实时混合系统辨识与在线确定性退火
Real-time Hybrid System Identification with Online Deterministic Annealing
AI总结：
本文提出一种基于双时间尺度随机逼近的实时辨识方法，通过在线确定性退火逐步估计切换信号与模式数量，适用于分段仿射及一般切换系统，兼顾计算效率与性能-复杂度权衡，仿真验证有效。
摘要：
我们提出了一种针对离散时间状态依赖切换系统的实时辨识方法，该方法适用于输入-输出域和状态空间域。具体而言，我们设计了一个以两个时间尺度运行的自适应算法系统；一个随机逼近算法在慢时间尺度上实现在线确定性退火方案，并估计模式切换信号，而一个递归辨识算法在较快时间尺度上运行，并基于切换信号的估计更新局部模型的参数。我们首先关注分段仿射系统，并基于双时间尺度随机逼近理论讨论可辨识性条件和收敛性质。与标准的切换系统辨识算法相比，所提出的方法逐步估计模式数量，适用于使用顺序数据采集的实时系统辨识。该算法的渐进性提高了计算效率，并对性能-复杂度权衡提供了实时控制。最后，我们解决了将所提方法应用于更一般切换系统辨识时出现的具体挑战。仿真结果验证了所提方法的有效性。
英文摘要：
We introduce a real-time identification method for discrete-time state-dependent switching systems in both the input--output and state-space domains. In particular, we design a system of adaptive algorithms running in two timescales; a stochastic approximation algorithm implements an online deterministic annealing scheme at a slow timescale and estimates the mode-switching signal, and an recursive identification algorithm runs at a faster timescale and updates the parameters of the local models based on the estimate of the switching signal. We first focus on piece-wise affine systems and discuss identifiability conditions and convergence properties based on the theory of two-timescale stochastic approximation. In contrast to standard identification algorithms for switched systems, the proposed approach gradually estimates the number of modes and is appropriate for real-time system identification using sequential data acquisition. The progressive nature of the algorithm improves computational efficiency and provides real-time control over the performance-complexity trade-off. Finally, we address specific challenges that arise in the application of the proposed methodology in identification of more general switching systems. Simulation results validate the efficacy of the proposed methodology.
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