论文标题
通过收缩分析和凸优化减少非线性观察者
Reduced-Order Nonlinear Observers via Contraction Analysis and Convex Optimization
论文作者
论文摘要
在本文中，我们提出了一种新的方法，通过收缩分析和凸优化设计非线性控制系统的全球收敛降低观察者。尽管收缩是一种自然适合国家估计的概念，但现有的解决方案在应用于物理系统时是局部或相对保守的。为了解决这个问题，我们表明此问题可以转化为离线搜索，以进行坐标转换，然后动态（横向）收缩。获得的足够条件包括一些易于验证的差分不平等，一方面，这些不平等现象确定了一类非常一般的“可检测”非线性系统，另一方面，可以表示为计算有效的凸优化，从而使设计过程更加系统性。本文还阐明了与一些公认的方法和概念的联系。最后，我们用几个数值和物理示例说明了所提出的方法，包括多项式，机械，机电和生化系统。
In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable for state estimation, the existing solutions are either local or relatively conservative when applying to physical systems. To address this, we show that this problem can be translated into an off-line search for a coordinate transformation after which the dynamics is (transversely) contracting. The obtained sufficient condition consists of some easily verifiable differential inequalities, which, on one hand, identify a very general class of "detectable" nonlinear systems, and on the other hand, can be expressed as computationally efficient convex optimization, making the design procedure more systematic. Connections with some well-established approaches and concepts are also clarified in the paper. Finally, we illustrate the proposed method with several numerical and physical examples, including polynomial, mechanical, electromechanical and biochemical systems.
