Control of the nonlinear wing rock motion of slender delta wings using a nonlinear H 1 robust method is presented. The wing rock motion is mathematically described by a nonlinear, ordinary differential equation with coef cients varying with angle of attack. In the time domain approach, the nonlinear H 1 robust control problem with state feedback is cast in terms of a Hamilton-Jacobi-Bellman inequality (HJBI). Assuming that the coef cients 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 1 state feedback control are compared with those obtained with the linear H 1 state feedback control, indicating the necessity of employing nonlinear feedback control for nonlinear dynamics.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.