ESTIMATE OF THE GUARANTEED VALUE IN A NONLINEAR DIFFERENTIAL GAME OF APPROACH

A non-linear differential game of approach is considered. An estimate of the guaranteed value function is derived. The formalization of the problem follows /1, 2/, using constructions based on the conjugate derivative of locally Lipschitzian functions and the Hamiltonian function characterizing the dynamics of the non-linear systems /3-7/. An auxiliary linear differential game of approach is introduced with a known u-stable guaranteed value function. The construction are based on the results of /8-10/. The Hamiltonians of the original non-linear system and the auxiliary linear system are not assumed to be related in any special way. An example is considered in which the proposed approach is used to construct a bound on the guaranteed value function. The problem is related to the previous studies /11-16/.