Linear Multimodel Time Optimization

Abstract

Robust time optimality can be considered as a particular case of the Lagrange problem, and therefore, the results obtained in the previous chapters allow us to formulate directly the Robust Maximum Principle for this time-optimization problem. As is shown in Chap. 8, the Robust Maximum Principle appears only as a necessary condition for robust optimality. But the specific character of the linear time-optimization problem permits us to obtain more profound results: in this case the Robust Maximum Principle appears as a necessary and sufficient condition. Moreover, for the linear robust time optimality it is possible to establish some additional results: the existence and uniqueness of robust controls, the piecewise constancy of robust controls for a polyhedral resource set, and a Feldbaum-type estimate for the number of intervals of constancy (or “switching”). All these aspects are studied below in detail.