Unconstrained Parameterization of Stable LPV Input-Output Models: with Application to System Identification
CoRR(2024)
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.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要