Nonlinear H_∞ method for control of wing rock motions

Control of the nonlinear wing rock motion of slender delta wings using a nonlinear H_∞ robust method is presented. The wing rock motion is mathematically described by a nonlinear, ordinary differential equation with coefficients varying with angle of attack. In the time domain approach, the nonlinear H_∞ robust control problem with state feedback is cast in terms of a Hamilton-Jacobi-Bellman inequality (HJBI). Assuming that the coefficients in the nonlinear equation of the wing rock motion satisfy a norm-bounded nonlinear criterion, the HJBI can be written in a matrix form. The state vector is represented as a series of closed-loop Lyapunov functions that result in reducing the HJBI to an algebraic Riccati inequality along with several other algebraic inequalities. These inequalities can be successively solved to a desired power in the series representation of the state vector in the HJB equation. The results of the nonlinear H_∞ state feedback control are compared with those obtained with the linear H_∞ state feedback control, indicating the necessity of employing nonlinear feedback control for nonlinear dynamics.