抽象线性系统观测中的动态补偿
Dynamics Compensation in Observation of Abstract Linear Systems
摘要：
本文是四篇系列论文的第二部分，主要针对抽象线性系统的传感器动态补偿问题。讨论了两个主要问题。第一个是关于系统观测中的传感器动态补偿，第二个是关于线性系统输出调节中的扰动动态补偿。这两个问题都可以用抽象级联系统的状态观测问题来描述。我们从同一个抽象的线性系统的观点来考虑这两个明显不同的问题。对抽象级联系统提出了一种新的观测器设计方案，并证明了观测误差的指数收敛性。结果表明，基于误差的观测器设计的输出调节问题可以转化为一个传感器的动态补偿问题的众所周知的调节器方程。因此，基于跟踪误差观测器的输出调节问题的设计，利用开发的方法。作为应用，我们对具有输出时滞的常微分方程和具有常微分方程传感器动力学的不稳定热方程进行了充分的研究，以验证理论结果。对不稳定热系统进行了数值模拟，直观地验证了所提方法的有效性。
英文摘要：
This is the second part of four series papers, aiming at the problem of sensor dynamics compensation for abstract linear systems. Two major issues are addressed. The first one is about the sensor dynamics compensation in system observation and the second one is on the disturbance dynamics compensation in output regulation for linear system. Both of them can be described by the problem of state observation for an abstract cascade system. We consider these two apparently different problems from the same abstract linear system point of view. A new scheme of the observer design for the abstract cascade system is developed and the exponential convergence of the observation error is established. It is shown that the error based observer design in the problem of output regulation can be converted into a sensor dynamics compensation problem by the well known regulator equations. As a result, a tracking error based observer for output regulation problem is designed by exploiting the developed method. As applications, the ordinary differential equations (ODEs) with output time-delay and an unstable heat equation with ODE sensor dynamics are fully investigated to validate the theoretical results. The numerical simulations for the unstable heat system are carried out to validate the proposed method visually.
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