Optimal Control of the Constrained Reservoir System by the Discrete Linear Tracking

이산형선형추적(離散型線型追跡)에 의한 제약저수지계(制約貯水池系)의 최적(最適) 제어

The linear tracking theory has a great merit that its solution can be analytically obtained under the quadratic performance measure. However, this theory has not been applied to reservoir system operation yet, because the tracking assumes no boundness of the control and state vectors. This paper presents deriving the optimal control law and solving the Riccati equations for the discrete time horizon, and its application to the real system. And the additional necessary conditions for the saturated vectors of the control and/or state are also derived using the concept of the Pontryagin's minimum principle. The logic and its algorithm in this work are not so positive to give a general solution. In fact, it is a matter of modeling in terms of relative magnitude of disturbance and time-step size. However its application to the real environment of the Han river, which comprises six major reservoirs in series/parallel, demonstrated satisfactory results over 36 monthly stages.

저수지계(貯水池系)의 최적운영(最適運營)은 다차원문제(多次元問題)로서 일반적으로 O.R. 기법(技法)으로 해를 구할 수 있다. 본(本) 연구(硏究)에서는 선형추적리론(線型追跡理論)을 이산화(離散化)하여 2점(點) 경계치문제(境界値問題)를 풀었다. 이 이론의 적용에는 두가지 문제가 제기되는데 첫째, 추적(追跡)을 위한 기준(基準)이 미지수(未知數)이므로 무제약(無制約) 조건(條件)의 최적률(最適律)을 반복 적용하여 수렴치(收斂値)를 구하여 이로부터 추적기준(追跡基準)을 산출했다. 둘째, 상태 및 제어벡터의 제약조건(制約條件)의 처리는 Pontryagin의 최소원리(最小原理)로 해결하였다.