Synchronous Optimization Schemes for Dynamic Systems Through the Kernel-Based Nonlinear Observer Canonical Form

Although some dynamic behaviors are commonly modeled as the linear or bilinear systems, recent studies have consistently noted the existence of significant nonlinearities in these behaviors. Here, this work attempts to devise effective models and optimization approaches to represent and analyze the nonlinear phenomena ground on the online measured data. A kernel-based nonlinear observer canonical form is put forward by exploiting the fitting superiorities of kernel functions, which comprises the classical linear and bilinear state-space models as the special cases. The utilization of polynomial properties reduces the difficulty of identification while preserving the capacity of state-space models to fit nonlinear characteristics. Aiming to fulfilling simultaneous state and parameter estimation, a nonlinear state observer-based separable hierarchical forgetting gradient (NSO-SHFG) algorithm is devised in accordance with the extended Kalman filtering and the decomposition technique. The convergence analysis is established to verify the theoretical results, and the feasibility of the NSO-SHFG algorithm is validated by simulations.