Equivalent gaming formulations of the problem of designing the maximum robust controls

Consideration was given to the problem of designing the maximum robust control of a dynamic system under uncertainty. The set of system requirements was defined by the normal operation conditions. In the case under study, it was defined as constraints on the values of the functionals specified on the system trajectories. The system robustness measure was defined, and the problem of its maximization by an appropriate choice of control was posed. Two theorems which reduced the maximum robustness problem to two gaming problems of minimax and maximin calculation were proved. Two problems – design of a system which has one degree of freedom is robust at most to the variations of the external action and design of the elastic characteristic of the undercarriage of a landing craft – were solved by way of example.