Zaher Ashraf A
Physics Department, Science College, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait.
Chaos. 2008 Jun;18(2):023114. doi: 10.1063/1.2907737.
A simple technique is introduced to build fast state observers for chaotic systems when only a scalar time series of the output is available. This technique relies on using a backstepping-like approach via introducing new virtual states that can be observed using the drive-response synchronization mechanism. The proposed dynamic structure of the virtual states allows for employing control parameters that can adjust the convergence rate of the observed states. In addition, these control parameters can be used to improve the transient performance of the response system to accommodate small and large variations of the initial conditions, thus achieving superior performance to conventional synchronization techniques. Simple Lyapunov functions are used to estimate the range of the control parameters that guarantees stable operation of the proposed technique. Three benchmark chaotic systems are considered for illustration; namely, the Lorenz, Chua, and Rossler systems. The conflict between stability and agility of the states observer is analyzed and a simple tuning mechanism is introduced. Implementation of the proposed technique in both analog and digital forms is also addressed and experimental results are reported ensuring feasibility and real-time applicability. Finally, advantages and limitations are discussed and a comparison with conventional synchronization methods is investigated.
本文介绍了一种简单的技术，用于在仅可获得输出的标量时间序列时为混沌系统构建快速状态观测器。该技术依赖于通过引入新的虚拟状态，采用类似反步法的方法，这些虚拟状态可利用驱动-响应同步机制进行观测。所提出的虚拟状态动态结构允许采用能够调整观测状态收敛速率的控制参数。此外，这些控制参数可用于改善响应系统的瞬态性能，以适应初始条件的小变化和大变化，从而实现优于传统同步技术的性能。使用简单的李雅普诺夫函数来估计保证所提技术稳定运行的控制参数范围。为进行说明，考虑了三个基准混沌系统，即洛伦兹系统、蔡氏系统和罗斯勒系统。分析了状态观测器稳定性与敏捷性之间的冲突，并引入了一种简单的调谐机制。还讨论了所提技术的模拟和数字形式实现，并报告了实验结果，确保了可行性和实时适用性。最后，讨论了优点和局限性，并与传统同步方法进行了比较。
