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ISSN: 2165-784X

Journal of Civil & Environmental Engineering
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Research Article

A Discrete-Time Quasi-Theoretical Solution of the Modified Riccati Matrix Algebraic Equation

Tahar Latreche*
Magistere in Civil Engineering, B.P. 129 Salem Lalmi, 40003 Khenchela, Algeria
Corresponding Author : Tahar Latreche
Magistere in Civil Engineering
B.P. 129 Salem Lalmi, 40003 Khenchela, Algeria
Tel: +213-7-78936882
E-mail: [email protected]
Received October 07, 2014; Accepted October 21, 2014; Published October 27, 2014
Citation: Latreche T (2014) A Discrete-Time Quasi-Theoretical Formulation of the Optimal Control Matrix According to the QR Method. J Civil Environ Eng 4:157. doi: 10.4172/2165-784X.1000157
Copyright: © 2014 Latreche T. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract

In this paper, based on MacLaurin’s series and the Riccati equation, an algebraic quadratic equation will be developed and hence, its two roots, which represent the minimizing and maximizing optimal control matrices, would be deducted easier. Otherwise, a step-by-step algorithm to compute the control matrix for every step of time according to the preceding responses and a new signal pick will be explained. The proposed method presents a new discrete-time solution for the problem of optimal control in the linear or nonlinear cases of systems subjected to arbitrary signals. As an example, a system (structure) of three degrees of freedom, subjected to a strong earthquake is analyzed. The versus time displacements and the stiffness forces versus displacements of the system, for the two uncontrolled and controlled cases are graphically shown and clarify the great reduction of the controlled system results, in comparison with the uncontrolled system ones. The curves of variations of the elements of the optimal control matrix versus discrete-time are also presented.

Keywords

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