Synchronization of Complex Dynamical Networks Subject to Noisy Sampling Interval and Packet Loss

This article focuses on the sampled-data synchronization issue for a class of complex dynamical networks (CDNs) subject to noisy sampling intervals and successive packet losses. The sampling intervals are subject to noisy perturbations, and categorical distribution is used to characterize the sampling errors of noisy sampling intervals. By means of the input delay approach, the CDN under consideration is first converted into a delay system with delayed input subject to dual randomness and probability distribution characteristic. To verify the probability distribution characteristic of the delayed input, a novel characterization method is proposed, which is not the same as that of some existing literature. Based on this, a unified framework is then established. By recurring to the techniques of stochastic analysis, a probability-distribution-dependent controller is designed to guarantee the mean-square exponential synchronization of the error dynamical network. Subsequently, a special model is considered where only the lower and upper bounds of delayed input are utilized. Finally, to verify the analysis results and testify the effectiveness and superiority of the designed synchronization algorithm, a numerical example and an example using Chua's circuit are given.

T-S Fuzzy Model-Based Fault Detection for Continuous Stirring Tank Reactor

Continuous stirring tank reactors are widely used in the chemical production process, which is always accompanied by nonlinearity, time delay, and uncertainty. Considering the characteristic of the actual reaction of the continuous stirring tank reactors, the fault detection problem is studied in terms of the T-S fuzzy model. Through a fault detection filter performance analysis, the sufficient condition for the filtering error dynamics is obtained, which meets the exponential stability in the mean square sense and the given performance requirements. The design of the fault detection filter is transformed into one that settles the convex optimization issue of linear matrix inequality. Numerical analysis shows the effectiveness of this scheme.

Synchronization of Stochastic Complex Dynamical Networks Subject to Consecutive Packet Dropouts

This paper studies the modeling and synchronization problems for stochastic complex dynamical networks subject to consecutive packet dropouts. Different from some existing research results, both probability characteristic and upper bound of consecutive packet dropouts are involved in the proposed approach of controller design. First, an error dynamical network with stochastic and bounded delay is established by step-delay method, where the randomness of the bounded delay can be verified later by the probability theory method. A new modeling method is introduced to reflect the probability characteristic of consecutive packet dropouts. Based on the proposed model, some sufficient conditions are proposed under which the error dynamical network is globally exponentially synchronized in the mean square sense. Subsequently, a probability-distribution-dependent controller design procedure is then proposed. Finally, two numerical examples with simulations are provided to validate the analytical results and demonstrate the less conservatism of the proposed model method.

Reliable control for positive switched systems with random nonlinearities

This paper proposes a reliable control of positive switched systems with random nonlinearities which may induce the security problem of the systems. The random nonlinearities are governed by stochastic variables obeying the Bernoulli distribution. A switched linear copositive Lyapunov function is employed for the systems. Using a matrix decomposition approach, the gain matrix of controller is formulated by the sum of nonnegative and non-positive components. A reliable controller is designed for positive switched systems with actuator faults by virtue of linear programming. Under the designed reliable controller, the systems can resist some possible security risks triggered by random nonlinearities and actuator faults. The obtained approach is developed for systems subject to exogenous disturbances. Finally, two examples are provided to verify the validity of the obtained results.

Optimal Filtered and Smoothed Estimators for Discrete-Time Linear Systems With Multiple Packet Dropouts Under Markovian Communication Constraints

This paper concentrates on the linear least mean square (LLMS) filtered and smoothed estimators for networked linear stochastic systems. Multiple packet losses, Markovian communication constraints, and superposed process noise are considered simultaneously. In order to reduce the channel load during communication, at every step, just one transmission node is permitted to send data packets. Hence, a Markovian communication protocol is utilized to arrange the packets of these transmission nodes. Moreover, multiple data packet dropouts occur during transmission due to an imperfect communication channel. Therefore, the global observation information cannot be obtained by the state estimator. The real state of Markov chain is assumed to be unknown to the estimator except the transition probability matrix. By means of the innovation analysis approach and orthogonal projection principle, we design Kalman-like estimators in a recursive form. Finally, through simulation experiments, we verify the effectiveness and superiority of the designed algorithm.

