It is a challenging problem to estimate time-varying time delay and parameters, especially for systems subject to disturbances with unknown statistics in measurements. The desirable filter should be sensitive to unmodeled dynamics caused by random changes in time delay and parameters, and also be robust to disturbances. Recently, we proposed a finite-horizon robust Kalman filter (RKF) through designing and simultaneously minimizing the upper bounds of unknown covariances of prediction errors, filtering residuals and estimation errors. Unfortunately, unmodeled dynamics and disturbances must be hypothesized to be zero-mean white noises in the RKF. To cope with more general unmodeled dynamics and/or disturbances, a class of jump Markov stochastic systems (JMSS) subject to unmodeled dynamics and disturbances is considered in this article so that a priori system information, such as the value range of unknown and/or randomly changing parameters, can be introduced. Through combining the RKF with the interacting multiple model (IMM) estimation technique, a RKF/IMM algorithm is proposed for such JMSS. Then it is applied to estimate timevarying time delay and parameters of a continuous stirred tank reactor (CSTR) with sensors subject to Gaussian disturbances with unknown means and/or covariances. The RKF/IMM algorithm is compared with the extended Kalman filter (EKF), the strong tracking filter (STF) and the RKF through computer simulations. The results show that, in the case that measurement disturbances are zero-mean noise with unknown covariances, the RKF/IMM and RKF achieve almost the same accurate estimates, which are superior to those of the STF and EKF; in the case that such disturbances have unknown covariances and time-varying means, only the RKF/IMM remains the ability to estimate time-varying time delay and parameters. Furthermore the RKF/IMM has unique ability to identify the disturbance mean no matter whether it is constant or time-varying. Moreover, the RKF/IMM algorithm is shown having strong robustness against the a priori filter parameters, this may be attractive in practical applications.

In this paper, a robust fault detection and identification approach based on an adaptive observer is developed for uncertain continuous linear time-invariant systems with multiple discrete time-delays in both states and outputs. State and output faults of bias type that may evolve slowly or abruptly are considered, and the delay system is disturbed by unstructured bounded unknown inputs. Based on the scheme of [Trunov, A. B., & Polycarpou, M. M. (2000). Automated fault diagnosis in nonlinear multivariable systems using a learning methodology. IEEE Transactions on Neural Networks, 11, 91–101], a novel adaptive observer for detecting and estimating faults in the considered system is constructed, and robustness with respect to unknown inputs and sensitivity to faults of the detecting scheme are rigorously analyzed. The fault estimate and the state estimation error are then proved to be uniformly bounded. Finally, simulations of a heating process demonstrate that the proposed approach can detect the faults shortly after the occurrences without any false alarm and can approximate the faults with desired accuracy.

An asynchronous data fusion problem based on a kind of multirate multisensor dynamic system is studied. The system is observed by multirate sensors independently, with the state model known at the finest scale. Under the assumption that the sampling rates of sensors decrease successively by any positive integers, the discrete dynamic system models are established based on each single sensor and an asynchronous multirate multisensor state fusion estimation algorithm is presented. Theoretically, the estimate is proven to be unbiased and the optimal in the sense of linear minimum covariance, the fused estimate is better than the Kalman filtering results based on each single sensor, and the accuracy of the fused estimate will decrease if any of the sensors' information is neglected. The feasibility and effectiveness of the algorithm are shown through simulations.

Nonlinear state prediction is of crucial importance to design controllers for nonlinear processes with input time delay. In this paper, the extended nonlinear state predictor (ENSP) we proposed is first outlined, which is used to predict the future states of a class of nonlinear processes with input time delay. A new concept of strong tracking predictor (STP) is then proposed, and an rthogonality principle is given as a criterion to design the STP. On the basis of the orthogonality principle, the ENSP is modified, which results in a STP. After the detailed STP algorithm is presented, we prove that the STP is locally asymptotically convergent for a class of nonlinear deterministic processes if some sufficient conditions are satisfied. In the presence of measurement noise, it is further proved that the proposed STP is exponentially bounded under certain conditions. Finally, computer simulations with a MIMO nonlinear model are presented, which illustrate that the proposed STP can predict accurately the future states of a class of nonlinear time delay processes no matter whether the states change suddenly or slowly, in addition, it has definite robustness against model/plant mismatches.

Combining the repetitive learning strategy and the optimality principle, this Letter proposes a time-delayed method to control chaotic maps. This method can effectively stabilize unstable periodic orbits within chaotic attractors in the sense of least mean square. Numerical simulations of some chaotic maps verify the effectiveness of this method.