Model reconstruction-based joint estimation method and convergence analysis for nonlinear dynamic networks with time-delays

Establishing a suitable model of the studied nonlinear dynamic system is the basis and prerequisite for system analysis and design. Radial basis functions have the characteristics of simple form and flexible node configuration, which make it possible to form network models to fit complex nonlinear properties. Unlike most radial basis function network model estimation techniques assumed known time-delay, this paper concentrates on the combined parameter and time-delay estimation for this type of network models. To deal with the unknown time-delay, some additional variables are incorporated to formulate an extended identification framework grounded in redundant rule. Building upon this framework, a rolling window hierarchical gradient recursive sub-algorithm is derived to compute the parameter estimates using the recombined observation technique, and a threshold strategy is presented to filter out the redundant parameter estimates when determining the time-delay. Subsequently, a joint parameter and time-delay estimation algorithm is proposed to identify nonlinear dynamic networks with time-delays. The convergence property of the algorithm is analyzed, and its performance is validated through two case studies.