Multi-packet transmission aero-engine DCS neural network sliding mode control based on multi-kernel LS-SVM packet dropout online compensation

In view of the strong nonlinear characteristics of the multi-packet transmission Aero-engine DCS with induced delay and random packet dropout, a neural network PID approach law sliding-mode controller using sliding window strategy and multi-kernel LS-SVM packet dropout online compensation is proposed. Firstly, the time-delay term in the system model is transformed equivalently, to establish the discrete system model of multi-packet transmission without time-delay; furthermore, the construction of multi-kernel function is transformed into kernel function coefficient optimization, and the optimization problem can be solved by the chaos adaptive artificial fish swarm algorithm, then the online predictive compensation will be made for data packet dropout of multi-packet transmission through the sliding window multi-kernel LS-SVM. After that, a sliding-mode controller design method of proportional integral differential approach law based on neural network is proposed. And online adjustment of PID approach law parameters can be achieved by nonlinear mapping of neural network. Finally, Truetime is used to simulate the method. The results shows that when the packet dropout rate is 30% and 60%, the average error of packet dropout prediction of multi-kernel LS-SVM reduces 29.21% and 44.66% compared with that of combined kernel LS-SVM, and the chattering amplitude of the proposed neural network PID approach law sliding-mode controller is decreased compared with other five approach law methods respectively. This controller can ensure a fast response speed, which shows that this method can achieve a better tracking control of the aeroengine network control system.

Finite-time dissipative filtering for uncertain discrete-time systems with state and disturbance-dependent noise over fading channels

This paper concerns with the finite-time exponential dissipative filtering problem for a class of discrete stochastic system subject to randomly occurring uncertainties and channel fadings. A modified Lth-order Rice fading model is presented to better characterize the multipath fading phenomena in real wireless communication environment. Our objective is to design a filter such that the filtering error system is finite-time stochastic bounded with a prespecified exponential dissipative performance. With the aid of the auxiliary function, a new set of sufficient conditions is derived for the existence of an acceptable filter which can degrade into the conditions for filtering with H_∞ performance. Then, the filter gains are obtained by solving these inequality sufficient conditions. Finally, an illustrative example is given to demonstrate the validity of the proposed approach.

Failure Identification of Dump Truck Suspension Based on an Average Correlation Stochastic Subspace Identification Algorithm

This paper proposes a fault identification method based on an improved stochastic subspace modal identification algorithm to achieve high-performance fault identification of dump truck suspension. The sensitivity of modal parameters to suspension faults is evaluated, and a fault diagnosis method based on modal energy difference is established. The feasibility of the proposed method is validated by numerical simulation and full-scale vehicle tests. The result shows that the proposed average correlation signal based stochastic subspace identification (ACS-SSI) method can identify the fluctuation of vehicle modal parameters effectively with respect to different spring stiffness and damping ratio conditions, and then fault identification of the suspension system can be realized by the variation of the modal energy difference (MED).

Adaptive Reliable $H_\infty $ Static Output Feedback Control Against Markovian Jumping Sensor Failures

This paper investigates the adaptive static output feedback (SOF) control problem for continuous-time linear systems with stochastic sensor failures. A multi-Markovian variable is introduced to denote the failure scaling factors for each sensor. Different from the existing results, the failure parameters are stochastically jumping and their bounds of are unknown. An adaptive reliable SOF control method is proposed, where the controller parameters are updated automatically to compensate for the failure effects on systems. A novel cubic absolute Lyapunov function is proposed to design adaptive laws only using measured output with sensor failures, and the convergence of jumping adaptive parameters is ensured by a trajectory initialization approach. The resultant designs can guarantee the asymptotic stability with an adaptive performance of closed-loop systems regardless of sensor failures. Finally, the simulation results on the "Raptor-90" helicopter are given to show the effectiveness of the proposed approaches.

