Optimal Periodic Control Processes

本研究的目的是推广和澄清周期最优控制理论的一些最新成果。特别是，将研究一些理论和计算问题：证明充分条件，如果以最小的方式减弱，也是必要的；证明了如何构造一个相邻的最优周期调节器，并将其推广到一类特殊的系统，以获得极限环的全局稳定性；研究了该周期调节器与线性二次型调节器的关系及其相关的对称代数Riccati方程；说明周期约束、有界状态约束和/或控制约束如何包含在周期最优控制公式中；利用周期反馈增益确定不确定动力系统鲁棒性的影响；并将其充要条件推广到参数缓慢变化的拟周期最优控制问题。预计这些结果将对化学过程控制和飞行力学等不同领域产生重大影响。

The goal of this research is to generlize and clarify a number of recent results on periodic optimal control theory. In particular, a number of theoretical and computational issues will be investigated: to show that the sufficiency condition, if weakened in a minimal way, is also necessary; to show how a neighboring optimum periodic regulator can be constructed and, for a special class of systems, generalized to obtain global stability to a limit cycle; to study the relationship of this periodic regulator with that of the linear-quadratic regulator and its associated symmetric algebraic Riccati equation; to indicate how the periodic constraints, bounded state and/or control constraints, can be included in the periodic optimal control formulation; to determine the effects on robustness of uncertain dynamical systems by using periodic feedback gains; and to extend the necessary and sufficient conditions to quasi-periodic optimal control problems with slowly varying parameters. It is expected that these results could have significant impact on such diverse areas as chemical process control and flight mechanics.