Guaranteed cost control of affine nonlinear systems via partition of unity method

Abstract

We consider the problem of guaranteed cost control (GCC) of affine nonlinear systems in this paper. Firstly, the general affine nonlinear system with the origin being its equilibrium point is represented as a linear-like structure with state-dependent coefficient matrices. Secondly, partition of unity method is used to approximate the coefficient matrices, as a result of which the original affine nonlinear system is equivalently converted into a linear-like system with modeling error. A GCC law is then synthesized based on the equivalent model in the presence of modeling error under certain error condition. The control law ensures that the system under control is asymptotically stable as well as that a given cost function is upper-bounded. A suboptimal GCC law can be obtained via solving an optimization problem in terms of linear matrix inequality (LMI), in stead of state-dependent Riccati equation (SDRE) or Hamilton–Jacobi equations that are usually required in solving nonlinear optimal control problems. Finally, a numerical example is provided to illustrate the validity of the proposed method.