Difficulties often arise when we apply the gradient type algorithms employing penalty functions to optimal control problems with variable final time. There is another class of optimal control problems for which the necessary conditions for optimality require a zero gradient at the final time. This causes the gradient-type algorithms, in their standard forms, to become incapable of changing the terminal value of the control variable at each iteration and the rate of convergence is adversely affected. In this paper, we first apply a new transformation method developed by Polak [19] which transforms the variable final time problem into a fixed final time problem. Second, an improved gradient-type algorithm is developed to overcome the zero terminal gradient problem. It is shown that, by applying this transformation and improved algorithm to four examples, not only the variable final time and zero terminal gradient problems are solved and the control vector updated in the correct direction but the rate of convergence of the improved algorithm is faster than that of the traditional gradient-type algorithms.
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December 1987
Research Papers
Improved Gradient-Type Algorithms for Zero Terminal Gradient Optimal Control Problems
Chung-Feng Kuo,
Chung-Feng Kuo
Mechanical and Aerospace Engineering Department, Arizona State University, Tempe, AZ 85287
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Chen-Yuan Kuo
Chen-Yuan Kuo
Mechanical and Aerospace Engineering Department, Arizona State University, Tempe, AZ 85287
Search for other works by this author on:
Chung-Feng Kuo
Mechanical and Aerospace Engineering Department, Arizona State University, Tempe, AZ 85287
Chen-Yuan Kuo
Mechanical and Aerospace Engineering Department, Arizona State University, Tempe, AZ 85287
J. Dyn. Sys., Meas., Control. Dec 1987, 109(4): 355-362 (8 pages)
Published Online: December 1, 1987
Article history
Received:
September 1, 1986
Online:
July 21, 2009
Citation
Kuo, C., and Kuo, C. (December 1, 1987). "Improved Gradient-Type Algorithms for Zero Terminal Gradient Optimal Control Problems." ASME. J. Dyn. Sys., Meas., Control. December 1987; 109(4): 355–362. https://doi.org/10.1115/1.3143867
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