Asymptotic Solution of a Cheap Control Problem for Systems with Delays

V.Y. Glizer (Israel)


Time delay system, cheap control problem, asymptotic expansion, control boundedness


A finite horizon quadratic cheap control of a linear system with point-wise and distributed time delays in the state vari able is considered. By a linear transformation, this problem is converted to an equivalent linear-quadratic cheap control problem for a much simpler (undelayed) system. For this new problem, asymptotic expansions of the optimal control and the optimal value of the cost functional are constructed. The boundedness of the optimal control is established. The limit of the optimal value of the cost functional is obtained. The maximal achievable accuracy of the optimal control in the original cheap control problem is derived. An illustrative example is presented.

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