A new method for estimating a higher bound of the region of attraction of a nonlinear system is developed for state-dependent Riccati equation controller. The methodology can be applied to SDRE-controlled systems for improving the stability properties of such systems. The method calculates a Lyapumov function for the linearized system near the origin, and is then applied to the complete nonlinear system. The generation of a grid in a region of the state space is necessary, and the procedure must be run on the grid points, resulting in a computationally intensive procedure especially for large size systems. The procedure is similar with the only difference being the overvaluing matrix, which has to be found with respect to the closed loop matrix resulting from the SDRE control. This implies that the SDRE has to be solved pointwise because the closed form solution is not known in general, which makes the gridding of the state space necessary.
Estimation of the Region of Attraction for SDRE Controllers
2006-01-01
Abstract
A new method for estimating a higher bound of the region of attraction of a nonlinear system is developed for state-dependent Riccati equation controller. The methodology can be applied to SDRE-controlled systems for improving the stability properties of such systems. The method calculates a Lyapumov function for the linearized system near the origin, and is then applied to the complete nonlinear system. The generation of a grid in a region of the state space is necessary, and the procedure must be run on the grid points, resulting in a computationally intensive procedure especially for large size systems. The procedure is similar with the only difference being the overvaluing matrix, which has to be found with respect to the closed loop matrix resulting from the SDRE control. This implies that the SDRE has to be solved pointwise because the closed form solution is not known in general, which makes the gridding of the state space necessary.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