Adaptively Adjusted Event-Triggering Mechanism on Fault Detection for Networked Control Systems

This paper studies the problem of adaptively adjusted event-triggering mechanism-based fault detection for a class of discrete-time networked control system (NCS) with applications to aircraft dynamics. By taking into account the fault occurrence detection progress and the fault occurrence probability, and introducing an adaptively adjusted event-triggering parameter, a novel event-triggering mechanism is proposed to achieve the efficient utilization of the communication network bandwidth. Both the sensor-to-control station and the control station-to-actuator network-induced delays are taken into account. The event-triggered sensor and the event-triggered control station are utilized simultaneously to establish new network-based closed-loop models for the NCS subject to faults. Based on the established models, the event-triggered simultaneous design of fault detection filter (FDF) and controller is presented. A new algorithm for handling the adaptively adjusted event-triggering parameter is proposed. Performance analysis verifies the effectiveness of the adaptively adjusted event-triggering mechanism, and the simultaneous design of FDF and controller.

Event-Triggered Fault Detection of Nonlinear Networked Systems

This paper investigates the problem of fault detection for nonlinear discrete-time networked systems under an event-triggered scheme. A polynomial fuzzy fault detection filter is designed to generate a residual signal and detect faults in the system. A novel polynomial event-triggered scheme is proposed to determine the transmission of the signal. A fault detection filter is designed to guarantee that the residual system is asymptotically stable and satisfies the desired performance. Polynomial approximated membership functions obtained by Taylor series are employed for filtering analysis. Furthermore, sufficient conditions are represented in terms of sum of squares (SOSs) and can be solved by SOS tools in MATLAB environment. A numerical example is provided to demonstrate the effectiveness of the proposed results.

Real-Time Fault Detection Approach for Nonlinear Systems and its Asynchronous T-S Fuzzy Observer-Based Implementation

This paper is concerned with a real-time observer-based fault detection (FD) approach for a general type of nonlinear systems in the presence of external disturbances. To this end, in the first part of this paper, we deal with the definition and the design condition for an L _∞ / L ₂ type of nonlinear observer-based FD systems. This analytical framework is fundamental for the development of real-time nonlinear FD systems with the aid of some well-established techniques. In the second part, we address the integrated design of the L _∞ / L ₂ observer-based FD systems by applying Takagi-Sugeno (T-S) fuzzy dynamic modeling technique as the solution tool. This fuzzy observer-based FD approach is developed via piecewise Lyapunov functions, and can be applied to the case that the premise variables of the FD system is nonsynchronous with the premise variables of the fuzzy model of the plant. In the end, a case study on the laboratory setup of three-tank system is given to show the efficiency of the proposed results.

Robust $H_{\infty }$ Self-Triggered Control of Networked Systems Under Packet Dropouts

This paper is concerned with robust H_∞ self-triggered control of networked systems. The system considered here includes parameter uncertainties, packet dropouts, and time delays. The time delay is described in a stochastic way, which takes a value from a given finite set. In order to compensate for the existence of deterministic packet dropouts, a new self-triggered control scheme is proposed. The main feature of the proposed self-triggered control strategy is that the next control task is predicted based on the self-triggered technique, in which the predicted event interval is divided equally for the sake of packet dropouts. The triggered condition is developed to ensure the stability of the uncertain sampled system by utilizing an uncertain algebraic Riccati equation and the comparison principle. Finally, an example of the inverted pendulum of a cart is provided to illustrate the effectiveness of the proposed results.

