An iterative strategy for fixed final state optimal control problems via simple cell mapping

A novel strategy is proposed to solve the fixed final state optimal control problem using the simple cell mapping method. A nonuniform time step simple cell mapping is developed to create a general database from which solutions of various optimal control problems can be obtained. An iterative backward search strategy is proposed to eliminate degenerated paths and improve the solution accuracy. This approach can accurately delineate the switching curves and eliminate nonoptimal paths. The well-known minimum time control problem of moving a point mass from any initial condition to the origin of the phase plane is studied with bang-bang controls. The analytical solutions of the problem provide a yardstick to examine the accuracy and convergence of the method. The cell size dependence of the solution accuracy is studied numerically. Numerical results are also presented to show the convergence of the iterative search algorithm. The proposed iterative search algorithm is also found to relax considerably the demands for small cells.