Nonlinear Optimal Control for Parameter-Dependent Polynomial Nonlinear Systems

In this paper, we address the nonlinear optimal control problem for parameter-dependent nonlinear systems with polynomial vector fields. Based on the state dependent coefficient form, sufficient conditions to guarantee the closed-loop stability and bounded performance index are presented as state dependent linear matrix inequalities, which can be formulated as sum-of-squares based conditions and solved by semidefinite programming. A parameter-dependant Lyapunov function is adopted to reduce the conservativeness of the controller design.