用参数例子分析有限时域状态约束问题的最大值原理。第二部分：双边国家限制的问题
Analyzing a Maximum Principle for Finite Horizon State Constrained Problems via Parametric Examples. Part 2: Problems with Bilateral State Constraints
摘要：
本文给出了R。文特尔[ \textit{Optimal Control}，Birkhäuser，Boston，2000;定理~9.3.1]通过参数例子进行了分析。后者起源于V.~ Basco，P.~ Cannarsa和H.~ Frankowska，类似于数学经济学中的最优增长问题。这些参数的例子的解决方案的存在性，建立通过调用Filippov的存在性定理迈耶问题。由于最大值原理只是局部最优过程的一个必要条件，因此需要大量的额外研究来获得一个全面的综合，许多过程被怀疑是局部极小。我们的分析不仅有助于深入理解这一原则，而且还可以作为将其应用于有意义的经济最优增长模型原型的样本。本文的第一部分研究了单边状态约束问题。双边国家约束的问题将在第二部分讨论。
英文摘要：
In the present paper, the maximum principle for finite horizon state constrained problems from the book by R. Vinter [\textit{Optimal Control}, Birkhäuser, Boston, 2000; Theorem~9.3.1] is analyzed via parametric examples. The latter has origin in a recent paper by V.~Basco, P.~Cannarsa, and H.~Frankowska, and resembles the optimal growth problem in mathematical economics. The solution existence of these parametric examples is established by invoking Filippov's existence theorem for Mayer problems. Since the maximum principle is only a necessary condition for local optimal processes, a large amount of additional investigations is needed to obtain a comprehensive synthesis of finitely many processes suspected for being local minimizers. Our analysis not only helps to understand the principle in depth, but also serves as a sample of applying it to meaningful prototypes of economic optimal growth models. Problems with unilateral state constraints have been studied in Part 1 of the paper. Problems with bilateral state constraints are addressed in this Part 2.
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