论文标题
分半线性无限维系统的扩展基于Kalman滤波器的观察者设计
Extended Kalman filter based observer design for semilinear infinite-dimensional systems
论文作者
论文摘要
在许多物理应用中，系统的状态随空间变量和时间而变化。这种系统的状态是通过部分微分方程建模的，并在无限维空间上演变。由延迟差异方程建模的系统也是无限维系统。这些系统的完整状态无法衡量。观察者设计是从可用测量中估算状态的重要工具。对于线性系统（有限和无限维度），如果满足噪声的某些假设，则KALMAN滤波器对误差的最小变化提供了估计值。扩展的卡尔曼滤波器（EKF）是非线性有限维系统的一种扩展。在本文中，我们将EKF扩展到半线性无限二维系统。在温和的假设下，我们证明了定义EKF的方程式的适当性。显示了误差动力学的局部指数稳定性。仅假定可检测性，而不是可观察性，因此即使对于有限维系统，此结果也是新的。在一个示例中，通过实施无限维EKF的有限维近似值来说明结果。
In many physical applications, the system's state varies with spatial variables as well as time. The state of such systems is modelled by partial differential equations and evolves on an infinite-dimensional space. Systems modelled by delay-differential equations are also infinite-dimensional systems. The full state of these systems cannot be measured. Observer design is an important tool for estimating the state from available measurements. For linear systems, both finite- and infinite-dimensional, the Kalman filter provides an estimate with minimum-variance on the error, if certain assumptions on the noise are satisfied. The extended Kalman filter (EKF) is one type of extension to nonlinear finite-dimensional systems. In this paper we provide an extension of the EKF to semilinear infinite-dimensional systems. Under mild assumptions we prove the well-posedness of equations defining the EKF. Local exponential stability of the error dynamics is shown. Only detectability is assumed, not observability, so this result is new even for finite-dimensional systems. The results are illustrated with implementation of finite-dimensional approximations of the infinite-dimensional EKF on an example.
