Decomposition technique for minimum time trajectories

A decomposition technique is presented for minimum-time trajectories which are characterized by intermediate constraints and discontinuities. The optimization of such multiple are trajectories is usually a formidable task. One optimization method, trajectory decomposition, breaks the original trajectory at points of discontinuity into separate arcs and then optimizes each are subject to prescribed boundary conditions. This constitutes a first level of control. Each first-level solution is evaluated by a second-level controller, which iteratively specifies new are boundary conditions in order to achieve an optimum solution. Unfortunately, this two-level method cannot be applied directly to minimum-time trajectories. The two-level trajectory decomposition method is extended here to a three-level technique for treating the minimum-time trajectory. The first level again optimizes each are for specified intervention parameters. The new second level, the time interface controller, exploits certain homogeneity properties to satisfy time transversality conditions at all boundaries and to couple the first-level solution arcs in time. The third level, the state interface controller, satisfies state transversality conditions at the arc junctions iteratively while driving the trajectory to its optimum. The new three-level procedure represents a feasible decomposition because each solution trajectory in the iterative sequence is physically realizable. The technique also offers a decentralization of control effort and reduction of initial-value sensitivities. An example problem is formulated.