Haibo Lu

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In this paper, the existence of step-like contrast structure for a class of singularly perturbed optimal control problem is shown by the contrast structure theory. By means of direct scheme of boundary function method, we construct the uniformly valid asymptotic solution for the singularly perturbed optimal control problem. Finally , an example is presented(More)
Finite element method and analytic method are used to safety evaluation of a penstock laid on downstream surface of dam and its expansion pipe on the following issues: (i) Concrete cracking zone, maximum crack width and stress in liner and bars are calculated and analyzed with allowable value; (ii) Relative displacement at both sides of the joint between(More)
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