On Switched Controller Design for Robust Control of Uncertain Polynomial Nonlinear Systems Using Sum of Squares

Abstract

This manuscript presents a switched control design for robust control of a class of uncertain nonlinear systems. In particular, it is considered a class of nonlinear systems whose dynamics are described by polynomial functions, that depend on the state vector of the system, with uncertain parameters. The design procedure can be represented in terms of sum of squares. The proposed switched control procedure uses a switching law to select at each instant of time a state-feedback polynomial gain, which belongs to a set of gains obtained from the proposed design procedure. The aim of the switching law is to choose a state-feedback polynomial gain that minimizes the time derivative of a polynomial Lyapunov function. A numerical example, using a chaotic Lorenz system with parametric uncertainties, illustrates the validity of the proposed approach.