Polynomial-Approximation-Based Control for Nonlinear Systems

This paper is concerned with the stabilization problem for nonlinear systems. A new polynomial-approximation-based approach for modeling nonlinear systems is first proposed. The nonlinearity is approximated by polynomials, and the approximation errors are treated as modeling uncertainties. The original nonlinear systems are converted into polynomial systems with modeling uncertainties. In order to highlight the approximation accuracy, the piecewise polynomial approximation functions are utilized. A novel polynomial state-feedback controller is designed to solve the stabilization problem. Furthermore, switched polynomial state-feedback controllers are designed to improve the performance. The stabilization conditions are presented in terms of sum of squares, which can be numerically solved via SOSTOOLS. Finally, simulation examples are provided to demonstrate the feasibility of the proposed method and show its advantage over the polynomial-fuzzy-model-based approach.