Game-theoretic control problem for a material point of an uncertain mass

We consider the motion control problem for a material point whose mass is u ncertain but lies within given limits. The point moves along a horizontal l ine under the action of two bounded forces, a control force and a disturban ce, the control force being stronger than the disturbance. We construct a c ontrol synthesis that steers a point of any admissible mass to the origin u nder any realization of the disturbance. The proposed control synthesis is shown to give the minimal guaranteed time of motion among all feedback cont rol laws.