Optimal Periodic Control Processes

本研究的目的是概括和澄清一些 周期最优控制理论的最新研究成果 特别是 将研究一些理论和计算问题： 证明充分条件，如果以最小的方式削弱， 也是必要的，以显示如何相邻的最佳周期调节器 可以被构造，并且对于一类特殊的系统，可以被推广到 得到了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周期调节器， 其相关的对称代数Riccati方程;指出如何 周期性约束、有界状态和/或控制约束可以 包括在周期性最优控制公式中;确定 不确定动态系统鲁棒性的影响 定期反馈增益;并扩展必要和充分的 慢变时滞拟周期最优控制问题的条件 改变参数。 预计这些结果可能会 对化学过程控制等不同领域产生重大影响 飞行力学

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.