Solution of Fixed Final State Optimal Control Problems via Simple Cell Mapping

Abstract

A strategy is proposed to solve the fixed final state optimal control problem using the simple cell mapping method. A non-uniform time step simple cell mapping is developed to create a general database from which solutions of various optimal control problems can be obtained. A two-stage backward search algorithm is proposed to eliminate degenerated paths often associated with the simple cell mapping. The proposed method can accurately delineate the switching curves and eliminate false limit cycles in the solution. The method is applied to two optimal control problems with bang-bang control. 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 first. This example has exact solutions available which provide a yardstick to examine the accuracy of the method. The cell size dependence of the solution accuracy is studied numerically. The second example is a variable stiffness feedback control problem with tuning range saturation. The strategy proposed is able to provide the switching curves in the phase plane. This result has not been obtained before.