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.