An adaptive disturbance accommodation approach for robust control and fault detection in uncertain stochastic systems
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The detailed formulation and analysis of a robust control scheme for multi-input multi-output uncertain stochastic systems known as the disturbance accommodating controller is presented. Instead of dealing with system uncertainties and external disturbances separately, the disturbance accommodating control scheme lumps the overall effects of these errors in a to-be-determined model-error vector, and then utilizes a Kalman filter in the feedback loop for simultaneously estimating the system states and the model-error vector from noisy measurements. The estimated states are then used to develop a nominal control law while the estimated model-error vector is used as a signal synthesis adaptive correction to the nominal control input to minimize the adverse effects of system uncertainties and the external disturbances. Since the model-error dynamics is unknown, the process noise covariance associated with the model-error dynamics is used to empirically tune the Kalman filter to yield accurate estimates. This dissertation presents a detailed stability analysis, which examines the explicit dependency of the controlled system's closed-loop performance on the assumed process noise covariance. Development of a robust adaptive disturbance accommodating controller for multi-input multi-output uncertain stochastic systems based on a stochastic adaptive scheme for selecting the appropriate process noise covariance that would guarantee closed-loop stability is presented. The presented approach concurrently tackles the problem of designing robust controllers and estimators for uncertain stochastic systems by indirectly adapting for the estimator gain though updating the estimator parameters such as the process noise covariance matrix in real-time. As presented here, the proposed adaptive disturbance accommodating control scheme can be easily extended to develop robust controllers for saturating systems by adapting for the controller gains along with the estimator parameters. In nonlinear stochastic systems, the proposed adaptive disturbance accommodating control scheme can be exploited for complexity mitigation as well as disturbance attenuation. Since the disturbance accommodating controller is extensively used for fault accommodation, robust fault detection and identification scheme based on the disturbance accommodating control theory is also presented. Though the results presented in this dissertation are supported by detailed mathematical proofs, several numerical simulations are also presented here to further validate the efficiency and applicability of the proposed approaches.