A Newton Algorithm for implementation of SDRE Controllers

State-Dependent-Riccati-Equation (SDRE) is a recently introduced control method that attempts to establish a systematic procedure for dealing with a general class of nonlinear systems. Some of the known limitations of the SDRE techniques are the high computational load due to recurrent Riccati equation and the lack of an a priori global stability guarantee. This paper analyzes the former problem introducing a new method for solving on-line the SDRE. This method is based on a modified Newton algorithm which is able to speed up the computational time and gives good results in terms of precision of the approximated solution. The method is compared with the standard Schur method for solving the SDRE at every step, and with the recently introduced θ-D method, on a nonlinear H8 control system. The results show that the Newton method produces results as good as the other two methods with a lower computational time (about 66% lower than the Schur method, and about 25% lower than the θ-D method). The total computational time of the Newton method strictly depends on the maximum error allowed. Moreover, the norm of the residual of the SDRE is limited by a fixed value, while with the approximated θ-D method, it is not. The paper introduces a new method to estimate the Region Of Attraction (ROA) of a nonlinear system as well. This method builds a Lyapunov function of the linearized system, then this function is applied to the complete nonlinear system. The results of the proposed method are less conservative than a recently introduced method even if the computational load is still large, especially for large systems. Finally the paper presents the application of SDRE to control of a missile using an LQR-like cost index. The SDRE control is capable of controlling the missile avoiding saturation of the actuators.