solution of the original optimal control problem is obtained through solving a linear model-based optimal control problem with adjustable parameters iteratively. The adjustments of these parameters are based on the differences between the real plant and the linear model that are measured. The main feature of the algorithm proposed is the integration of system optimization and parameter estimation in an interactive way so that the correct filtered solution of the original optimal control problem is obtained when the convergence is achieved. For illustration, a nonlinear continuous stirred reactor tank problem is studied. The simulation results obtained demonstrate the efficiency of the algorithm proposed.

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Mathematics Subject Classification: Primary: 93E20, 93E11; Secondary: 93C10.

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