论文标题
随时间变化的非线性系统可观察性和可控性的等级条件
Rank Conditions for Observability and Controllability for Time-varying Nonlinear Systems
论文作者
论文摘要
本文提供了可观察性等级条件的扩展，并将可控性等级条件扩展到时变非线性系统。以前的条件检查状态可观察性和可控性，仅考虑不明确取决于时间的非线性系统，或者对于时间变化的系统，它们仅考虑线性案例。在本文中，提供了一般的分析条件。本文表明，这两个新条件（扩展可观察性等级条件和扩展可控性等级条件）将可观察性和可控性的众所周知的排名条件降低到两种更简单的时间变化的线性系统和时间变化的非线性系统中。提出的新条件会自动工作，并且可以处理任何系统，而与其复杂性（状态维度，非线性类型等）无关。简单的例子说明了这两个条件。此外，这两个新条件用于研究月球模块的可观察性和可控性能。对于该系统，由于重量的变化和惯性矩的变化，动力学表现出明显的时间依赖性。这些变化是燃料消耗的结果。为了研究该系统的可观察性和可控性能，需要扩展可观察性等级条件和本文引入的扩展可控性等级条件。该论文表明，即使在主火箭发动机赋予恒定功率的限制下，该状态也是弱局部可控的。另外，它在偏航角上较弱地可局部可观察到。
This paper provides the extension of the observability rank condition and the extension of the controllability rank condition to time-varying nonlinear systems. Previous conditions to check the state observability and controllability, only account for nonlinear systems that do not explicitly depend on time, or, for time-varying systems, they only account for the linear case. In this paper, the general analytic conditions are provided. The paper shows that both these two new conditions (the extended observability rank condition and the extended controllability rank condition) reduce to the well known rank conditions for observability and controllability in the two simpler cases of time-varying linear systems and time-invariant nonlinear systems. The proposed new conditions work automatically and can deal with any system, independently of its complexity (state dimension, type of nonlinearity, etc). Simple examples illustrate both these conditions. In addition, the two new conditions are used to study the observability and the controllability properties of a lunar module. For this system, the dynamics exhibit an explicit time-dependence due to the variation of the weight and the variation of the moment of inertia. These variations are a consequence of the fuel consumption. To study the observability and the controllability properties of this system, the extended observability rank condition and the extended controllability rank condition introduced by this paper are required. The paper shows that, even under the constraint that the main rocket engine delivers constant power, the state is weakly locally controllable. Additionally, it is weakly locally observable up to the yaw angle.
