A Hybrid Gradient Algorithm for Linear Regression with Hybrid Signals
A Hybrid Gradient Algorithm for Linear Regression with Hybrid Signals
复制标题
混合信号线性回归的混合梯度算法
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
R. Sanfelice
中科院分区：
文献类型：
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作者：
Adnane Saoud;M. Maghenem;R. Sanfelice
针对一类包含未知参数的线性输入/输出关系，提出了一种混合梯度下降算法来估计输入和输出为混合信号时的未知参数。这些信号可以在正常时间内连续变化（或流动），也可以在孤立的时间实例中离散变化（或跳跃）。为了估计未知参数，我们开发了一种梯度下降算法，该算法在流动期间连续更新估计，并在跳跃时即时更新估计。本文提出的混合梯度算法在连续时间和离散时间条件下对现有梯度下降算法进行了推广。在众所周知的持续激励条件的松弛（混合）版本下，提出的混合梯度下降算法以指数级速度估计参数。给出了一个说明性的例子，显示了我们的方法的能力，而经典算法不能保证收敛。
Given a linear input/output relationship involving unknown parameters, we propose a hybrid gradient descent algorithm to estimate the unknown parameters when the inputs and the outputs are hybrid signals. These signals are allowed to change continuously during ordinary time - or flow - and to change discretely - or jump - at isolated time instances. To estimate the unknown parameters, we develop a gradient descent algorithm that updates the estimates continuously during flows and instantaneously at jumps. The proposed hybrid gradient algorithm generalizes the existing gradient descent algorithms in the continuous-time and the discrete-time settings. Under a relaxed (hybrid) version of the well-known persistence of excitation condition, the proposed hybrid gradient descent algorithm estimates the parameters exponentially fast. An illustrative example is presented, showing the capabilities of our approach while classical algorithms fails to ensure the convergence.