具有伪单调算子的非线性微分包含约束的最优控制

摘要

In this paper, we study the optimal control problem of nonlinear differential inclusions with principle operator being psendomonotone. First, we give some properties of solutions of certain evolution equations. Further, we prove the existence of admissible trajectories for evolution inclusions. Then, we extend the Fillipov's selection theorem and discuss a general Lagrange type optimal control problem. Finally, we present an example that demonstrates the applicability of our results.%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.