Controllability Gramian of Nonlinear Gaussian Process State Space Models with Application to Model Sparsification ?

摘要

For linear control systems, the so-called controllability Gramian has played an important role to quantify how effectively the dynamical states can be driven to a target one by a suitable driving input. On the other hand, thanks to the availability of Big Data, the Gaussian process state space model, a data-driven probabilistic modeling framework, has attracted much attention in recent years. In this paper, we newly introduce the concept of the controllability Gramian for nonlinear dynamics represented by the Gaussian process state space model, aiming at better understanding of this new modeling framework. Then, its effective calculation method and application to model sparsification are investigated.