Dynamic IQC-Based Control of Uncertain LFT Systems With Time-Varying State Delay

This paper presents a new exact-memory delay control scheme for a class of uncertain systems with time-varying state delay under the integral quadratic constraint (IQC) framework. The uncertain system is described as a linear fractional transformation model including a state-delayed linear time-invariant (LTI) system and time-varying structured uncertainties. The proposed exact-memory delay controller consists of a linear state-feedback control law and an additional term that captures the delay behavior of the plant. We first explore the delay stability and the L₂ -gain performance using dynamic IQCs incorporated with quadratic Lyapunov functions. Then, the design of exact-memory controllers that guarantee desired L₂ -gain performance is examined. The resulting delay control synthesis conditions are formulated in terms of linear matrix inequalities, which are convex on all design variables including the scaling matrices associated with the IQC multipliers. The IQC-based exact-memory control scheme provides a novel approach for delay control designs via convex optimization, and advances existing control methods in two important ways: 1) better controlled performance and 2) simplified design procedure with less computational cost. The effectiveness and advantages of the proposed approach have been demonstrated through numerical studies.

A Stochastic Framework for Robust Fuzzy Filtering and Analysis of Signals-Part I

There are numerous applications across all the spectrum of scientific areas that demand the mathematical study of signals/data. The two typical study areas of theoretical research on signal/data processing are of modeling (i.e., understanding of signal's behavior) and of analysis (i.e., evaluation of given signal for finding its association to existing signal models). The objective of this paper is to provide a stochastic framework to design both fuzzy filtering and analysis algorithms in a unified manner. The signals are modeled via linear-in-parameters models (e.g., a type of Takagi-Sugeno fuzzy model) based on variational Bayes (VB) methodology. This gives rise to the "negative free energy maximizing" filtering algorithm. The issue of intractability was handled first by carefully choosing the priors as conjugate to the likelihood and then by using Stirling approximation for the Gamma function. This paper highlighted that it was analytically possible to maximize the information theoretic quantity, "mutual information," exactly in the same manner as maximizing "negative free energy" in VB methodology. This gives rise to the "variational information maximizing" analysis algorithm. The robustness of the methodology against data outliers is achieved by modeling the noises with Student- t distributions. The framework takes into account the inputs noises as well apart from the usually considered output noise. The robustness of the adaptive filtering algorithm against noise is shown by a deterministic analysis where an upper bound on the magnitude of estimation errors is derived.

System Identification in Presence of Outliers

The outlier detection problem for dynamic systems is formulated as a matrix decomposition problem with low rank and sparse matrices, and further recast as a semidefinite programming problem. A fast algorithm is presented to solve the resulting problem while keeping the solution matrix structure and it can greatly reduce the computational cost over the standard interior-point method. The computational burden is further reduced by proper construction of subsets of the raw data without violating low-rank property of the involved matrix. The proposed method can make exact detection of outliers in case of no or little noise in output observations. In case of significant noise, a novel approach based on under-sampling with averaging is developed to denoise while retaining the saliency of outliers, and so-filtered data enables successful outlier detection with the proposed method while the existing filtering methods fail. Use of recovered "clean" data from the proposed method can give much better parameter estimation compared with that based on the raw data.

Reliable Mixed H∞ and Passivity-Based Control for Fuzzy Markovian Switching Systems With Probabilistic Time Delays and Actuator Failures

This paper is concerned with the problem of reliable mixed H ∞ and passivity-based control for a class of stochastic Takagi-Sugeno (TS) fuzzy systems with Markovian switching and probabilistic time varying delays. Different from the existing works, the H∞ and passivity control problem with probabilistic occurrence of time-varying delays and actuator failures is considered in a unified framework, which is more general in some practical situations. The main aim of this paper is to design a reliable mixed H∞ and passivity-based controller such that the stochastic TS fuzzy system with Markovian switching is stochastically stable with a prescribed mixed H∞ and passivity performance level γ > 0 . Based on the Lyapunov-Krasovskii functional (LKF) involving lower and upper bound of probabilistic time delay and convex combination technique, a new set of delay-dependent sufficient condition in terms of linear matrix inequalities (LMIs) is established for obtaining the required result. Finally, a numerical example based on the modified truck-trailer model is given to demonstrate the effectiveness and applicability of the proposed design techniques.

