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On the existence of an optimal synthesis for a class of linear discrete-time systems with quadratic costs and a fixed target point

We use the dynamic programming and approximation techniques to prove the existence of an optimal synthesis for a class of linear discrete time systems with quadratic costs and a fixed target point, in which the optimal control law is given in the feedback form of time and state. Our result establishes an analogy in synthesizing fixed target point linear quadratic regulator problems between linear continuous time systems and this class of linear discrete time systems.