控制输入约束下连续时间随机系统的不稳定性条件
Instabilizability Conditions for Continuous-Time Stochastic Systems Under Control Input Constraints
摘要：
本文研究了连续时间线性随机系统的约束控制问题。我们表明，对于某些系统参数设置，约束控制策略永远无法实现稳定。具体来说，我们探索一类控制策略，约束有一个有界的平均二阶矩伊藤型随机微分方程的加性和乘性噪声。我们证明了在一定的系统参数和控制约束的边界常数的设置，发散的系统状态的二阶矩是不可避免的，无论初始状态值和控制策略如何设计。
英文摘要：
In this paper, we investigate constrained control of continuous-time linear stochastic systems. We show that for certain system parameter settings, constrained control policies can never achieve stabilization. Specifically, we explore a class of control policies that are constrained to have a bounded average second moment for Ito-type stochastic differential equations with additive and multiplicative noise. We prove that in certain settings of the system parameters and the bounding constant of the control constraint, divergence of the second moment of the system state is inevitable regardless of the initial state value and regardless of how the control policy is designed.
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