Transition to nonlinear H∞ optimal control from inverse-optimal solution for Euler-Lagrange system

One of recent achievements in the field of nonlinear H_∞ optimal control theories for Euler-Lagrange systems is the analytic solution to the Hamilton-Jacobi-Isaacs (HJI) equation associated to the so-called nonlinear H_∞ inverse-optimal control. In this paper, we address the problem of nonlinear H_∞ optimal control design for an Euler-Lagrange system, rather than the inverse-optimal problem. By introducing a technique of control weight loosening and state weight strengthening, we show that the associated HJI inequality, not the equation, for nonlinear H_∞ optimal control can be solved also analytically using the inverse-optimal solution.