Bernoulli Stochastic Variables Research Articles

Event-triggered networked H∞ control of discrete-time nonlinear singular systems

This paper is concerned with H∞ controller design for a class of discrete-time nonlinear singular system which is controlled over a communication network. The network-induced delay is considered, and its distribution characteristic is described by a Bernoulli stochastic variable. A novel event-triggered control scheme is proposed in order to save the limited network communication bandwidth. Based on the Lyapunov–Kravoskii stability theory, a delay-distribution-dependent criterion is derived which guarantees the closed-loop networked discrete-time nonlinear singular system is regular, causal, and stable with a certain H∞ performance index. A co-design method for the H∞ controller and the event-triggered scheme is presented by using the singular value decomposition technology. An numerical example is given to illustrate the effectiveness of the proposed method.

$$H_{\infty }$$ H ∞ filter design for delayed static neural networks with Markovian switching and randomly occurred nonlinearity

The paper is concerned with the problem of $$H_{\infty }$$ filter design for delayed static neural networks with Markovian switching and randomly occurred nonlinearity. The random phenomenon is described in terms of a Bernoulli stochastic variable. Based on the reciprocally convex approach, a lower bound lemma is proposed to handle the double- and triple-integral terms in the time derivative of the Lyapunov function. Finally, the optimal performance index is obtained via solving linear matrix inequalities(LMIs). The result is not only less conservative but the time derivative of the time delay can be greater than one. Numerical examples with simulation results are provided to illustrate the effectiveness of the developed results.

Exponential H ∞ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities

This paper is concerned with the exponential $H_{\infty}$ filtering problem for a class of discrete-time switched neural networks with random time-varying delays based on the sojourn-probability-dependent method. Using the average dwell time approach together with the piecewise Lyapunov function technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with random time-varying delays which are characterized by introducing a Bernoulli stochastic variable. Based on the derived $H_\infty$ performance analysis results, the $H_\infty$ filter design is formulated in terms of Linear Matrix Inequalities (LMIs). Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed design procedure.

Consensus Analysis of Second-Order Multi-Agent Networks With Sampled Data and Packet Losses

In this paper, we address the consensus problem of second-order multi-agent system with sampled-data and packet losses. A Bernoulli stochastic variable is used to characterize the random packet losses in second-order multi-agent system with sampled-data information, in which packet losses are modeled in a successive way. Based on the matrix exponential and stochastic analysis techniques, several sufficient conditions are given to ensure the almost surely synchronization of second-order multi-agent networks with sampled-data and packet losses, where the graph among the agents is a directed network containing a directed spanning tree. Additionally, we further investigate the almost surely consensus for such system containing time-delays and packed dropouts. On this occasion, the communication graph among the agents is represented by an undirected connected graph. Furthermore, it is found that the probability of packet losses and the modulus of eigenvalues of the Laplace matrix play a vital role in achieving almost surely consensus. In the end, the developed results are applied to the coordination of multiple vehicles. Two examples are provided to illustrate the effectiveness of our results.

Random adaptive control for cluster synchronization of complex networks with distinct communities

SummaryIn this paper, we investigate the cluster synchronization for complex networks with time‐varying delayed couplings, stochastic disturbance, and non‐identical nodes in different clusters. Based on randomly occurring controllers, some Bernoulli stochastic variables are introduced to describe the controllers, then, a fraction of nodes in clusters, which have direct connections to the other clusters, is controlled, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the mean square cluster synchronization pattern for all initial values by means of Lyapunov stability theory, It differential formula, and LMI approach. Besides, by designing the randomly occurring adaptive update law, some suitable control gains are obtained. Finally, numerical simulations are also given to demonstrate the effectiveness and validity of the main result. Copyright © 2015 John Wiley & Sons, Ltd.

Pinning distributed synchronization of stochastic dynamical networks: a mixed optimization approach.

This paper is concerned with the problem of pinning synchronization of nonlinear dynamical networks with multiple stochastic disturbances. Two kinds of pinning schemes are considered: 1) pinned nodes are fixed along the time evolution and 2) pinned nodes are switched from time to time according to a set of Bernoulli stochastic variables. Using Lyapunov function methods and stochastic analysis techniques, several easily verifiable criteria are derived for the problem of pinning distributed synchronization. For the case of fixed pinned nodes, a novel mixed optimization method is developed to select the pinned nodes and find feasible solutions, which is composed of a traditional convex optimization method and a constraint optimization evolutionary algorithm. For the case of switching pinning scheme, upper bounds of the convergence rate and the mean control gain are obtained theoretically. Simulation examples are provided to show the advantages of our proposed optimization method over previous ones and verify the effectiveness of the obtained results.

Exponential H∞ filtering for discrete-time switched neural networks with random delays.

