切换控制用于量化反馈系统：不变性与极限环分析
Switched control for quantized feedback systems: invariance and limit cycle analysis
AI总结：
本文研究了在控制动作和被控变量测量中存在量化效应的离散时间线性时不变系统反馈控制问题，提出了一种切换控制方案以最小化控制和被控变量的量化影响，针对一个常见的计算系统模型（如线程调度、时钟同步和资源分配），分析了在加性常数扰动下受控系统呈现周期解的必要和充分条件。
摘要：
我们研究了在控制动作和被控变量测量中存在量化效应的离散时间线性时不变系统的反馈控制。虽然在某些应用中量化效应可以被忽略，但在需要高精度控制的情况下，必须在控制设计中显式考虑这些效应。本文针对一个简单的积分器模型（具有单位延迟），该模型在计算系统领域非常常见，例如在线程调度、时钟同步和资源分配中。我们证明了切换控制方案在性能上优于无切换方案，后者忽略了量化效应。我们分析了在控制输入受到加性常数扰动的情况下，受控系统表现出周期解的必要和充分条件。仿真结果提供了该方法有效性的证据。
英文摘要：
We study feedback control for discrete-time linear time-invariant systems in the presence of quantization both in the control action and in the measurement of the controlled variable. While in some application the quantization effects can be neglected, when high-precision control is needed, they have to be explicitly accounted for in control design. In this paper we propose a switched control solution for minimizing the effect of quantization of both the control and controlled variables in the case of a simple integrator with unitary delay, a model that is quite common in the computing systems domain, for example in thread scheduling, clock synchronization, and resource allocation. We show that the switched solution outperforms the one without switching, designed by neglecting quantization, and analyze necessary and sufficient conditions for the controlled system to exhibit periodic solutions in the presence of an additive constant disturbance affecting the control input. Simulation results provide evidence of the effectiveness of the approach.
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