Mean square stability for Kalman filtering with Markovian packet losses

You, Keyou; Fu, Minyue; Xie, Lihua

doi:10.1016/j.automatica.2011.09.015

Cited by 211 publications

(171 citation statements)

References 23 publications

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“…It can be seen from [1,24] that among the topics on optimal estimation and control for the system with packet loss, there are some closely related fundamental issues: the stability of the estimator [25,26], the distribution and convergence of the estimation error covariance [27,28], the estimation performance evaluation [29,30], and the stability of the closed-loop system [14,31]. These four issues have been fully investigated for TCP-like systems, but they are seldom studied for SS-UDP systems.…”

Section: A Background and Motivationsmentioning

confidence: 99%

“…Its stability was studied in the pioneering work [25] where it is pointed out that there exists a critical value which determines the boundedness of the expected estimation error covariance (EEC), i.e., E[P k ]. Following [25], various aspects have been further researched, including the bound for the critical value [32], the distribution for EEC [27,28], the Markov packet losses case [26,[33][34][35]. In [29,30], the authors pointed out that P({P k ≤ M }) is a better evaluation for the estimation performance than the quantity E[P k ], and then obtained the lower and upper bounds for P({P k ≤ M }).…”

Section: B Related Work and Contributionsmentioning

confidence: 99%

“…As P k is a random quantity, the stability of the estimator is usually examined by the boundedness of E[P k ], as in [22,25,26].…”

Section: B Problems Formulationmentioning

confidence: 99%

“…For the SS-UDP system, the feedback gain L k can be computed offline by (25a)(25b) (26), butx k and P k in (7) and (8) depend on u k−1 . Thus, the separation principle still does not hold.…”

Section: Remarkmentioning

confidence: 99%

See 3 more Smart Citations

Optimal Estimation and Control for Lossy Network: Stability, Convergence, and Performance

Lin

Shi

et al. 2017

IEEE Trans. Automat. Contr.

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Abstract-In this paper, we study the problems of optimal estimation and control, i.e., the linear quadratic Gaussian (LQG) control, for systems with packet losses but without acknowledgment. Such acknowledgment is a signal sent by the actuator to inform the estimator of the incidence of control packet losses. For such system, which is usually called as a User Datagram Protocol (UDP)-like system, the optimal estimation is nonlinear and its calculation is time-consuming, making its corresponding optimal LQG problem complicated. We first propose two conditions: 1) the sensor has some computation abilities; and 2) the control command, exerted to the plant, is known to the sensor. For a UDP-like system satisfying these two conditions, we derive the optimal estimation. By constructing the finite and infinite product probability measure spaces for the estimation error covariances (EEC), we give the stability condition for the expected EEC, and show the existence of a measurable function to which the EEC converges in distribution, and propose some practical methods to evaluate the estimation performance. Finally, the LQG controllers are derived, and the conditions for the mean square stability of the closed-loop system are established.

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Section: A Background and Motivationsmentioning

confidence: 99%

Section: B Related Work and Contributionsmentioning

confidence: 99%

“…As P k is a random quantity, the stability of the estimator is usually examined by the boundedness of E[P k ], as in [22,25,26].…”

Section: B Problems Formulationmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

See 2 more Smart Citations

Optimal Estimation and Control for Lossy Network: Stability, Convergence, and Performance

Lin

Shi

et al. 2017

IEEE Trans. Automat. Contr.

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“…Stability analysis of Kalman filter for networked systems with random packet losses has been provided in, to name just a few, [77][78][79][80][81]. It is shown in [77] that there exists a critical value of observation arrival probability under which the expected error covariance is likely to grow unbounded.…”

Section: Treatments Of Network-induced Phenomenamentioning

confidence: 99%

Particle filtering with applications in networked systems: a survey

Wang

Yuan

2016

Complex Intell. Syst.

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The particle filtering algorithm was introduced in the 1990s as a numerical solution to the Bayesian estimation problem for nonlinear and non-Gaussian systems and has been successfully applied in various fields including physics, economics, engineering, etc. As is widely recognized, the particle filter has broad application prospects in networked systems, but network-induced phenomena and limited computing resources have led to new challenges to the design and implementation of particle filtering algorithms. In this survey paper, we aim to review the particle filtering method and its applications in networked systems. We first provide an overview of the particle filtering methods as well as networked systems, and then investigate the recent progress inThe work of W. Li, Y. Yuan and L.

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Hybrid‐triggered scheme asynchronous control for hidden Markov jump systems with partially unknown probabilities and cyber attacks

Guo

2022

Asian Journal of Control

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This paper is concerned with the issue of hybrid‐triggered scheme H∞ asynchronous control for networked Markov jump systems (MJSs) with probabilistic cyber attacks. First, in view of the subsistent phenomenon that the controller cannot capture the system modes synchronously, the hidden Markov model (HMM) with partly unknown probabilities is introduced in this article to describe such asynchronous phenomenon. In addition, the hybrid‐triggered scheme includes time‐triggered scheme and event‐triggered scheme, in which the switching signal between two schemes obeys random Bernoulli distribution. By utilizing Lyapunov stability theory and matrix inequality technique, some sufficient conditions are developed, which can guarantee the networked MJSs mean‐square asymptotically stable (MSAS) and H∞ performance; also, the desired controller gains are obtained by singular value decomposition (SVD) methods. Moreover, as the special cases of the results above, three corollaries are given. Finally, a numerical example and a pulse width‐modulation‐driven boost converter (PWMDBC) model are provided to demonstrate the usefulness and reliability of our developed approaches.

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Mean square stability for Kalman filtering with Markovian packet losses

Cited by 211 publications

References 23 publications

Optimal Estimation and Control for Lossy Network: Stability, Convergence, and Performance

Optimal Estimation and Control for Lossy Network: Stability, Convergence, and Performance

Particle filtering with applications in networked systems: a survey

Hybrid‐triggered scheme asynchronous control for hidden Markov jump systems with partially unknown probabilities and cyber attacks

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