面向LPV-SS模型最大似然估计的高效方法
Towards Efficient Maximum Likelihood Estimation of LPV-SS Models
AI总结：
本文提出了一种结合最新LPV输入输出识别方法和LPV-IO到LPV状态空间实现方案以及最大似然细化步骤的模块化LPV-SS识别方法，通过相关分析或贝叶斯脉冲响应估计估计底层系统的马尔可夫系数序列，然后使用基减霍尔曼方法进行LPV-SS实现，并通过梯度或期望最大化优化方法从最大似然角度细化LPV-SS模型估计，通过蒙特卡洛研究验证了该方法的有效性。
摘要：
如何高效地识别具有调度变量的线性参数变化（LPV）离散时间状态空间（SS）模型的多输入多输出（MIMO）模型仍是一个开放性问题，因为文献中提出的识别方法严重受到维度灾难的影响，或者依赖于对测量信号行为的过度限制的近似。然而，获得目标系统的SS模型对于许多LPV控制合成方法至关重要，因为这些合成工具几乎全部针对上述系统动态表示进行公式化。因此，在本文中，我们通过结合最新LPV输入输出（IO）识别方法与LPV-IO到LPV-SS实现方案以及最大似然细化步骤来解决该问题。所得到的模块化LPV-SS识别方法在统计效率方面具有优势，同时计算负载相对较低。该方法包含以下三个步骤：1）使用相关分析或贝叶斯脉冲响应估计估计底层系统的马尔可夫系数序列，然后2）使用基减霍尔曼方法对估计的系数进行LPV-SS实现，3）通过梯度或期望最大化优化方法从最大似然角度细化LPV-SS模型估计。通过蒙特卡洛研究验证了完整识别方案的有效性，其中所提出的方 法与现有识别MIMO LPV系统的方案进行了比较。
英文摘要：
How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification methods proposed in the literature suffer heavily from the curse of dimensionality and/or depend on over-restrictive approximations of the measured signal behaviors. However, obtaining an SS model of the targeted system is crucial for many LPV control synthesis methods, as these synthesis tools are almost exclusively formulated for the aforementioned representation of the system dynamics. Therefore, in this paper, we tackle the problem by combining state-of-the-art LPV input-output (IO) identification methods with an LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step. The resulting modular LPV-SS identification approach achieves statical efficiency with a relatively low computational load. The method contains the following three steps: 1) estimation of the Markov coefficient sequence of the underlying system using correlation analysis or Bayesian impulse response estimation, then 2) LPV-SS realization of the estimated coefficients by using a basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate from a maximum-likelihood point of view by a gradient-based or an expectation-maximization optimization methodology. The effectiveness of the full identification scheme is demonstrated by a Monte Carlo study where our proposed method is compared to existing schemes for identifying a MIMO LPV system.
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