Almost Finite-Time Observers for a Family of Nonlinear Continuous-Time Systems
Almost Finite-Time Observers for a Family of Nonlinear Continuous-Time Systems
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一族非线性连续时间系统的几乎有限时间观测器
DOI：
10.1109/lcsys.2022.3172366
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发表时间：
2022
影响因子：
3
通讯作者：
Malisoff, Michael
中科院分区：
文献类型：
--
作者：
Mazenc, Frederic;Malisoff, Michael
针对一类非线性系统，提出了一种新的观测器设计方法，该方法不要求系统在不可测状态下是仿射的。在线性输出测量下，观测器确保观测误差指数收敛到零。指数收敛的速度收敛到无穷大，因为动态的非线性状态依赖部分的增长率收敛到零，所以我们称观测器几乎有限时间。在全局Lipschitz条件下的状态依赖部分的动态，我们的全局结果确保收敛的观察员，所有的初始状态。对于非线性的情况下，在原点是两个顺序，我们提供本地的结果，确保指数收敛的观测误差为零，当初始状态是足够小的。我们将结果应用到一个模型的摩擦摆，并与Lotka-Volterra非线性动力学。
We provide a new class of observers for a class of nonlinear systems which are not required to be affine in the unmeasured states. The observers ensure exponential convergence of the observation errors to zero, under linear output measurements. The rate of exponential convergence converges to infinity, as the growth rate of the nonlinear state-dependent part of the dynamics converges to zero, so we call the observers almost finite-time. Under global Lipschitz conditions on the state-dependent part of the dynamics, our global result ensures convergence of the observers, for all initial states. For cases where the nonlinearity is of order two at the origin, we provide local results ensuring exponential convergence of the observation errors to zero, when the initial state is small enough. We apply the results to a model of a pendulum with friction, and to dynamics with Lotka-Volterra nonlinearities.