Efficient Output Solution for Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

Sie Long Kek,Mohd Ismail Abdul Aziz,Kok Lay Teo

doi:10.1155/2015/659506

Abstract

A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.

Highlights

Many real world problems can be formulated as the stochastic dynamical systems [1,2,3]
The data-driven method that could be applied in the fault diagnosis provides an efficient identification approach for stochastic systems
We propose a computational approach for optimal control of the nonlinear stochastic dynamical system in discrete time

Summary

Introduction

Many real world problems can be formulated as the stochastic dynamical systems [1,2,3]. We propose a computational approach for optimal control of the nonlinear stochastic dynamical system in discrete time. Our aim is to obtain the optimal output solution of the original optimal control problem from a mathematical model. The output, which is measured from the real plant, is fed back into the parameter estimation problem. This operation is implemented to establish a matching scheme, in turn, updating the optimal solution of the model used at each iteration step.

Problem Statement

System Optimization with Parameter Estimation

Convergence Analysis

Illustrative Example

Findings

Concluding Remarks