| Many important practical processes (such as biological processes, chemical processes, etc.) feature both nonlinear and time delays. Existing nonlinear state estimation methods, including extended Kalman filter, are powerful only for non-time-delay system. In this research, a novel online state estimation method for nonlinear systems with a general time-delay structure was developed. The estimation method is derived from optimal control theory that minimizes measurement errors and state estimation errors. For convenience of derivation, we first consider a nonlinear system with time delays only in its states to derive a nonlinear state estimator. Then the results are extended to the case where time delays are also in inputs and outputs. The proposed method is applied to the tracking problem. The results show that the proposed method offer several advantages compared to other approaches. These include fast convergence, short computation time, and low energy needed for the controller. Simulations and experiments conducted on a bioreactor system showed that the proposed estimation method gave very accurate estimations of fluorescent proteins and cell concentrations over a wide rage of operating conditions. The proposed estimation method has proven to be effective for complex nonlinear systems with time delays. |
