Optimal and H(infinity) suboptimal feedback control of dynamical nonlinear systems for control of wing rock motion

{dollar}Hsb{lcub}infty{rcub}{dollar} suboptimal control of a nonlinear system using nonlinear state feedback is presented in this dissertation. In the time domain approach, the nonlinear {dollar}Hsb{lcub}infty{rcub}{dollar} suboptimal control problem using state feedback is dominated by a Hamilton-Jocobi-Bellman (HJB) inequality. Proper selection of a closed loop Lyapunov function as a series form of the state variables is shown to result in the reduction of this HJB equation to an Algebraic Riccati equation along with several other algebraic equations. These equations can be solved successively as the closed loop Lyapunov equations based on the powers of the state vector of the HJB equation. Since the feedback controller is determined from the derivative of the closed loop Lyapunov function, the resulting closed loop system will always have the larger stable region than that of the linear controller. The wing rock motion of slender delta wings presented by Reference (1) is employed to illustrate the method. It is shown that the nonlinear state {dollar}Hsb{lcub}infty{rcub}{dollar} state feedback control will generate a larger stable region than the linear {dollar}Hsb{lcub}infty{rcub}{dollar} state feedback case for a nonlinear system.