A Discrete-Time Quasi-Theoretical Solution of the Modified Riccati Matrix Algebraic Equation
[1]
Tahar Latreche, Temporary Teacher at University of Khenchela, Department of Civil Engineering, Salem Lalmi, 40003 Khenchela, Algeria.
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.
Optimal Control, Nonlinear Systems, Modified Riccati Equation, Quasi-Theoretical Solution, Discrete-Time Algorithm
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