On Feedback Control Techniques of Nonlinear Analytic Systems

This paper presents three approaches dealing with the feedback control of nonlinear analytic systems. The first one treats the optimal control resolution for a control-affine nonlinear system using the State Dependant Riccati Equation (SDRE) method. It aims to solve a nonlinear optimal control problem through a Riccati equation that depends on the state. The second approach treats a procedure of constructing an analytic expression of a nonlinear state feedback solution of an optimal regulation problem with the help of Kronecker tensor notations. The third one deals with the global asymptotic stabilization of the nonlinear polynomial systems. The designed state feedback control law stabilizes quadratically the studied systems. Our main contribution in this paper is to carry out a stability analysis for this kind of systems and to develop new sufficient conditions of stability. A numerical-simulation-based comparison of the three methods is finally performed.