Observer-based control for singular nonhomogeneous Markov jump systems with packet losses

This paper is concerned with the observer-based H_∞ control for a class of singular Markov jump systems over a finite-time interval, where the transition probability (TP) is time-varying and is limited to a convex hull. Due to the limited capacity of network medium, packet losses are presented in the underlying systems. Firstly, using a stochastic Lyapunov functional, a sufficient condition on singular stochastic H_∞ finite-time boundedness for the corresponding closed-loop error systems is provided. Subsequently, a linear matrix inequality (LMI) condition on the existence of the H_∞ observer-based controller is developed from a new perspective. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed controller design method, wherein it is shown that the proposed method yields less conservative results than those in the literature.     

Event-triggered delayed impulsive control for nonlinear systems with applications

In this paper, we investigate the Lyapunov stability for general nonlinear systems by means of the event-triggered impulsive control (ETIC), in which the delayed impulses are greatly taken into account. On the basis of impulsive control theory, a set of Lyapunov-based sufficient conditions for uniform stability and asymptotic stability of the addressed system are obtained in the framework of event triggering, under which Zeno behavior is excluded. It is shown that our results depend on the event-triggering mechanism (ETM) and the time delays. Then the mentioned results are applied to synchronization of chaotic systems and moreover, a kind of impulsive controllers is designed in form of linear matrix inequality (LMI), where the delayed impulsive control can be activated only when events happen. In the end, to illustrate the validity of the mentioned theoretical results, we present a numerical example.     

Event-triggered stabilisation for stochastic delayed differential systems with exogenous disturbances

In this paper, the practically input-to-state stabilization issue is considered for the stochastic delayed differential systems (SDDSs) with exogenous disturbances. To reduce the transmission frequency of the feedback control signal, the proposed SDDSs are stabilized by an event-triggered strategy. The concept of the practically input-to-state stability (ISS) is used to describe the dynamic performance of control target in the event-triggered schemes and exogenous disturbances. Besides, the considered SDDSs is stabilized by an event-triggered feedback controller which is represented by linear matrix inequalities. Moreover, lower bound of the interaction time of the event-triggered control method is obtained to avoid the Zeno behavior of the proposed event-triggering scheme. Finally, the effectiveness of the conclusion is verified by a numerical example.     

State estimation for networked systems with Markovian communication constraints and multiple packet dropouts

In this paper, the state estimation problem for discrete-time networked systems with communication constraints and random packet dropouts is considered. The communication constraint is that, at each sampling instant, there is at most one of the various transmission nodes in the networked systems is allowed to access a shared communication channel, and then the received data are transmitted to a remote estimator to perform the estimation task. The channel accessing process of those transmission nodes is determined by a finite-state discrete-time Markov chain, and random packet dropouts in remote data transmission are modeled by a Bernoulli distributed white sequence. Using Bayes’ rule and some results developed in this study, two state estimation algorithms are proposed in the sense of minimum mean-square error. The first algorithm is optimal, which can exactly compute the minimum mean-square error estimate of system state. The second algorithm is a suboptimal algorithm obtained under a lot of Gaussian hypotheses. The proposed suboptimal algorithm is recursive and has time-independent complexity. Computer simulations are carried out to illustrate the performance of the proposed algorithms.     

Decentralized control for multi-sensors networked systems with different transmission delays and packet dropouts

In this paper, the linear quadratic (LQ) optimal decentralized control and stabilization problems are investigated for multi-sensors networked control systems (MSNCSs) with multiple controllers of different information structure. Specifically, for a MSNCS, in view of the packet dropouts and the transmission delays, each controller may access different information sets. To begin with, the sufficient and necessary solvability conditions for the LQ decentralized control problems are developed. Consequently, for the purpose of deriving the optimal decentralized control strategy, an innovative orthogonal decomposition method is proposed to decouple the forward and backward stochastic difference equations (FBSDEs) from the maximum principle. In the following, we show that the optimal decentralized controller can be calculated according to a set of Riccati-type equations. Finally, a stabilizing controller is derived for the stabilization problem.     

Estimation fusion for networked systems with multiple asynchronous sensors and stochastic packet dropouts

This paper studies the asynchronous state fusion estimation problem for multi-sensor networked systems subject to stochastic data packet dropouts. A set of Bernoulli sequences are adopted to describe the random packet losses with different arriving probabilities for different sensor communication channels. The asynchronous sensors considered in this paper can have arbitrary sampling rates and arbitrary initial sampling instants, and may even sample the system non-uniformly. Asynchronous measurements collected within the fusion interval are transformed to the fusion time instant as a combined equivalent measurement. An optimal asynchronous estimation fusion algorithm is then derived based on the transformed equivalent measurement using the recursive form of linear minimum mean squared error (LMMSE) estimator. Cross-correlations between involved random variables are carefully calculated with the stochastic data packet dropouts taken into account. A numerical target tracking example is provided to illustrate the feasibility and effectiveness of the proposed algorithm.     

Observer-based event-triggered sliding mode control for delayed systems with unknown disturbances

This paper develops the observer-based event-triggered sliding mode control strategy for delayed systems involving unknown disturbances. This strategy comprises a triggering rule which can effectively save resources and an observer-based control law which can drive the states of delayed systems into the practical sliding mode band in some finite time. Some sufficient conditions coupled with this control strategy are proposed to guarantee the robust performance of the delayed systems. Significant outcome of this strategy is that it can be applied to the case in which the disturbances are unmeasured or unknown. Finally, two numerical examples and its simulations are presented to show the performance of the systems and effectiveness of this control strategy.     

