Optimal Parameter Estimation for Long-Term Prediction in the Presence of Model Mismatch

For nonlinear multi-input multi-output (MIMO) systems such as multilink robotic manipulators, finding a correct, physically derived model structure is almost impossible, so that significant model mismatch is nearly inevitable. Moreover, in the presence of model mismatch, the use of least-squares minimization of the one-step-ahead prediction error (residual error) to estimate unknown parameters in a given model structure often leads to model predictions that are extremely inaccurate beyond a short time interval. In this paper, we develop a method for optimal parameter estimation for accurate long-term prediction models in the presence of significant model mismatch in practice. For many practical cases, where a correct model and the correct number of degrees of freedom for a given model structure are unknown, we combine the use of long-term prediction error with frequency-based regularization to produce more accurate long-term prediction models for actual MIMO nonlinear systems.