An L2 Disturbance Attenuation Solution to the Nonlinear Benchmark Problem

In this paper, we use the theory of L2 disturbance attenuation for linear (H1) and nonlinear systems to obtain solutions to the Nonlinear Benchmark Problem (NLBP) proposed in the paper by Bupp et. al.1. By considering a series expansion solution to the Hamilton-Jacobi-Isaacs Equation associated with the nonlinear disturbance attenuation problem, we obtain a series expansion solution for a nonlinear controller. Numerical simulations compare the performance of the third order approximation of the nonlinear controller with its rst order approximation (which is the same as the linear H1 controller obtained from the linearized problem.)