论文标题
关于最佳控制策略的波动和一类线性二次调节器的能力
On the Volatility of Optimal Control Policies and the Capacity of a Class of Linear Quadratic Regulators
论文作者
论文摘要
众所周知，从工程学的角度来看，高度挥发性控制法律虽然对某些系统的理论最佳，但对于受控系统而言，这通常是有害的。在本文中，我们关注调节器在离散时间线性二次调节器（LQR）中的控制过程的时间波动。我们在本文中进行的调查发掘了LQR的任务最小化的成本功能与其控制定律的时间变化之间的令人惊讶的联系。 我们首先表明，最佳控制系统始终意味着高水平的控制波动率，即，在不牺牲成本的情况下，不可能降低最佳控制过程中的波动性。我们还表明，类似于通信系统，每个LQR都有与之相关的$容量〜区域$，它决定并量化在给定的控制波动级时可以实现多少成本。这还确定了一个事实，即没有可接受的控制政策可以同时实现低波动性和低成本。然后，我们采用此分析来解释在失控的电力市场中经常观察到的时间价格波动的现象。
It is well known that highly volatile control laws, while theoretically optimal for certain systems, are undesirable from an engineering perspective, being generally deleterious to the controlled system. In this article we are concerned with the temporal volatility of the control process of the regulator in discrete time Linear Quadratic Regulators (LQRs). Our investigation in this paper unearths a surprising connection between the cost functional which an LQR is tasked with minimizing and the temporal variations of its control laws. We first show that optimally controlling the system always implies high levels of control volatility, i.e., it is impossible to reduce volatility in the optimal control process without sacrificing cost. We also show that, akin to communication systems, every LQR has a $Capacity~Region$ associated with it, that dictates and quantifies how much cost is achievable at a given level of control volatility. This additionally establishes the fact that no admissible control policy can simultaneously achieve low volatility and low cost. We then employ this analysis to explain the phenomenon of temporal price volatility frequently observed in deregulated electricity markets.
