Multi-Input Deadbeat Linear-Quadratic Optimal Control. Multi-Input Discrete-Time Optimal Regulator with the Fixed Terminal State Condition.:Multi-Input Discrete-Time Optimal Regulator with the Fixed Terminal State Condition

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This paper discusses the optimal regulator problem for the multi-input linear time-invariant discrete-time system with the zero terminal state. By using the general form of the inputs which satisfy the zero terminal state condition, the system is transformed into the new time-variant system with the time-variant structure of the new input. The performance index is transformed into the sum of the quadratic forms of the new state vectors and the new input vectors with the cross terms, and the new terminal state is free. The optimal inputs are given by the variable gain state feedback in the first phase, by linear combinations of the constant gain state feedback and the variable gain state feedback in the second phase, and by the constant gain state feedback in the third phase. The variable gains are obtained by using the nonstationary Riccati equation. All gains are independent of the initial state of the system.
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