Physics informed trajectory inference of a class of nonlinear systems using a closed-loop output error technique

Trajectory inference is a hard problem when states measurements are noisy and if there is no high-fidelity model available for estimation; this may arise into high-variance and biased estimates results. This article proposes a physics informed trajectory inference of a class of nonlinear systems. The approach combines the advantages of state and parameter estimation algorithms to infer the trajectory that follows the nonlinear system using online noisy state measurements. The algorithm is composed of a parallel estimated model constructed in terms of a low-pass filter parameterization. The estimated model defines a physics informed model that infers the trajectory of the real nonlinear system with noise attenuation capabilities. The parameters of the estimated model are updated by a closed-loop output error identification algorithm which uses the estimated states instead of the noisy measurements to avoid biased estimation. Stability and convergence of the proposed technique is assessed using Lyapunov stability theory. Simulations studies are carried out under different scenarios to verify the effectiveness of the proposed inference algorithm.