Error Bounds for Kernel-Based Linear System Identification with Unknown Hyperparameters

Applying regularization in reproducing kernel Hilbert spaces has been successful linear system identification using stable designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from posterior covariance, which are useful robust and stochastic control. However, require knowledge of true hyperparameters design. They can be inaccurate with estimated lightly damped systems or presence high noise. In this work, we provide reliable quantification estimation when unknown. The obtained by first constructing high-probability set marginal likelihood function. Then worst-case covariance is found within set. proposed bound proven to contain model probability its validity demonstrated numerical simulation.