Combined state and parameter estimation for Hammerstein systems with time delay using the Kalman filtering

Abstract

SUMMARYThis paper discusses the state and parameter estimation problem for a class of Hammerstein state space systems with time-delay. Both the process noise and the measurement noise are considered in the system. Based on the observable canonical state space form and the key term separation, a pseudo-linear regressive identification model is obtained. For the unknown states in the information vector, the Kalman filter is used to search for the optimal state estimates. A Kalman-filter based least squares iterative and a recursive least squares algorithms are proposed. Extending the information vector to include the latest information terms which are missed for the time-delay, the Kalman-filter based recursive extended least squares algorithm is derived to obtain the estimates of the unknown time-delay, parameters and states. The numerical simulation results are given to illustrate the effectiveness of the proposed algorithms.

Model‐based vs data‐driven adaptive control: An overview

“…To conclude this section about fully model‐based adaptation, we can cite other recent works, ie, post the latest general survey paper, which can be classified under the model‐based paradigm: for nonlinear models,) for models with time delay,) with parameter‐independent realization controllers, with input/output quantization,) under state constraints,) under inputs and actuator‐bandwidth constraints,) for Markovian jump systems,) for switched systems,) for partial differential equation (PDE)–based models,) for nonminimum/minimum‐phase systems,) to achieve adaptive regulation and disturbance rejection,) multiple‐model and switching adaptive control,) linear quadratic regulator (LQR)–based adaptive control, model predictive control–based adaptive control,) applications of model‐based adaptive control,) for sensor/actuator fault mitigation,) for rapidly time‐varying uncertainties, nonquadratic Lyapunov function–based MRAC, for stochastic systems,) retrospective cost adaptive control, persistent excitation–free/data accumulation–based control or concurrent adaptive control, sliding mode–based adaptive control,) set‐theoretic–based adaptive controller with performance guarantees, sampled data systems, and robust adaptive control …”

“…For systems with time delays affecting the control input, recent works have focused on constant time delays (see, eg, the works of Ma et al, Nguyen et al, and Hussain et al); however, the case of time‐varying time delays is a challenging problem, which is important in many applications, eg, control over networks with time‐varying communication delays of a group of moving robots.…”

Tracking of power quality disturbances using sparse model–based extended Kalman filters

“…Extended Kalman filter is evolved from the Kalman filter 22 through generation of extended matrices, namely, measurement matrix and state transition matrix used for nonlinear systems. The state estimation process is accomplished through state prediction and state filtering steps.…”

“…The EKF algorithm is based on measurement equation and state equation, which can be expressed as given in Equation (22) and Equation (23), respectively,̂k…”

Biased compensation recursive least squares-based threshold algorithm for time-delay rational models via redundant rule

“…Both the VB and the CS recovery algorithms are off-line algorithms. In order to estimate the time-delay systems based on on-line algorithms, Ma et al provided a Kalman filter-based least squares iterative and a recursive least squares algorithms for timedelay Hammerstein systems with the assumption that the time-delay is known in prior [25]. Chen et al proposed a recursive least squares based redundant parameter method for time-delay systems, in which the time-delay is unknown [26].…”