抄録
The optimal control problem of a linear system with time-delay for a quadratic performance index is discussed.
The problem is formulated as that of a coupled system of a lumped parameter subsystem and a distributed parameter subsystem which corresponds to a group of time-delay elements.
The optimal control is derived by applying the principle of optimality, and is given in a form of a linear combination of states of the both subsystems.
In other words, the optimal control is realized by a linear feedback of a present value x(t) and a history x(τ), t-θ(t)≤τ<t, of the state of the lumped parameter subsystem. Furthermore, it is shown that the optimal feedback gains are the solutions of the Riccati type ordinary and partial differential equations.
