论文标题
非线性随机系统的随机相对程度和路径控制
Stochastic Relative Degree and Path-wise Control of Nonlinear Stochastic Systems
论文作者
论文摘要
我们解决了一组非线性随机微分方程所描述的系统的路径控制。对于这类系统，我们引入了随机相对程度和坐标的变化概念，该坐标将动力学转化为随机正常形式。正常形式对设计线性的状态反馈控制的设计具有重要功能，该控制是线性的，并使动力学确定性。我们观察到，这种控制是理想主义的，即它在实际上是不可实现的，因为它采用了布朗运动的反馈（永远无法使用）来消除噪音。使用理想主义控制作为起点，我们引入了一个混合控制体系结构，该体系结构可实现\ emph {实用}路径控制。该混合控制器使用状态的测量值来定期为动态噪声贡献。我们证明，随着补偿期接近零，混合控制器在极限中检索了理想主义的表现。我们解决了渐近输出跟踪的问题，在理想主义和实际框架中解决了它。我们最终通过数值示例来验证理论。
We address the path-wise control of systems described by a set of nonlinear stochastic differential equations. For this class of systems, we introduce a notion of stochastic relative degree and a change of coordinates which transforms the dynamics to a stochastic normal form. The normal form is instrumental for the design of a state-feedback control which linearises and makes the dynamics deterministic. We observe that this control is idealistic, i.e. it is not practically implementable because it employs a feedback of the Brownian motion (which is never available) to cancel the noise. Using the idealistic control as a starting point, we introduce a hybrid control architecture which achieves \emph{practical} path-wise control. This hybrid controller uses measurements of the state to perform periodic compensations for the noise contribution to the dynamics. We prove that the hybrid controller retrieves the idealistic performances in the limit as the compensating period approaches zero. We address the problem of asymptotic output tracking, solving it in the idealistic and in the practical framework. We finally validate the theory by means of a numerical example.
