论文标题
了解PD控制对于不确定随机系统的能力
Understanding the Capability of PD Control for Uncertain Stochastic Systems
论文作者
论文摘要
在本文中，我们关注一类不确定随机控制系统的全局稳定性问题，其中漂移项和扩散项都是状态变量的非线性函数和控制变量。我们将表明，工程实践中广泛应用的比例衍生（PD）控制能够以既定的平方意义在全球范围内稳定这种系统，前提是非线性函数的部分衍生物的上限满足了某些代数不平等。还将证明，稳定的PD参数只能从二维有限的凸集中选择，这与现有的有关PD控制的不确定随机系统的文献是显着的差异。此外，引入了这些界限的特定多项式，该多项式可用于确定在哪个条件下，PD控制无法稳定系统，从而证明了PD控制的基本局限性。
In this article, we focus on the global stabilizability problem for a class of second order uncertain stochastic control systems, where both the drift term and the diffusion term are nonlinear functions of the state variables and the control variables. We will show that the widely applied proportional-derivative(PD) control in engineering practice has the ability to globally stabilize such systems in the mean square sense, provided that the upper bounds of the partial derivatives of the nonlinear functions satisfy a certain algebraic inequality. It will also be proved that the stabilizing PD parameters can only be selected from a two dimensional bounded convex set, which is a significant difference from the existing literature on PD controlled uncertain stochastic systems. Moreover, a particular polynomial on these bounds is introduced, which can be used to determine under what conditions the system is not stabilizable by the PD control, and thus demonstrating the fundamental limitations of PD control.
