Adaptive parameter estimation for a general dynamical system with unknown states

103

Joint estimation of states and time-varying parameters of linear stochastic systems is of practical importance for fault diagnosis and fault tolerant control. The known fact is that measurements have outliers. They can significantly degrade the properties of linearly recursive algorithms, which are designed to work in presence of Gaussian noises. This article proposes two kinds of strategies for joint parameter-state robust estimation of linear stochastic models in presence of all possible faults and non-Gaussian noises. In the form of Theorem, joint robust algorithm for systems with sensor and component faults, as well as the algorithm for systems with parameter faults are proposed. Because of their good features in robust filtering, Masreliez-Martin filter represents a cornerstone for realization of the proposed robust algorithms for joint state-parameter estimation. The good features of proposed robust estimation algorithms, in relation to algorithms based on other widely-used filters, are illustrated by simulation results. On the other side, intensive research in the field of mathematical modeling of pneumatic servo drives has shown that their mathematical models are nonlinear in which a lot of important details cannot be included in the model. Also, it has been well known that the nonlinear model can be approximated by a linear model with time-varying parameters. Due to the abovementioned reasons, it can be assumed that the pneumatic cylinder model is a linear stochastic model with variable parameters. The good practical values of the proposed robust joint algorithm to identification of the pneumatic cylinder are illustrated by experimental results.

“…Bearing in mind block structure (24), estimates of a priori and a posteriori extended state vectors in algorithm (23) are given by the following relations:…”

Section: Lemma 1 Letmentioning

confidence: 99%

“…Matrix elements of a posteriori covariance matrix P(k|k) has the form (27). Bearing in mind block structure (24), estimates of a priori and a posteriori extended state vectors in algorithm (34) are given by the following relations:…”

Section: Joint Estimation Algorithm For Systems With Parameter Faultsmentioning

confidence: 99%

State and parameter joint estimation of linear stochastic systems in presence of faults and non‐Gaussian noises

Stojanović

Zhang

2020

103

“…35,36 In this article, we adopt the state observer to estimate system states, which is simpler in structure but can also achieve good performance. According to the considered bilinear state space model, the following bilinear state observer is designed to generate the states: [37][38][39] x t+1 = Ax t + Bx t u t + gu t .…”

Section: The State Estimation Algorithmmentioning

confidence: 99%

“…Then, we can obtain the estimates of system parameters, noise variance, and transition probability from Equations (30)-(32), (33)- (34), and (36)- (37), respectively.…”

Section: Vb M-stepmentioning

confidence: 99%

Variational Bayesian identification for bilinear state space models with Markov‐switching time delays

Fei

Xiong

et al. 2020

This article studies the parameter identification problem for bilinear state space models with time-varying time delays. Considering the correlation of time delays, the Markov chain switching mechanism is adopted to model the delay sequence. Based on the observer canonical form, the bilinear state space model is transformed into a regressive form. A bilinear state observer is designed to estimate the state variables. Under the variational Bayesian scheme, the system parameters, discrete delays, and the Markov transition probabilities are identified by using the measurement data. A numerical example and a continuous stirred tank reactor simulation are employed to validate the effectiveness of the proposed algorithm.

“…11 System identification and parameter estimation are widely used to establish mathematical models of dynamical systems 12,13 and are basic for adaptive control and fault diagnosis, 14 and so on. In the field of system identification, much attention has been focused on various identification algorithms, including the least squares (LS) methods, 15 the Kalman filter, 16,17 and the subspace identification. 18 The LS methods are suitable for linear parameter system identification and can also deal with the identification problems for the nonlinear ExpAR model under certain special conditions.…”

Section: Introductionmentioning

confidence: 99%

Two‐stage recursive identification algorithms for a class of nonlinear time series models with colored noise

Ding

Gan

et al. 2020

Self Cite

This article concentrates on the recursive identification algorithms for the exponential autoregressive model with moving average noise. Using the decomposition technique, we transform the original identification model into a linear and nonlinear subidentification model and derive a two-stage least squares (LS) extended stochastic gradient (ESG) algorithm. In order to improve the parameter estimation accuracy, we employ the multi-innovation identification theory and develop a two-stage LS multi-innovation ESG algorithm. A simulation example is provided to test the effectiveness of the proposed algorithms.