A Discrete-Time Algorithm for the Resolution of the Nonlinear Riccati Matrix Differential Equation for the Optimal Control

Abstract

The Riccati Matrix Differential Equation (RMDE) is an interesting equation in different fields of science and engineering practice. In fact, that the arithmetic solution for this matrix differential equation in the general case of varying-time matrices is very difficult to find. The literature offers the solution of this differential equation in the case of dependant constant matrices (i.e. invariant-time matrices). The present approach is an approximate 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 in fact, is a discrétisation of the exact matrix solution, that evaluates for any so small step of time, and which is function of the solution of the preceding step of time and the constitute equation matrices. The proposed algorithm is verified, for a controlled structure under 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 offer good differences between the controlled and the uncontrolled systems.