An ℒ2 disturbance attenuation approach to the nonlinear benchmark problem

Uses the theory of L₂ disturbance attenuation for linear (ℋ_∞) and nonlinear systems to obtain solutions to the nonlinear benchmark problem (NLBP) proposed in the companion paper by Bupp et al. (1995). By considering a series expansion solution to the Hamilton-Jacobi-Isaacs equation associated with the nonlinear disturbance attenuation problem, the authors 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 first order approximation (which is the same as a linear ℋ_∞ controller obtained from the linearized problem.)