Using Lyapunov Vectors and Dichotomy to Solve Hyper-Sensitive Optimal Control Problems

The dichotomic basis method for solving completely hyper-sensitive optimal control problems is modified by using Lyapunov exponents and vectors. It is shown that the asymptotic Lyapunov vectors form dichotomic transformations that decouple the unstable dynamics from the stable dynamics. For numerical implementation, finite-time Lyapunov vectors are used to approximate the asymptotic Lyapunov vectors and to construct an approximate dichotomic basis. A reinitialization process is introduced to decrease the error accumulation. The new basis identifies the stable and unstable directions more accurately than the eigenvectors of the Jacobian matrix