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SUMMARYConsiderable e ort has been devoted to develop optimal control methods for reducing structural response under seismic forces. In this study analytical solution of the linear regulator problem applied widely to the control of earthquake-excited structures is obtained by using the su cient conditions of optimality even though almost all of the optimal controls proposed previously for structural control are based on the necessary conditions of optimality. Since the resulting optimal closed-open-loop control cannot be implemented for civil structures exposed to earthquake forces, the solution of the optimal closed-openloop control is carried out approximately based on the prediction of the seismic acceleration values in the near future. Upon obtaining the relation between the exact optimal solution and future values of seismic accelerations, it is shown numerically that the solution of the optimal closed-open-loop control problem can be performed approximately by using only the ÿrst few predicted seismic acceleration values if a given norm criteria is satisÿed. Calculated performance measures indicate that the suggested approximate solution is better than the closed-loop control and as we predict the future values of the excitation more accurately, it will approach the optimal solution.

A linear, completely nonhomogeneous, generally nonlocal, multipoint problem is investigated for a second-order ordinary integro-differential equation with generally nonsmooth coefficients, satisfying some general conditions like p-integrability and boundedness. A system of three integro-algebraic equations named the adjoint system is introduced for the solution. The solvability conditions are found by the solutions of the homogeneous adjoint system in an "alternative theorem". A version of a Green's functional is introduced as a special solution of the adjoint system. For the problem with a nontrivial kernel also a notion of a generalized Green's functional is introduced by a projection operator defined on the space of solutions. It is also shown that the classical Green and Cauchy type functions are special forms of the Green's functional.

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Longwall coal mining is an economical method for coal extraction that allows most of the coal to be extracted from a wide rectangular panel. The roof of the working face area is temporarily held up by supports which advance as the mine face advances. A basin‐like subsidence trough develops at the ground surface over the panel as the panel roof behind the supports collapses. A dynamic subsidence front causes a water‐level drop at wells ahead of the panel. We examine the effects of subsidence on water‐level by introducing a sink that moves with the mining face, using the one‐dimensional flow equation. To test the validity of this method, we estimated aquifer parameters of Trivoli Sandstone aquifer over a longwall coal mine in the Illinois Basin by analyzing water‐level versus time data measured from three observation wells. The presented method predicts a value of transmissivity and storage coefficient that is reasonably close to the average of pumping test results. With this method we provide solutions to two significant problems: (1) Presubs(2) water‐level drops can be predicted for a planned longwall mine if the aquifer parameters are known.