Optimal Control for Certain Nonlinear Systems in which Control Variables Appear Linearly

概要

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This paper is concerned with the problem of optimal control for systems which are linear in control but nonlinear in state. It is shown that there is a large class of control systems in which optimal singular trajectories are allowed to lie only on a certain hypersurface when a condition similar to the normality condition for linear time-optimal control systems is fulfilled. It follows from this result that the optimal control becomes totally bang-bang or totally singular. Furthermore, for a special class of position control systems including a nonlinear element and a controller, it is proved that the optimal control becomes totally bang-bang, provided that the controlled system is controllable and observable. Finally some practical examples are given to see whether the proposed criterion is applicable or not to characterizing the type of optimal control.
一般社団法人日本機械学会の論文