Abstract

This paper considers the design problem of a stochastic linear-quadratic controller over an infinite time-horizon with dynamic scaling of the coefficients in the state equation and the cost criterion. Dynamic scaling means multiplying the coefficients by a positive time-varying function. The optimality criteria used are extensions of the long-term average cost and pathwise long-term average cost. The integral of the scaling function is applied to normalize the performance indices. It is shown that, the optimal control law is time-invariant and can be obtained through a steady-state optimal strategy known for the autonomous system.

中文翻译：

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具有系数动态标度的随机线性控制器设计中最优控制的时间不变性。

摘要

考虑状态方程中的系数和成本准则的动态缩放，在无限的时间范围内考虑了随机线性二次控制器的设计问题。动态缩放意味着将系数乘以正时变函数。所使用的最优性标准是长期平均成本和逐步长期平均成本的扩展。缩放函数的积分用于归一化性能指标。结果表明，最优控制律是时不变的，可以通过自治系统已知的稳态最优策略来获得。