U.S.-Polish Collaborative Research on Variational Methods inthe Control of Nonlinear Systems

9527672舍特勒这一美国-波兰合作研究奖授予“非线性系统控制中的变分方法”。主要研究人员是华盛顿大学的Heinz Schaettler博士，以及罗兹大学数学研究所的Andrej Nowakowski和Stanislaw Walczak博士。研究人员将结合他们在场论领域的最优控制理论、Dubovitskii-Milyutin方法和非规则/异常优化问题方面的专业知识，开发出关于最优性和最优控制问题充分条件的广泛而全面的理论。极值场和/或动态规划的概念从使用希尔伯特不变积分的推广的经典观点以及从哈密尔顿-雅各比-贝尔曼方程的解的现代观点提供了理论基础。他们将研究极值的几何性质和值函数的奇点之间的联系。特别是，他们将分析最优异常极值在构造正则综合，即最优极值领域中所起的作用。他们将特别关注目前只有有限的最优性必要条件的Dirichlet型控制系统。这项应用数学研究实现了将美国和波兰的顶尖专家聚集在一起，在平等、互惠和互利的基础上，在共同利益和能力强的领域结合互补努力和能力的计划目标。***

9527672 Schaettler This U.S.-Polish Cooperative Research award is on "Variational Methods in the Control of Nonlinear Systems." The principal researchers are Dr. Heinz Schaettler of Washington University, and Drs. Andrej Nowakowski and Stanislaw Walczak of the Institute of Mathematics of Lodz University. The researchers will combine their expertise in optimal control theory in the area of field theory, the Dubovitskii-Milyutin method, and nonregular/abnormal optimization problems to develop a broad and comprehensive theory of sufficient conditions for optimality and optimal control problems. The notion of a field of extremals and/or dynamic programming provide the theoretical basis both from a classical viewpoint using generalizations of Hilbert's invariant integral as well as from a modern perspective in the context of solutions to the Hamilton-Jacobi-Bellman equation. They will investigate links between geometric properties of extremals and singularities of the value function. In particular, they will analyze the role optimal abnormal extremals play in the construction of a regular synthesis, viz., an optimal field of extremals. They will give special attention to control systems of Dirichlet type for which currently only limited necessary conditions for optimality are available. This research in applied mathematics fulfills the program objectives of bringing together leading experts in the U.S. and Poland to combine complementary efforts and capabilities in areas of strong mutual interest and competence on the basis of equality, reciprocity, and mutuality of benefit. ***