Abstract This work is devoted to establish the optimal solutions of impulsive optimal controls for a class of Lagrange problem. Using the approximate method and fixed point theorem, the corresponding semilinear system is solvable under some appropriate assumptions. From the derived results, we propose to construct two kinds of minimizing sequences of approximating solutions to obtain the optimal solutions. The new results obtained here actually give rise to a general technique useful also for other optimal control problems with multiple solutions.

中文翻译：

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一类拉格朗日问题脉冲最优控制的近似解

摘要 本文致力于为一类拉格朗日问题建立脉冲最优控制的最优解。使用近似方法和不动点定理，相应的半线性系统在一些适当的假设下是可解的。根据推导出的结果，我们建议构造两种近似解的最小化序列以获得最优解。这里获得的新结果实际上产生了一种通用技术，也适用于其他具有多种解决方案的最优控制问题。