Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey

Copyright © 2013 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey

The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out

Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays

This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2013 IEEE.This paper is concerned with the gain-constrained recursive filtering problem for a class of time-varying nonlinear stochastic systems with probabilistic sensor delays and correlated noises. The stochastic nonlinearities are described by statistical means that cover the multiplicative stochastic disturbances as a special case. The phenomenon of probabilistic sensor delays is modeled by introducing a diagonal matrix composed of Bernoulli distributed random variables taking values of 1 or 0, which means that the sensors may experience randomly occurring delays with individual delay characteristics. The process noise is finite-step autocorrelated. The purpose of the addressed gain-constrained filtering problem is to design a filter such that, for all probabilistic sensor delays, stochastic nonlinearities, gain constraint as well as correlated noises, the cost function concerning the filtering error is minimized at each sampling instant, where the filter gain satisfies a certain equality constraint. A new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the pre-specified filter gain constraint. A simulation example is provided to illustrate the effectiveness of the proposed filter design approach.This work was supported in part by the National Natural Science Foundation of China by Grants 61273156, 61028008, 60825303, 61104125, and 11271103, National 973 Project by Grant 2009CB320600, the Fok Ying Tung Education Fund by Grant 111064, the Special Fund for the Author of National Excellent Doctoral Dissertation of China by Grant 2007B4, the State Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. by Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Variance-constrained state estimation for networked multi-rate systems with measurement quantization and probabilistic sensor failures

This paper is concerned with the variance-constrained state estimation problem for a class of networked multi-rate systems (NMSs) with network-induced probabilistic sensor failures and measurement quantization. The stochastic characteristics of the sensor failures are governed by mutually independent random variables over the interval [0,1]. By applying the lifting technique, an augmented system model is established to facilitate the state estimation of the underlying NMSs. With the aid of the stochastic analysis approach, sufficient conditions are derived under which the exponential mean-square stability of the augmented system is guaranteed, the prescribed H∞ performance constraint is achieved, and the individual variance constraint on the steady-state estimation error is satisfied. Based on the derived conditions, the addressed variance-constrained state estimation problem of NMSs is recast as a convex optimization one that can be solved via the semi-definite program method. Furthermore, the explicit expression of the desired estimator gains is obtained by means of the feasibility of certain matrix inequalities. Two additional optimization problems are considered with respect to the H∞ performance index and the weighted error variances. Finally, a simulation example is utilized to illustrate the effectiveness of the proposed state estimation method

An open-loop approach to calculate noise-induced transitions

Bistability permits the co-existence of two distinct cell fates in a population of genetically identical cells. Noise induced transitions between two fates of a bistable system are difficult to calculate due to the intricate interplay between nonlinear dynamics and noise in bistable positive feedback loops. Here we opened multivariable feedback loops at the slowest variable to obtain the open-loop function and the fluctuations in the open-loop output. By the subsequent reclosing of the loop, we calculated the mean first passage time (MFPT) using the Fokker-Planck equation in good agreement with the exact stochastic simulation. When an external component interacts with a feedback component, it amplifies the extrinsic noise in the loop. Consequently, the open-loop function is shifted and the transition rates between the two states in the closed loop are increased. Despite this shift, the open-loop output reflects the system faithfully to predict the MFPT in the feedback loop. Therefore, the open-loop approach can help theoretical analysis. Furthermore, the measurement of the mean value, variance, and the reaction time-scale of the open-loop output permits the prediction of MFPT simply from experimental data, which underscores the practical value of the stochastic open-loop approach

Estimation, filtering and fusion for networked systems with network-induced phenomena: New progress and prospects

In this paper, some recent advances on the estimation, filtering and fusion for networked systems are reviewed. Firstly, the network-induced phenomena under consideration are briefly recalled including missing/fading measurements, signal quantization, sensor saturations, communication delays, and randomly occurring incomplete information. Secondly, the developments of the estimation, filtering and fusion for networked systems from four aspects (linear networked systems, nonlinear networked systems, complex networks and sensor networks) are reviewed comprehensively. Subsequently, some recent results on the estimation, filtering and fusion for systems with the network-induced phenomena are reviewed in great detail. In particular, some latest results on the multi-objective filtering problems for time-varying nonlinear networked systems are summarized. Finally, conclusions are given and several possible research directions concerning the estimation, filtering, and fusion for networked systems are highlighted

A Robust Recursive Filter for Nonlinear Systems with Correlated Noises, Packet Losses, and Multiplicative Noises

A robust filtering problem is formulated and investigated for a class of nonlinear systems with correlated noises, packet losses, and multiplicative noises. The packet losses are assumed to be independent Bernoulli random variables. The multiplicative noises are described as random variables with bounded variance. Different from the traditional robust filter based on the assumption that the process noises are uncorrelated with the measurement noises, the objective of the addressed robust filtering problem is to design a recursive filter such that, for packet losses and multiplicative noises, the state prediction and filtering covariance matrices have the optimized upper bounds in the case that there are correlated process and measurement noises. Two examples are used to illustrate the effectiveness of the proposed filter

Performance analysis with network-enhanced complexities: On fading measurements, event-triggered mechanisms, and cyber attacks

Copyright © 2014 Derui Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Nowadays, the real-world systems are usually subject to various complexities such as parameter uncertainties, time-delays, and nonlinear disturbances. For networked systems, especially large-scale systems such as multiagent systems and systems over sensor networks, the complexities are inevitably enhanced in terms of their degrees or intensities because of the usage of the communication networks. Therefore, it would be interesting to (1) examine how this kind of network-enhanced complexities affects the control or filtering performance; and (2) develop some suitable approaches for controller/filter design problems. In this paper, we aim to survey some recent advances on the performance analysis and synthesis with three sorts of fashionable network-enhanced complexities, namely, fading measurements, event-triggered mechanisms, and attack behaviors of adversaries. First, these three kinds of complexities are introduced in detail according to their engineering backgrounds, dynamical characteristic, and modelling techniques. Then, the developments of the performance analysis and synthesis issues for various networked systems are systematically reviewed. Furthermore, some challenges are illustrated by using a thorough literature review and some possible future research directions are highlighted.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 61203139, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Adaptive Quantizers for Estimation

In this paper, adaptive estimation based on noisy quantized observations is studied. A low complexity adaptive algorithm using a quantizer with adjustable input gain and offset is presented. Three possible scalar models for the parameter to be estimated are considered: constant, Wiener process and Wiener process with deterministic drift. After showing that the algorithm is asymptotically unbiased for estimating a constant, it is shown, in the three cases, that the asymptotic mean squared error depends on the Fisher information for the quantized measurements. It is also shown that the loss of performance due to quantization depends approximately on the ratio of the Fisher information for quantized and continuous measurements. At the end of the paper the theoretical results are validated through simulation under two different classes of noise, generalized Gaussian noise and Student's-t noise