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All Journal Journal of the Indonesian Mathematical Society Limits: Journal of Mathematics and Its Applications
I. Pranoto
Department of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia
Mathematics

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ON THE OPTIMAL CONTROL COMPUTATION OF LINEAR SYSTEMS Tjahjana, H.; Pranoto, I.; Muhammad, H.; Naiborhu, J.
Journal of the Indonesian Mathematical Society Volume 15 Number 1 (April 2009)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.15.1.40.13-20

Abstract

In this paper, we consider a numerical method for designing optimal controlon Linear Quadratic Regulator (LQR) problem. In the optimal control design process through Pontryagin Maximum Principle (PMP), we obtain a system of diferential equations in state and costate variables. This system lacks of initial condition on the adjoint variables, and this situation creates classic dificulty for solving optimal control problems.This paper proposes a constructive method to approximate the initial condition of the adjoint system.DOI : http://dx.doi.org/10.22342/jims.15.1.40.13-20
The Application of The Steepest Gradient Descent for Control Design of Dubins Car for Tracking a Desired Path Miswanto, Miswanto; Pranoto, I.; Muhammad, H; Mahayana, D
Limits: Journal of Mathematics and Its Applications Vol 4, No 1 (2007)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (227.887 KB) | DOI: 10.12962/j1829605X.v4i1.1404

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 H Muhammad H. Muhammad H. Tjahjana J. Naiborhu Mahayana, D Miswanto Miswanto