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

小行星9527672 这个美国-波兰合作研究奖是关于“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海因茨·沙特勒博士和罗兹大学数学研究所的安德烈·诺瓦科夫斯基博士和斯坦尼斯瓦夫·沃尔扎克博士。 研究人员将联合收割机结合他们在场论领域的最优控制理论的专业知识，Dubovitskiiii-Milyovitian方法和非规则/异常优化问题，以开发一个广泛而全面的最优性和最优控制问题的充分条件理论。 极值和/或动态规划领域的概念提供了理论基础，无论是从经典的观点，使用希尔伯特不变积分的推广，还是从现代的角度来看，在解决方案的范围内的汉密尔顿-雅可比-贝尔曼方程。 他们将调查极值和奇异值函数的几何性质之间的联系。 特别是，他们将分析的作用，最佳异常极值发挥建设一个定期的综合，即，极值的最优域 他们将特别注意狄利克雷型控制系统，目前只有有限的必要条件为最优性。 这项应用数学研究实现了汇集美国和波兰领先专家的计划目标，在平等，互惠和互利的基础上，在强烈的共同利益和能力领域联合收割机互补努力和能力。 ***

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. ***