浅水長波流れに対する制御理論の応用

概要

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This paper presents a method for control of flood propagating through a reservoir or river channel using the combination of the finite element method and optimal control theory. The numerical model of the flood propagation can be expressed by the linear two-dimensional shallow water equation and the equation can be solved by the two-step explicit finite element method. As the boundary conditions, inflow discharge as the external force of optimal control problem is imposed on upstream site. The control vector is chosen as the outflow discharge, and is imposed on downstream site for the gate operation. Discretized shallow water equation by FEM is used for the state equation of the optimum problem. The performance function is formulated' by water elevation and control discharge. Then introducing a vector of Lagrange multiplier, We define the H function which is so called Hamiltonian. After that, using Euler equation and transversality condition as the necessary conditions for such optimum problem, eventually the two point boundary-value problem for state vector and the multiplier is introduced. To solve this problem, the conjugate gradient method and the Sakawa-Shindo method which minimizes the Hamiltonian directly, are mainly used in this paper. It is shown that the water elevation can be controlled as flat as possible by adjusting the control discharge of the dam gate in numerical examples.
1991-03-15