稳定LPV输入输出模型的无约束参数化：在系统辨识中的应用
Unconstrained Parameterization of Stable LPV Input-Output Models: with Application to System Identification
AI总结：
针对离散时间线性参数变化输入输出模型稳定性约束需数值验证的难题，提出基于Cayley变换的无约束参数化方法，可生成任意参数下的稳定模型，并在仿真示例中验证了其辨识有效性。
摘要：
确保通过系统辨识方法估计的离散时间（DT）线性参数变化（LPV）输入输出（IO）模型的稳定性是一个具有挑战性的问题，因为已知的稳定性约束只能通过数值方式验证，例如通过求解线性矩阵不等式。本文提出了一种无约束的DT-LPV-IO参数化方法，该方法对任意模型参数选择都能生成稳定的模型。为实现这一点，本文证明了所有二次稳定的DT-LPV-IO模型都可以通过约束在单位球内的变换系数函数的映射生成，即满足小增益条件。随后通过Cayley变换对单位球进行重新参数化，得到了所有二次稳定DT-LPV-IO模型的无约束参数化形式。作为特例，还得到了所有稳定DT线性时不变传递函数的无约束参数化形式。在一个位置随变质量-阻尼-弹簧系统的仿真示例中，验证了采用神经网络系数函数的稳定DT-LPV-IO模型的辨识效果。
英文摘要：
Ensuring stability of discrete-time (DT) linear parameter-varying (LPV) input-output (IO) models estimated via system identification methods is a challenging problem as known stability constraints can only be numerically verified, e.g., through solving Linear Matrix Inequalities. In this paper, an unconstrained DT-LPV-IO parameterization is developed which gives a stable model for any choice of model parameters. To achieve this, it is shown that all quadratically stable DT-LPV-IO models can be generated by a mapping of transformed coefficient functions that are constrained to the unit ball, i.e., a small-gain condition. The unit ball is then reparameterized through a Cayley transformation, resulting in an unconstrained parameterization of all quadratically stable DT-LPV-IO models. As a special case, an unconstrained parameterization of all stable DT linear time-invariant transfer functions is obtained. Identification using the stable DT-LPV-IO model with neural network coefficient functions is demonstrated on a simulation example of a position-varying mass-damper-spring system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
