Mathematical Sciences: The Bellman Equation and its Application in Control Problems

这个项目将考虑使用最小控制的系统的可控性，使用极大极小控制的线性动力学，快速振荡系统的最优控制，以及多个最小化问题。弱溶液，特别是粘度溶液，将在整个过程中大量使用。在快速振荡系统的情况下，将研究惯性控制而不是可测量控制的影响。这些研究在工程设计、经济学、决策理论和各种控制系统中都有应用。

This project will consider controllability of systems using minimin control, linear dynamics using minimax control, optimal control of rapidly oscillating systems, and multiple minimization problems. Weak solutions, in particular viscosity solutions, will be used intensively throughout. The effect of inertial controls rather than measurable controls will be examined in the case of rapidly oscillating systems. These studies have applications in engineering design, economics, decision theory, and a variety of control systems.