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All Journal Limits: Journal of Mathematics and Its Applications
H. Muhammad
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Computer Science & IT Mathematics

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The Application of The Steepest Gradient Descent for Control Design of Dubins Car for Tracking a Desired Path Miswanto; I. Pranoto; H. Muhammad; D. Mahayana
Limits: Journal of Mathematics and Its Applications Vol. 4 No. 1 (2007): Limits: Journal of Mathematics and Its Applications Volume 4 Nomor 1 Edisi Mei
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

In this paper, we consider the control design of the Dubins car system to track a desired path. We design the control of the Dubins car system using optimal control approach. The control of the Dubins car system is designed for tracking the desired path. Instead of the usual quadratic cost function, a special type of cost functional which includes a tracking error term will be considered. By this special cost functional, the minimum tracking error of path of the Dubins car toward a desired path using Pontryagin Maximum Principle is obtained. The analytical solution of the Hamiltonian system is di±cult to obtain. So, a numerical solution with the steepest gradient descent method is proposed. The numerical results are given at the last section of this paper.
Co-Authors D. Mahayana I. Pranoto Miswanto