具有伪单调算子的非线性微分包含约束的最优控制(英文)

Optimal Controls of Nonlinear Evolution Inclusions withPseudomonotone Operator

英文关键词:evolution inclusion  set-valued analysis  pseudomonotone operator  upper semicontinuity  support function  parabolic system.

中文摘要:

      本文研究一类受主算子为伪单调算子的非线性微分包含约束的最优控制问题．首先,探讨抛物型发展方程的柯西问题其解的性质及微分包含问题的容许轨线的存在性;然后,利用一个新的可测选择定理解决了受非线性微分包含约束的最优控制的存在性,最后,给一例子加以说明所获结果的应用性．

英文摘要:

      In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further, we prove the existence of admissibletrajectories for evolution inclusions. Then, we extend the Fillipov's selection theoremand discuss a general Lagrange type optimal control problem. Finally, we present anexample that demonstrates the appplicability of our results.