Low-order self-tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems

Based on the modified state-space self-tuning control (STC) via the observer/Kalman filter identification (OKID) method, an effective low-order tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems is proposed in this paper. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). Then, the above identified model in a general coordinate form is transformed to an observer form to provide a computationally effective initialization for a low-order on-line “auto-regressive moving average process with exogenous (ARMAX) model”-based identification. Furthermore, the proposed approach uses a modified Kalman filter estimate algorithm and the current-output-based observer to repair the drawback of the system multiple failures. Thus, the fault-tolerant control (FTC) performance can be significantly improved. As a result, a low-order state-space self-tuning control (STC) is constructed. Finally, the method is applied for a three-tank system with various faults to demonstrate the effectiveness of the proposed methodology.     

A least squares identification algorithm for a state space model with multi-state delays

A parameter estimator is presented for a state space model with time delay based on the given input–output data. The basic idea is to expand the state equations and to eliminate some state variables, and to substitute the state equation into the output equation to obtain the identification model which contains the information vector and parameter vector. A least squares algorithm is developed to estimate the system parameter vectors. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.     

Parameter and state estimation algorithm for single-input single-output linear systems using the canonical state space models

This paper presents a new parameter and state estimation algorithm for single-input single-output systems based on canonical state space models from the given input–output data. Difficulties of identification for state space models lie in that there exist unknown noise terms in the formation vector and unknown state variables. By means of the hierarchical identification principle, those noise terms in the information vector are replaced with the estimated residuals and a new least squares algorithm is proposed for parameter estimation and the system states are computed by using the estimated parameters. Finally, an example is provided.