Learning stable Gaussian process state space models

Data-driven nonparametric models gain importance as control systems are increasingly applied in domains where classical system identification is difficult, e.g., because of the system's complexity, sparse training data or its probabilistic nature. Gaussian process state space models (GP-SSM) are a data-driven approach which requires only high-level prior knowledge like smoothness characteristics. Prior known properties like stability are also often available but rarely exploited during modeling. The enforcement of stability using control Lyapunov functions allows to incorporate this prior knowledge, but requires a data-driven Lyapunov function search. Therefore, we propose the use of Sum of Squares to enforce convergence of GP-SSMs and compare the performance to other approaches on a real-world handwriting motion dataset.