A Discrete-Time Algorithm for the Resolution of the Nonlinear Riccati Matrix Differential Equation for the Optimal Control
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Tahar Latreche, Doctorate student at Constantine University, Algeria B.P. 129 Salem Lalmi, 40003 Khenchela, Algeria.
The Riccati Matrix Differential Equation (RMDE) is an interesting equation in different fields of science and engineering practice. In fact, that the arithmetic solution of this equation in the general case of varying-time matrices is very difficult to find. The literature offers different methods and solutions for this differential equation in the case of constant matrices (i.e. invariant-time matrices). The present approach is an approximate, and a sufficiently precise, discrete-time method for the resolution of the matrix differential equation of Riccati in the general case of varying-time (dependant of time) matrices; the method indeed, is a discretisation of the exact matrix solution, which is evaluating for every step of time, and which is function of the solution of the preceding step of time and the composed equation nonlinear matrices. The proposed algorithm is verified, for a controlled structure subjected to the Modified El-Centro earthquake by a comparison with the same uncontrolled structure, which constitutes by a two Degrees Of Freedom (2DOF) system. The results of this comparison show good differences between the controlled and the uncontrolled systems.
Riccati Matrix Differential Equation, Discrete-Time Algorithm, Varying-Time Matrices, Active Control, Nonlinear Quadratic Regulator
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