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Research Papers

The Use of the Differential Transform Method to Solve Time-Invariant State-Feedback Optimal Control Problems

[+] Author and Article Information
H. Saberi Nik

Department of Mathematics,
Neyshabur Branch,
Islamic Azad University,
Neyshabur, Iran
e-mail: saberi_hssn@yahoo.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 24, 2011; final manuscript received February 19, 2013; published online May 10, 2013. Assoc. Editor: Rama K. Yedavalli.

J. Dyn. Sys., Meas., Control 135(4), 041005 (May 10, 2013) (5 pages) Paper No: DS-11-1222; doi: 10.1115/1.4023974 History: Received July 24, 2011; Revised February 19, 2013

In this paper, the differential transform method (DTM) is applied for solving time-invariant state-feedback control problems. The optimal equations are obtained using the Pontryagin's maximum principle (PMP) and Bellman's Dynamic Programming. We present the closed-loop optimal control of linear plants with quadratic performance index. The results reveal that the proposed methods are very effective and simple. Comparisons are made between the results of two proposed methods and the exact solutions.

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References

Figures

Grahic Jump Location
Fig. 1

The exact and DTM solutions of Example 4.1 for n = 15

Grahic Jump Location
Fig. 2

The exact and DTM solutions of Example 4.2 for n = 10

Grahic Jump Location
Fig. 3

The exact and DTM solutions of Example 4.3 for n = 10

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