Sun Hong-fei

On common solutions of Riccati inequalities: for plannar case

Some examples are presented to show the significance of the study of the common positive definite solutions to a set of algebraic Riccati inequalities (ARIs). A necessary and sufficient condition for the existence of common positive definite solutions of a set of second-order Riccati inequalities is derived. This condition provides a new algorithm of computing the common solutions of ARIs. Unlike LMI method, the computing collapse will not occur with the increase of the number of Riccati inequalities due to the fact that our approach handles the ARIs one by one rather than simultaneously.

Guaranteed cost control for nonlinear systems based on the sum of squares technique

This paper proposes a guaranteed cost control method for a nonlinear system with parametric uncertainties by using the sum of squares (SOS) technique. The nonlinear ship course control is chosen as a case study. The mathematical model of the nonlinear ship motion system is rewritten as a linear-like system, and a guaranteed cost controller is designed by using Lyapunov method and the SOS method. The simulation results show that the guaranteed cost controller proposed in this paper behaves good robustness against the nonlinearity and uncertainties.