Input-Output Approach to Control for Fuzzy Markov Jump Systems With Time-Varying Delays and Uncertain Packet Dropout Rate

This paper is concerned with H∞ control problem for a class of discrete-time Takagi-Sugeno fuzzy Markov jump systems with time-varying delays under unreliable communication links. It is assumed that the data transmission between the plant and the controller are subject to randomly occurred packet dropouts satisfying Bernoulli distribution and the dropout rate is uncertain. Based on a fuzzy-basis-dependent and mode-dependent Lyapunov function, the existence conditions of the desired H∞ state-feedback controllers are derived by employing the scaled small gain theorem such that the closed-loop system is stochastically stable and achieves a guaranteed H∞ performance. The gains of the controllers are constructed by solving a set of linear matrix inequalities. Finally, a practical example of robot arm is provided to illustrate the performance of the proposed approach.

Optimal performance of networked control systems with bandwidth and coding constraints

The optimal tracking performance of multiple-input multiple-output (MIMO) discrete-time networked control systems with bandwidth and coding constraints is studied in this paper. The optimal tracking performance of networked control system is obtained by using spectral factorization technique and partial fraction. The obtained results demonstrate that the optimal performance is influenced by the directions and locations of the nonminimum phase zeros and unstable poles of the given plant. In addition to that, the characters of the reference signal, encoding, the bandwidth and additive white Gaussian noise (AWGN) of the communication channel are also closely influenced by the optimal tracking performance. Some typical examples are given to illustrate the theoretical results.

Control of Nonlinear Networked Systems With Packet Dropouts: Interval Type-2 Fuzzy Model-Based Approach

In this paper, the problem of fuzzy control for nonlinear networked control systems with packet dropouts and parameter uncertainties is studied based on the interval type-2 fuzzy-model-based approach. In the control design, the intermittent data loss existing in the closed-loop system is taken into account. The parameter uncertainties can be represented and captured effectively via the membership functions described by lower and upper membership functions and relative weighting functions. A novel fuzzy state-feedback controller is designed to guarantee the resulting closed-loop system to be stochastically stable with an optimal performance. Furthermore, to make the controller design more flexible, the designed controller does not need to share membership functions and amount of fuzzy rules with the model. Some simulation results are provided to demonstrate the effectiveness of the proposed results.

Robust Frequency-Domain Constrained Feedback Design via a Two-Stage Heuristic Approach

Based on a two-stage heuristic method, this paper is concerned with the design of robust feedback controllers with restricted frequency-domain specifications (RFDSs) for uncertain linear discrete-time systems. Polytopic uncertainties are assumed to enter all the system matrices, while RFDSs are motivated by the fact that practical design specifications are often described in restricted finite frequency ranges. Dilated multipliers are first introduced to relax the generalized Kalman-Yakubovich-Popov lemma for output feedback controller synthesis and robust performance analysis. Then a two-stage approach to output feedback controller synthesis is proposed: at the first stage, a robust full-information (FI) controller is designed, which is used to construct a required output feedback controller at the second stage. To improve the solvability of the synthesis method, heuristic iterative algorithms are further formulated for exploring the feedback gain and optimizing the initial FI controller at the individual stage. The effectiveness of the proposed design method is finally demonstrated by the application to active control of suspension systems.

