Trajectory structures and transport

The special problem of transport in 2-dimensional divergence-free stochastic velocity fields is studied by developing a statistical approach, the nested subensemble method. The nonlinear process of trapping determined by such fields generates trajectory structures whose statistical characteristics are determined. These structures strongly influence the transport.Comment: Latex file 19 pages, includes 12 EPS figures. Extended version of the invited talk at the ITCPP, Santorini, 200

Stochastic Feedback Control of Systems with Unknown Nonlinear Dynamics

This paper studies the stochastic optimal control problem for systems with unknown dynamics. First, an open-loop deterministic trajectory optimization problem is solved without knowing the explicit form of the dynamical system. Next, a Linear Quadratic Gaussian (LQG) controller is designed for the nominal trajectory-dependent linearized system, such that under a small noise assumption, the actual states remain close to the optimal trajectory. The trajectory-dependent linearized system is identified using input-output experimental data consisting of the impulse responses of the nominal system. A computational example is given to illustrate the performance of the proposed approach.Comment: 7 pages, 7 figures, submitted to 56th IEEE Conference on Decision and Control (CDC), 201

Computational aspects of multilevel trajectory optimization

This paper presents new computational results in multilevel trajectory optimization. The original formulation of trajectory decomposition is extended and applied to a difficult multiple arc trajectory example, the low thrust interplanetary swingby problem. A numerical solution is obtained for this trajectory which is characterized by nonlinear, time variant differential equations and interior boundaries and discontinuities. The time domain decomposition of the trajectory is made at the boundaries between arc segments. A three level optimization hierarchy is employed to transform the first feasible trajectory iterate into a final solution trajectory. This example is characteristic of a large class of interplanetary swingby problems which defy solution by conventional computational methods because of multiple discontinuities, constraints, and severe numerical sensitivities. The multilevel approach appears to be effective in obtaining a solution to problems of this type when other more conventional methods are unsatisfactory

Towards database support for moving object data

To narrow down moving object challenges, the focus of this thesis is on four issues, namely, uncertainty handling for moving object data, faithful trajectory representation, trajectory compression techniques, and similarity measures for trajectories