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.