Optimal performance of networked control systems under the packet dropouts and channel noise

The optimal tracking performance of single-input single-output (SISO) discrete-time networked control systems (NCSs) with the packet dropouts and channel noise is studied in this paper. The communication channel is characterized by three parameters: the packet dropouts, channel noise and the encoding and decoding. The explicit expression of the optimal tracking performance is obtained by using the spectral factorization. It is shown that the optimal tracking performance dependents on the nonminimum phase zeros, unstable poles of the given plant, as well as the packet dropout probability, channel noise and the encoding and decoding. The optimal tracking performance is improved by two-parameter compensator. Finally, a typical example is given to illustrate the theoretical results.

Network-Based Robust H₂/H∞ Control for Linear Systems With Two-Channel Random Packet Dropouts and Time Delays

This paper focuses on the robust output feedback H₂/H∞ control issue for a class of discrete-time networked control systems with uncertain parameters and external disturbance. Sensor-to-controller and controller-to-actuator packet dropouts and time delays are considered simultaneously. According to the stochastic characteristic of the packet dropouts and time delays, a model based on a Markov jump system framework is proposed to randomly compensate for the adverse effect of the two-channel packet dropouts and time delays. To analyze the robust stability of the resulting closed-loop system, a Lyapunov function is proposed, based on which sufficient conditions for the existence of the H₂/H∞ controller are derived in terms of linear matrix inequalities, ensuring robust stochastic stability as well as the prescribed H₂ and H∞ performance. Finally, an angular positioning system is exploited to demonstrate the effectiveness and applicability of the proposed design strategy.

Network-Based Output Tracking Control for a Class of T-S Fuzzy Systems That Can Not Be Stabilized by Nondelayed Output Feedback Controllers

This paper investigates network-based output tracking control for a T-S fuzzy system that can not be stabilized by a nondelayed fuzzy static output feedback controller, but can be stabilized by a delayed fuzzy static output feedback controller. By intentionally introducing a communication network that produces proper network-induced delays in the feedback control loop, a stable and satisfactory tracking control can be ensured for the T-S fuzzy system. Due to the presence of network-induced delays, the fuzzy system and the fuzzy tracking controller operate in an asynchronous way. Taking the asynchronous operation and network-induced delays into consideration, the network-based tracking control system is modeled as an asynchronous T-S fuzzy system with an interval time-varying delay. A new delay-dependent criterion for L2 -gain tracking performance is derived by using the deviation bounds of asynchronous normalized membership functions and a complete Lyapunov-Krasovskii functional. Applying a particle swarm optimization technique with the feasibility of the derived criterion, a novel design algorithm is presented to determine the minimum L2 -gain tracking performance and control gains simultaneously. The effectiveness of the proposed method is illustrated by performing network-based output tracking control of a Duffing-Van der Pol's oscillator.

Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems

In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.

Further studies on control synthesis of discrete-time T-S fuzzy systems via augmented multi-indexed matrix approach

This paper is concerned with further studies on control synthesis of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To do this, a novel slack variable technique, which is homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions with arbitrary degrees, is presented by developing an efficient augmented multi-indexed matrix approach. Under the framework of homogenous matrix polynomials, the algebraic properties of both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions are collected into sets of augmented multi-indexed matrices. Thus, more information about the underlying normalized fuzzy weighting functions is involved into control synthesis. Consequently, the relaxation quality of control synthesis of discrete-time T-S fuzzy systems is improved significantly. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

A new design of robust H∞ sliding mode control for uncertain stochastic T-S fuzzy time-delay systems

In this paper, a novel dynamic sliding mode control scheme is proposed for a class of uncertain stochastic nonlinear time-delay systems represented by Takagi-Sugeno fuzzy models. The key advantage of the proposed scheme is that two very restrictive assumptions in most existing sliding mode control approaches for stochastic fuzzy systems have been removed. It is shown that the closed-loop control system trajectories can be driven onto the sliding surface in finite time almost certainly. It is also shown that the stochastic stability of the resulting sliding motion can be guaranteed in terms of linear matrix inequalities; moreover, the sliding-mode controller can be obtained simultaneously. Simulation results illustrating the advantages and effectiveness of the proposed approaches are also provided.