On a game problem involving systems with time delay

A dynamic programming approach is used to obtain feedback solutions to a game problem involving linear systems having a time delay. As is known, the optimal feedback gains in linear time delay systems with quadratic criterion are determined by partial differential equations [1]. In the particular case studied here, the solution to these equations can be obtained by first separating variables and then solving the resulting simpler equations. The optimal feedback control also has the advantage that it can be realized on-line.