Nonlinear state predictor for a class of nonlinear time-delay systems

Abstract

A nonlinear state predictor (NSP) for a class of nonlinear systems with input time delay is proposed. Similar to the extended Kalman filter, the idea of the NSP is first to calculate the future state predictors via the system model, then to adjust the predictors based on the predictive errors between current observations and their corresponding predictors. We first present a state predictive algorithm for a class of pseudo linear systems and then extend it to a class of nonlinear time delay systems. After the detailed NSP algorithm is presented, it is proved that the NSP is locally asymptotically convergent for a class of nonlinear deterministic systems if some sufficient conditions are satisfied. In the presence of measurement noise, it is further proved that the proposed NSP is extended exponentially bounded under certain conditions. Finally, computer simulations with two different nonlinear examples illustrate that the proposed NSP can effectively and accurately predict the future states for a class of nonlinear time-delay systems, no matter whether the state variables change quickly or slowly.