OPTIMAL FEEDBACK-CONTROL OF A NONLINEAR-SYSTEM - WING ROCK EXAMPLE

A procedure is presented for optimizing a state feedback control law f or a nonlinear system with respect to a positive performance index. Th e Hamilton-Jacobi-Bellman equation is employed to derive the optimalit y equations wherein this performance index is minimized. The closed-lo op Lyapunov function is assumed to have the same matrix form of state variables as the performance index, The constant interpolated terms of these matrix forms are easily determined so as to guarantee their pos itive definitenesses. The optimal nonlinear system is asymptotically s table in the large, as both the closed-loop Lyapunov function and perf ormance index are positive definite. An unstable wing rock equation of motion is employed to illustrate this method. It is shown that the wi ng rock model using nonlinear state feedback is asymptotically stable in the large. Both optimal linear and nonlinear state feedback cases a re evaluated.