Singular and Analytic Perturbations, Slow and Fast Time Scales in Control Theory and Viability Theory and their Applications

我们提出了一种创新的方法来解决几类重要的数学问题，这些问题的数据解析地依赖于小的扰动参数。在许多科学领域（生物技术、物理、工程等）都出现了时间尺度问题，特别是两种类型的进化（慢的和快的）的相互作用。我们期望开发新的技术来分析和渐近优化奇异摄动控制系统和马尔可夫决策过程。特别是，我们计划建立具有时间平均准则的一般非线性最优控制问题与由底层控制系统生成的极限职业测度空间中的线性规划问题之间的联系。

We propose an innovative approach to several important classes of mathematical problems, whose data depend analytically on small perturbation parameters. Time scale problems, and, in particular, the interaction of two types of evolution, slow and fast, arise in many scientific domains (biotechnology, physics, engineering, etc).We expect to develop new techniques for analysis and asymptotic optimisation of singularly perturbed control systems and Markov decision processes. In particular, we plan to establish links between general nonlinear optimal control problems with time average criteria and linear programming problems in the space of limit occupational measures generated by the underlying control system.