A novel on-line observer/Kalman filter identification method and its application to input-constrained active fault-tolerant tracker design for unknown stochastic systems

In this paper, a novel on-line observer/Kalman filter identification (OKID) method is presented for real-time control of unknown stochastic systems, and this on-line OKID method is applied for the design of a novel input-constrained active fault-tolerant tracker. The proposed on-line OKID method overcomes the discontinuity of the parameters identified in real-time, induced by the singular value decomposition (SVD) which is supposed to be carried out at each sampling instant if it is performed by the direct extension of the off-line OKID method to the on-line manner; as a consequence, real-time control can be implemented. Besides skipping the SVD at each sampling instant, the proposed on-line OKID method directly realizes the identified parameters in the observer-canonical form, without involving the conversion of the identified model in general coordinates into the observer-canonical form at each sampling instant; this speeds up the identification process. In addition, a systematic mechanism for tuning the weighting matrix ^Qc is proposed, to overcome the significant tracking error induced by drastic variations of the reference signals, inappropriate initialization or parameter variations caused by some system faults. As a result, the input-constrained problem under various system faults can also be solved by the approach. Illustrative examples demonstrate the effectiveness of the proposed approach.