慢可观系统的近最优控制
On near optimal control of systems with slow observables
摘要：
本文讨论了一个系统的控制问题，其特征在于控制对状态变量（称为观测量）的某些函数的动态的影响相对较弱，这些观测量的变化率比状态变量本身的变化率慢得多。该文件的贡献是双重的。首先，引入解近似于慢可观量轨迹的平均系统，证明了在慢可观量系统解上考虑时间折扣准则的最优控制问题的最优值收敛于相应的平均系统最优控制问题的最优值。其次，如何渐近最优控制的扰动问题的最优解的基础上，平均问题的最优解的构造方法被指出，充分和必要的最优性条件的平均问题，并概述了如何近最优解的构造方法可以用数字（构造与一个例子说明）。
英文摘要：
The paper deals with a problem of control of a system characterized by the fact that the influence of controls on the dynamics of certain functions of state variables (called observables) is relatively weak and the rates of change of these observables are much slower than the rates of change of the state variables themselves. The contributions of the paper are twofold. Firstly, the averaged system whose solutions approximate the trajectories of the slow observables is introduced, and it is shown that the optimal value of the problem of optimal control with time discounting criterion considered on the solutions of the system with slow observables (this problem is referred to as perturbed) converges to the optimal value of the corresponding problem of optimal control of the averaged system. Secondly, a way how an asymptotically optimal control of the perturbed problem can be constructed on the basis of an optimal solution of the averaged problem is indicated, sufficient and necessary optimality conditions for the averaged problem are stated, and a way how a near optimal solution of the latter can be constructed numerically is outlined (the construction being illustrated with an example).
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