Kernel Regression-Based State-Space Estimation of Continuous-Time Dynamic Systems From Noisy Sampled State Data

Despite various physical applications, state-space identification for continuous-time dynamic systems with noisy sampled data is less popular than discrete-time systems owing to unmeasurable state derivatives. Consequently, its scope is limited to linear or pre-parametrized systems. In this study, we formulate the identification as a (nonparametric) kernel regression problem applicable to nonlinear dynamic systems, which facilitates the joint assessment of the data fitness and fidelity of dynamics, that is, the error between the state derivative and the vector field. This is realized by employing "smooth" kernels, which facilitate the embedding of the state derivative into the reproducing kernel Hilbert space. To demonstrate the feasibility of the formulation, we extend the representer theorem, resulting in a finite dimensional albeit nonconvex minimization problem. To achieve fast linear estimation despite the nonconvexity, we propose a practical algorithm, called state-dynamics alternate descent, which is basically an unconstrained iterated quadratic programming. Furthermore, the proposed method was evaluated using the example of a simple nonlinear pendulum.