Abstract

In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.

Highlights

  • The model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error

  • The integrated optimal control and parameter estimation (ICOPE) algorithm, which solves the linear model-based optimal control problem iteratively, is proposed in the literature [18] [19]. The purpose of this algorithm is to provide the optimal solution of the discrete time nonlinear stochastic optimal control problem with the different structure and parameters

  • The linear model-based optimal control problem, which is simplified from the discrete time nonlinear stochastic optimal control problem, was solved iteratively

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Summary

Introduction

The real processes, which are modeled into the stochastic optimal control problem, are mostly nonlinear process. The integrated optimal control and parameter estimation (ICOPE) algorithm, which solves the linear model-based optimal control problem iteratively, is proposed in the literature [18] [19]. The purpose of this algorithm is to provide the optimal solution of the discrete time nonlinear stochastic optimal control problem with the different structure and parameters.

Problem Description
System Optimization with Least Square Updating Scheme
State Feedback Optimal Control Law
Least Squares Updating Scheme
Illustrative Example
Findings
Concluding Remarks
Full Text
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