Nonlinear H_∞ flight control of general six-degree-of-freedom motions

Application of nonlinear H_∞ control theory to flight vehicles whose complete six-degree-of-freedom nonlinear equations of motion are considered directly without linearization is investigated. Nonlinear flight control modes such as velocity control, body-rate control, attitude control, and hovering control are designed in a unified framework such that the derived nonlinear H_∞ control law is valid for arbitrary flight vehicles. The most difficult and challenging task involved in applying the nonlinear H_∞ control theory is to solve the associated Hamilton-Jacobi partial differential inequality (HJPDI). We show that the HJPDI of flight control problems can be solved analytically with simple manipulations. A closed-form expression for the nonlinear H_∞ flight controller is derived from the solution of HJPDI and is shown to be in the simple structure of proportional feedback. The numerical simulations show that the derived nonlinear H_∞ control law can ensure global and asymptotical stability of the closed-loop system and have strong robustness against wind gusts with varying statistical characteristics.