Sampling-Based Stability Evaluation with Second-Order Margins for Unknown Systems with Gaussian Processes
Yuji Ito, Kenji Fujimoto, Yukihiro Tadokoro · 2019
This paper proposes a method of guaranteeing stability of unknown systems that are identified by Gaussian process (GP) regressions. Stability conditions of the GPs, which are inequalities for an infinite number of states in the state space, are relaxed as inequalities for a finite number of sampled states. This relaxation invokes margins in the inequalities, degrading the accuracy when evaluating the stability. This paper derives novel margins whose sizes are second-order to the intervals between the sampled states. By shortening the intervals, the second-order margins become small compared to first-order margins given by existing approaches.