APPLICATION OF TIME VARYING EIGENSYSTEM REALIZATION ALGORITHM TO GUIDANCE AND CONTROL PROBLEMS

System identification method called the Time Varying Eigensystem Realization Algorithm is applied to input output simulated data of nonlinear system models. Resulting time varying model sequence is shown to approximate the first order departure motion dynamics about the nominal trajectory, leading to an effective model reduction procedure for nonlinear systems in discrete time. The time varying discrete time models thus obtained can be used for control and estimation purposes. The method is demonstrated on two representative problems in the present paper. First problem involves an optimal control problem involving the two dimensional motion of a point mass. It is conclusively demonstrated that in the presence of unstructured nonlinearities, using experimental (or simulated) data, models governing the departure motion dynamics can be explicitly constructed. These models are subsequently used in a perturbation guidance scheme. Subsequent example considers the dynamics of a point mass in a rotating tube apparatus. Models of the point mass are obtained from experimental data. Insights about the time varying coordinate systems are obtained by considering this physical example that naturally involves a time varying component.