This paper addresses the exponential H∞ filtering problem for a class of discrete-time switched neural networks with random time-varying delays. The involved delays are assumed to be randomly time-varying which are characterized by introducing a Bernoulli stochastic variable. Effects of both variation range and distribution probability of the time delays are considered. The nonlinear activation functions are assumed to satisfy the sector conditions. Our aim is to estimate the state by designing a full order filter such that the filter error system is globally exponentially stable with an expected decay rate and a H∞ performance attenuation level. The filter is designed by using a piecewise Lyapunov-Krasovskii functional together with linear matrix inequality (LMI) approach and average dwell time method. First, a set of sufficient LMI conditions are established to guarantee the exponential mean-square stability of the augmented system and then the parameters of full-order filter are expressed in terms of solutions to a set of LMI conditions. The proposed LMI conditions can be easily solved by using standard software packages. Finally, numerical examples by means of practical problems are provided to illustrate the effectiveness of the proposed filter design.

Robust Stability Criterion for Discrete‐Time Nonlinear Switched Systems with Randomly Occurring Delays via T–S Fuzzy Approach

This article investigates exponential stability of uncertain discrete‐time nonlinear switched systems with parameter uncertainties and randomly occurring delays via Takagi–Sugeno fuzzy approach. The randomness of time‐varying delay is characterized by introducing a Bernoulli stochastic variable that follows certain probability distribution. By adopting the average dwell‐time approach with Lyapunov–Krasovskii functional and using convex reciprocal lemma, delay‐dependent sufficient conditions for exponential stability of the switched fuzzy system are derived in terms of linear matrix inequalities (LMIs), which can be solved readily using any LMI solvers. Finally, illustrative examples are provided to demonstrate the effectiveness of the proposed approach. © 2014 Wiley Periodicals, Inc. Complexity 20: 49–61, 2015

Delay-probability-distribution-dependent stability criteria for discrete-time stochastic neural networks with random delays

The problem of delay-probability-distribution-dependent robust stability for a class of discrete-time stochastic neural networks (DSNNs) with delayed and parameter uncertainties is investigated. The information of the probability distribution of the delay is considered and transformed into parameter matrices of the transferred DSSN model. In the DSSN model, the time-varying delay is characterized by introducing a Bernoulli stochastic variable. By constructing an augmented Lyapunov-Krasovskii functional and introducing some analysis techniques, some novel delay-distribution-dependent mean square stability conditions for the DSSN, which are to be robustly globally exponentially stable, are derived. Finally, a numerical example is provided to demonstrate less conservatism and effectiveness of the proposed methods.

Cluster synchronization in directed networks of non-identical systems with noises via random pinning control

This paper is concerned with the issue of mean square cluster synchronization in directed networks, which consist of non-identical nodes infected by communication noises. The pinning control method is employed in designing controllers for guaranteeing cluster synchronization, meanwhile, all the controllers are supposed to occur with different probabilities by introducing the Bernoulli stochastic variables. Based on the Lyapunov stability theory and the stochastic theory, the sufficient synchronization conditions are derived and proved theoretically, which are mainly for the controllers to be designed and the noise intensities. Finally, some numerical examples are presented to demonstrate the effectiveness of the results.

Distributed synchronization of coupled neural networks via randomly occurring control.

In this paper, we study the distributed synchronization and pinning distributed synchronization of stochastic coupled neural networks via randomly occurring control. Two Bernoulli stochastic variables are used to describe the occurrences of distributed adaptive control and updating law according to certain probabilities. Both distributed adaptive control and updating law for each vertex in a network depend on state information on each vertex's neighborhood. By constructing appropriate Lyapunov functions and employing stochastic analysis techniques, we prove that the distributed synchronization and the distributed pinning synchronization of stochastic complex networks can be achieved in mean square. Additionally, randomly occurring distributed control is compared with periodically intermittent control. It is revealed that, although randomly occurring control is an intermediate method among the three types of control in terms of control costs and convergence rates, it has fewer restrictions to implement and can be more easily applied in practice than periodically intermittent control.

Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings

In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to Bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of Bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the Bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.

Fault detection for a class of networked nonlinear systems subject to imperfect measurements

This paper addresses the problem of fault detection (FD) for discrete-time networked systems with global Lipschitz conditions and imperfect measurements. By using Bernoulli stochastic variables and a switching signal, a unified model is proposed to describe four kinds of imperfect measurements, that is, access constraints, time delays, packet dropouts, and signal quantization. We aim to design a fault detection filter (FDF) such that, for all external disturbances and imperfect measurements, the error between the residual and fault is made as small as possible. The addressed FD problem is then converted into an auxiliary H ∞ filtering problem for discrete-time stochastic switched systems with multiple time-varying delays. By applying Lyapunov-Krasovskii approach, a sufficient condition for the existence of the FDF is derived in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired FDF can also be characterized. A numerical example is exploited to show the effectiveness of the results obtained.

Estimation for Stochastic Nonlinear Systems with Randomly Distributed Time‐Varying Delays and Missing Measurements

The estimation problem is investigated for a class of stochastic nonlinear systems with distributed time‐varying delays and missing measurements. The considered distributed time‐varying delays, stochastic nonlinearities, and missing measurements are modeled in random ways governed by Bernoulli stochastic variables. The discussed nonlinearities are expressed by the statistical means. By using the linear matrix inequality method, a sufficient condition is established to guarantee the mean‐square stability of the estimation error, and then the estimator parameters are characterized by the solution to a set of LMIs. Finally, a simulation example is exploited to show the effectiveness of the proposed design procedures.

