ABSTRACT

In this paper we provide two significant extensions to the recently developed parameter estimation-based observer design technique for state-affine systems. First, we consider the case when the full state of the system is reconstructed in spite of the presence of unknown, time-varying parameters entering into the system dynamics. Second, we address the problem of reduced order observers with finite convergence time. For the first problem, we propose a simple gradient-based adaptive observer that converges asymptotically under the assumption of generalised persistent excitation. For the reduced order observer we invoke the advanced dynamic regressor extension and mixing parameter estimator technique to show that we can achieve finite convergence time under the weak interval excitation assumption. Simulation results that illustrate the performance of the proposed adaptive observers are given. This include, an unobservable system, an example reported in the literature and the widely popular, and difficult to control, single-ended primary inductor converter.

摘要

在本文中，我们为最近开发的用于状态仿射系统的基于参数估计的观测器设计技术提供了两个重要的扩展。首先，我们考虑尽管存在未知的时变参数进入系统动力学，但仍重建系统的完整状态的情况。其次，我们解决了收敛时间有限的降阶观察者的问题。对于第一个问题，我们提出了一个简单的基于梯度的自适应观测器，它在广义假设下渐近收敛持续的兴奋。对于降阶观测器，我们调用了先进的动态回归器扩展和混合参数估计器技术来表明我们可以在弱区间激励假设下实现有限收敛时间。给出了说明所提出的自适应观测器性能的仿真结果。这包括不可观察的系统、文献中报道的示例以及广泛流行且难以控制的单端初级电感转换器。