Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements

Copyright @ 2012 ElsevierIn this paper, the extended Kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon. Both deterministic and stochastic nonlinearities are included in the system model, where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances. The phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval [0,1]. Such a probability distribution is allowed to be any commonly used distribution over the interval [0,1] with known conditional probability. The aim of the addressed filtering problem is to design a filter such that, in the presence of both the stochastic nonlinearities and multiple missing measurements, there exists an upper bound for the filtering error covariance. Subsequently, such an upper bound is minimized by properly designing the filter gain at each sampling instant. It is shown that the desired filter can be obtained in terms of the solutions to two Riccati-like difference equations that are of a form suitable for recursive computation in online applications. An illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme.This work was supported in part by the National 973 Project under Grant 2009CB320600, National Natural Science Foundation of China under Grants 61028008, 61134009 and 60825303, 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. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

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

Decentralized H

For large-scale systems which are modeled as interconnection of N networked control systems with uncertain missing measurements probabilities, a decentralized state feedback H∞ controller design is considered in this paper. The occurrence of missing measurements is assumed to be a Bernoulli random binary switching sequence with an unknown conditional probability distribution in an interval. A state feedback H∞ controller is designed in terms of linear matrix inequalities to make closed-loop system exponentially mean square stable and a prescribed H∞ performance is guaranteed. Sufficient conditions are derived for the existence of such controller. A numerical example is also provided to demonstrate the validity of the proposed design approach

Impulsive Vaccination SEIR Model with Nonlinear Incidence Rate and Time Delay

This paper aims to discuss the delay epidemic model with vertical transmission, constant input, and nonlinear incidence. Some sufficient conditions are given to guarantee the existence and global attractiveness of the infection-free periodic solution and the uniform persistence of the addressed model with time delay. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results

New Stability Criterion for Discrete-Time Genetic Regulatory Networks with Time-Varying Delays and Stochastic Disturbances

We propose an improved stability condition for a class of discrete-time genetic regulatory networks (GRNs) with interval time-varying delays and stochastic disturbances. By choosing an augmented novel Lyapunov-Krasovskii functional which contains some triple summation terms, a less conservative sufficient condition is obtained in terms of linear matrix inequalities (LMIs) by using the combination of the lower bound lemma, the discrete-time Jensen inequality, and the free-weighting matrix method. It is shown that the proposed results can be readily solved by using the Matlab software. Finally, two numerical examples are provided to illustrate the effectiveness and advantages of the theoretical results

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

Seeking the Important Nodes of Complex Networks in Product R&D Team Based on Fuzzy AHP and TOPSIS

How to seek the important nodes of complex networks in product research and development (R&D) team is particularly important for companies engaged in creativity and innovation. The previous literature mainly uses several single indicators to assess the node importance; this paper proposes a multiple attribute decision making model to tentatively solve these problems. Firstly, choose eight indicators as the evaluation criteria, four from centralization of complex networks: degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality and four from structural holes of complex networks: effective size, efficiency, constraint, and hierarchy. Then, use fuzzy analytic hierarchy process (AHP) to obtain the weights of these indicators and use technique for order preference by similarity to an ideal solution (TOPSIS) to assess the importance degree of each node of complex networks. Finally, taking a product R&D team of a game software company as a research example, test the effectiveness, operability, and efficiency of the method we established

Seeking the Important Nodes of Complex Networks in Product R&D Team Based on Fuzzy AHP and TOPSIS

How to seek the important nodes of complex networks in product research and development (R&D) team is particularly important for companies engaged in creativity and innovation. The previous literature mainly uses several single indicators to assess the node importance; this paper proposes a multiple attribute decision making model to tentatively solve these problems. Firstly, choose eight indicators as the evaluation criteria, four from centralization of complex networks: degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality and four from structural holes of complex networks: effective size, efficiency, constraint, and hierarchy. Then, use fuzzy analytic hierarchy process (AHP) to obtain the weights of these indicators and use technique for order preference by similarity to an ideal solution (TOPSIS) to assess the importance degree of each node of complex networks. Finally, taking a product R&D team of a game software company as a research example, test the effectiveness, operability, and efficiency of the method we established

Robust ∞ Filtering for a Class of Complex Networks with Stochastic Packet Dropouts and Time Delays

The robust ∞ filtering problem is investigated for a class of complex network systems which has stochastic packet dropouts and time delays, combined with disturbance inputs. The packet dropout phenomenon occurs in a random way and the occurrence probability for each measurement output node is governed by an individual random variable. Besides, the time delay phenomenon is assumed to occur in a nonlinear vector-valued function. We aim to design a filter such that the estimation error converges to zero exponentially in the mean square, while the disturbance rejection attenuation is constrained to a given level by means of the ∞ performance index. By constructing the proper Lyapunov-Krasovskii functional, we acquire sufficient conditions to guarantee the stability of the state detection observer for the discrete systems, and the observer gain is also derived by solving linear matrix inequalities. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method

Deconvolution Filtering for Nonlinear Stochastic Systems with Randomly Occurring Sensor Delays via Probability-Dependent Method

This paper deals with a robust H∞ deconvolution filtering problem for discrete-time nonlinear stochastic systems with randomly occurring sensor delays. The delayed measurements are assumed to occur in a random way characterized by a random variable sequence following the Bernoulli distribution with time-varying probability. The purpose is to design an H∞ deconvolution filter such that, for all the admissible randomly occurring sensor delays, nonlinear disturbances, and external noises, the input signal distorted by the transmission channel could be recovered to a specified extent. By utilizing the constructed Lyapunov functional relying on the time-varying probability parameters, the desired sufficient criteria are derived. The proposed H∞ deconvolution filter parameters include not only the fixed gains obtained by solving a convex optimization problem but also the online measurable time-varying probability. When the time-varying sensor delays occur randomly with a time-varying probability sequence, the proposed gain-scheduled filtering algorithm is very effective. The obtained design algorithm is finally verified in the light of simulation examples