Global Synchronization Stability for Stochastic Complex Dynamical Networks with Probabilistic Interval Time-Varying Delays

The synchronization problem for a class of complex dynamical networks with stochastic disturbances and probabilistic interval time-varying delays is investigated. Based on the stochastic analysis techniques and properties of the Kronecker product, some delay-dependent asymptotical synchronization stability criteria are derived in the form of linear matrix inequalities (LMIs). The solvability of derived conditions depends not only on the size of the delay, but also on the probability of Bernoulli stochastic variables. A numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

Fault detection for a class of discrete-time nonlinear systems subject to network-induced uncertainties

This paper addresses the problem of fault detection (FD) for discrete-time systems with global Lipschitz conditions and network-induced uncertainties. By utilizing Bernoulli stochastic variables and a switching signal, a unified measurement model is proposed to describe three kinds of network-induced uncertainties, that is, access constraints, time delays, and packet dropouts. We aim to design a mode-dependent fault detection filter (FDF) such that, for all external disturbances and the above uncertainties, the error between the residual and fault is made as small as possible. The addressed FD problem is then converted into an auxiliary H∞ filtering problem for discrete-time stochastic system with multiple time-varying delays. By applying the Lyapunov-Krasovskii approach, a sufficient condition for the existence of the FDF is derived in terms of certain linear matrix inequalities (LMI). When these LMIs are feasible, the explicit expression of the desired FDF can also be characterized. A numerical example is exploited to show the effectiveness of the results obtained. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Delay-Probability-Distribution-Dependent Stability Analysis for Stochastic Neural Networks with Mixed Time-Varying Delays: The Discrete-Time Case

The problem of delay-probability-distribution-dependent stability analysis for a class of discrete-time stochastic delayed neural networks (DSNNs) with mixed time delays is investigated. Here the mixed time delays are assumed to be discrete and distributed time delays and the uncertainties are assumed to be time varying norm bounded parameter uncertainties. The information of the probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred DSNN model, in which the time-varying delay is characterized by introducing a Bernoulli stochastic variable. By constructing a new augmented Lyapunov-Krasovskii functional and introducing some new analysis techniques, a novel delay-probability-distribution-dependent stable criterion for the DSNN to be stable in the mean square sense are derived. These criteria are formulated in the forms of linear matrix inequalities.

Synchronization of Discrete‐Time Stochastic Neural Networks with Random Delay

By using a Lyapunov‐Krasovskii functional method and the stochastic analysis technique, we investigate the problem of synchronization for discrete‐time stochastic neural networks (DSNNs) with random delays. A control law is designed, and sufficient conditions are established that guarantee the synchronization of two identical DSNNs with random delays. Compared with the previous works, the time delay is assumed to be existent in a random fashion. The stochastic disturbances are described in terms of a Brownian motion and the time‐varying delay is characterized by introducing a Bernoulli stochastic variable. Two examples are given to illustrate the effectiveness of the proposed results. The main contribution of this paper is that the obtained results are dependent on not only the bound but also the distribution probability of the time delay. Moreover, our results provide a larger allowance variation range of the delay, and are less conservative than the traditional delay‐independent ones.

Controller design for synchronization of an array of delayed neural networks using a controllable probabilistic PSO

In this paper, a controllable probabilistic particle swarm optimization (CPPSO) algorithm is introduced based on Bernoulli stochastic variables and a competitive penalized method. The CPPSO algorithm is proposed to solve optimization problems and is then applied to design the memoryless feedback controller, which is used in the synchronization of an array of delayed neural networks (DNNs). The learning strategies occur in a random way governed by Bernoulli stochastic variables. The expectations of Bernoulli stochastic variables are automatically updated by the search environment. The proposed method not only keeps the diversity of the swarm, but also maintains the rapid convergence of the CPPSO algorithm according to the competitive penalized mechanism. In addition, the convergence rate is improved because the inertia weight of each particle is automatically computed according to the feedback of fitness value. The efficiency of the proposed CPPSO algorithm is demonstrated by comparing it with some well-known PSO algorithms on benchmark test functions with and without rotations. In the end, the proposed CPPSO algorithm is used to design the controller for the synchronization of an array of continuous-time delayed neural networks.

Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay

This paper is concerned with the state estimation problem for a class of discrete-time stochastic neural networks (DSNNs) with random delays. The effect of both variation range and distribution probability of the time delay are taken into account in the proposed approach. The stochastic disturbances are described in terms of a Brownian motion and the time-varying delay is characterized by introducing a Bernoulli stochastic variable. By employing a Lyapunov-Krasovskii functional, sufficient delay-distribution-dependent conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimator which can be checked readily by the Matlab toolbox. The main feature of the results obtained in this paper is that they are dependent on not only the bound but also the distribution probability of the time delay, and we obtain a larger allowance variation range of the delay, hence our results are less conservative than the traditional delay-independent ones. One example is given to illustrate the effectiveness of the proposed result.