Linear multi-model time-optimization

A linear optimization problem with unknown parameters from a given finite set is tackled. The problem is to find the robust time-optimal control transferring a given initial point to a convex terminal compact set M for all unknown parameters in the shortest time. The robust maximum principle for this minimax problem is formulated. It gives a necessary and sufficient condition of robust optimality. Under natural conditions, the existence and uniqueness of robust optimal controls are proven when the resource set is a convex polytope. Several illustrating examples, including a bang–bang robust optimal control, are considered in detail.