An integrated optimal control algorithm for discrete-time nonlinear stochastic system

Kek, Sie Long; Teo, Kok Lay; Ismail, Azlyana

doi:10.1080/00207179.2010.531766

Cited by 18 publications

(25 citation statements)

References 7 publications

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“…For more detail, see [14] [18] [19] [33] for the proof of the derivation on this feedback optimal control law.…”

Section: Feedback Optimal Control Lawmentioning

confidence: 99%

“…Besides, the applications of the IOCPE algorithm in providing the expectation solution as well as the filtering solution of the discrete-time nonlinear stochastic optimal control problem have been well-demonstrated [14] [15]. In addition, the optimal output solution obtained from the IOCPE algorithm has been improved by using the weighted output residual [16], which is introduced into the model cost function, and the output matching scheme [17], where the adjusted parameter is introduced into the model output.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, using the linear optimal control model with model-reality differences in solving the nonlinear optimal control problem, especially for discrete-time nonlinear stochastic optimal control problem, is proposed [14] [15] [16] [17]. Such method is known as the integrated optimal control and parameter estimation (IOCPE) algorithm.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Discrete-Time Nonlinear Stochastic Optimal Control Problem Based on Stochastic Approximation Approach

Kek¹,

Sim²,

Leong³

et al. 2018

APM

Self Cite

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In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal control problem is impossible to be obtained, estimating the state dynamics is currently required. Here, it is assumed that the output can be measured from the real plant process. In our approach, the state mean propagation is applied in order to construct a linear model-based optimal control problem, where the model output is measureable. On this basis, an output error, which takes into account the differences between the real output and the model output, is defined. Then, this output error is minimized by applying the stochastic approximation approach. During the computation procedure, the stochastic gradient is established, so as the optimal solution of the model used can be updated iteratively. Once the convergence is achieved, the iterative solution approximates to the true optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, an example on a continuous stirred-tank reactor problem is studied, and the result obtained shows the applicability of the approach proposed. Hence, the efficiency of the approach proposed is highly recommended.

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“…For more detail, see [14] [18] [19] [33] for the proof of the derivation on this feedback optimal control law.…”

Section: Feedback Optimal Control Lawmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Discrete-Time Nonlinear Stochastic Optimal Control Problem Based on Stochastic Approximation Approach

Kek¹,

Sim²,

Leong³

et al. 2018

APM

Self Cite

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show abstract

“…Recently, 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.…”

Section: Introductionmentioning

confidence: 99%

Least Squares Solution for Discrete Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

Kek¹,

Li²,

Teo³

2017

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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.

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“…Particularly, the linear quadratic regulator (LQR) technique is recognized as a standard procedure in solving the linear optimal control problems [12] [13] [14] [15] [16]. Recently, an efficient computational method, which is based on LQR optimal control model, is proposed to solve the nonlinear stochastic optimal control problems in discrete time [17] [18] [19] [20].…”

Section: Introductionmentioning

confidence: 99%

A Gauss-Newton Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

Kek¹,

Li²,

Leong³

et al. 2017

OJOp

Self Cite

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Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.

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An integrated optimal control algorithm for discrete-time nonlinear stochastic system

Cited by 18 publications

References 7 publications

Discrete-Time Nonlinear Stochastic Optimal Control Problem Based on Stochastic Approximation Approach

Discrete-Time Nonlinear Stochastic Optimal Control Problem Based on Stochastic Approximation Approach

Least Squares Solution for Discrete Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

A Gauss-Newton Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

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