A Kalman filter approach to model-error control synthesis
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A new advancement in the model-error control synthesis approach, a robust control scheme for nonlinear systems, is presented. The traditional model-error control synthesis approach utilizes an optimal real-time estimator known as the nonlinear predictive filter to determine model error corrections to the control input using the one-step ahead technique. The nonlinear predictive filter requires full state knowledge to determine the model error, but the available information from measurements, i.e. sensor outputs, usually does not contain full state information and is most often corrupted by noise. Even after implementing an extended Kalman filter in the feedback loop, the existence of noise in the feedback loop results in poor model error determination by the predictive filter. This in turn results in a noisy control input and degradation of closed-loop system performance. This thesis introduces two new techniques by which the model-error control synthesis approach can be implemented on a nonlinear system. The first method utilizes two separate extended Kalman filters. Among the two filters, one is strictly used for noise filtration/state estimation and the other is used for model error prediction. The second scheme exploits a single extended Kalman filter for the simultaneous estimation of the system states and the model error. The simulation results indicate that the new model-error control synthesis approaches are extremely effective in providing closed-loop robustness in the presence of noisy measurement signal. Finally, a sensitivity of the controlled closed-loop system stability with respect to the process noise covariance is presented.