Dynamics of linear delayed systems with decaying disturbances

Dynamical systems in the real world are always subject to various disturbances. This paper studies the dynamics of linear delayed systems with decaying disturbances, both discrete- and continuous-time cases are considered. It is first shown that if an unforced linear system is exponentially stable, then the disturbed system has a dynamical property like exponential stability provided that the disturbance decays at an exponential rate, and has a dynamical property like asymptotic stability provided that the disturbance asymptotically approaches zero. These results are then applied to block triangular systems in the presence of time-varying delays, leading to criteria for checking the stability properties of this class of systems by considering diagonal blocks of system matrices. Particularly, a block triangular system is exponentially stable if and only if each system described by the diagonal blocks of system matrices is exponentially stable. Finally, a numerical example is presented to illustrate the theoretical results.     

Quantized stabilization of switched systems with switching delays and packet loss

This paper is concerned with the problem of designing an observer-based quantized feedback controller for the continuous-time switched linear systems, in which the transmission of switching signal is subject to unbounded delays and packet loss. To deal with the unbounded switching delays, we design a constant $\overline{d}$ to determine that the switching signal received by controller is ignored or not. Based on that, if the signal is timestamped, the controller’s mode is uniquely determined. Moreover, we adjust the quantizer parameters in real time depending on the actual transmission situations to ensure the unsaturation of quantizer and thus the boundness of quantization error. Within this setup, we derive a maximum allowable packet loss rate ensuring the mean square stability of the closed-loop switched systems. An illustrative example is given to show the usefulness of the proposed framework for the quantized stabilization of some classes of switched systems.     

Robust control design for delayed periodic piecewise time-varying systems with actuator faults

This paper is mainly focused on the stabilization problem of uncertain delayed periodic piecewise time-varying systems inclusive of disturbances and faults in actuators. More specifically, the considered system is encompassed of periodic dynamics, which exhibits the nature of switched systems with fixed switching sequence and dwell time. The control protocol is configured in the form of both the present and past state information of the addressed system with passive performance. Moreover, the proposed control approach discloses the stabilization issue mainly by resolving the effect of faults in actuator components. Precisely, the desired periodic gain matrices of the developed controller are calculated by way of solving some matrix inequalities which are derived by making use of Lyapunov stability theory and matrix polynomial approach. As a result, the asymptotic stability of the considered system is ensured in conjunction with satisfied disturbance attenuation index. Conclusively, the simulation results of two numerical examples including mass-spring damping system are presented for validating the theoretical result.     

Optimal tracking performance and design of networked control systems with packet dropouts

The optimal tracking problem for single-input–single-output (SISO) networked control system over a communication channel with packet dropouts is studied in this paper. The tracking performance is measured by the energy of the error signal between the output of the plant and the reference signal. It is shown that the optimal tracking performance is constrained by nonminimum phase zeros, unstable poles, the characteristics of the reference signal and packet dropout probability, and the optimal controller is obtained. It is also shown that when the communication constraint does not exist, the optimal tracking performance reduces to the existing normal tracking performance of the control system without a communication channel. The result shows how the packet dropouts probability of a communication channel may fundamentally constrain a control system's tracking ability. Some typical examples and simulations are given to illustrate the theoretical results.     

Stability analysis of networked control systems with round-robin scheduling and packet dropouts

In this paper, the stability of networked control systems (NCSs) with communication constraints at both channels is investigated. A Conventional Round-Robin Scheduling (CRRS) is applied to deal with the communication constraints issue for its simple structure. Furthermore, a Dynamic Round-Robin Scheduling (DRRS), which can preserve the controllability and the detectability of the systems, is considered. For the unreliable communication channels, two independent homogeneous Markov chains are selected to model the packet dropouts phenomenon in the sensor-to-controller (S/C) channel and the controller-to-actuator (C/A) channel. According to the periodic property of the Round-Robin Scheduling (RRS), an auxiliary system with augmented Markov chain is established by the lifting technique to facilitate the stability analysis of the closed-loop system. A necessary and sufficient condition of the exponential mean-square stability for the NCSs is derived. Two illustrative examples are shown to demonstrate the effectiveness of the proposed stability analysis method.     

Robust fault detection of linear systems over networks with bounded packet loss

This paper is devoted to the fault detection of linear systems over networks with bounded packet loss. The inputs and the measurements of the monitored system are transmitted to a fault detection node over an unreliable network with bounded packet loss. The packet loss process is assumed to be arbitrary or Markovian in this paper. Due to the bounded packet loss process, the monitored system is modeled as a switched system by re-sampling it at each time instant when the measurements arrive at the fault detection node. A fault detection filter for this switched system is designed in this paper to satisfy some performance constraints. The filter updates only at the time instant when new measurements arrive at the fault detection node and the input data packets' lost are considered as external disturbances. Finally, the numerical example and simulations have demonstrated the usefulness of the proposed method.     

Cluster searching strategies for collaborative recommendation systems

In-memory nearest neighbor computation is a typical collaborative filtering approach for high recommendation accuracy. However, this approach is not scalable given the huge number of customers and items in typical commercial applications. Cluster-based collaborative filtering techniques can be a remedy for the efficiency problem, but they usually provide relatively lower accuracy figures, since they may become over-generalized and produce less-personalized recommendations. Our research explores an individualistic strategy which initially clusters the users and then exploits the members within clusters, but not just the cluster representatives, during the recommendation generation stage. We provide an efficient implementation of this strategy by adapting a specifically tailored cluster-skipping inverted index structure. Experimental results reveal that the individualistic strategy with the cluster-skipping index is a good compromise that yields high accuracy and reasonable scalability figures.     

New gain-scheduling control conditions for time-varying delayed LPV systems

This paper investigates the problem of stability and state-feedback control design for linear parameter-varying systems with time-varying delays. The uncertain parameters are assumed to belong to a polytope with bounded known variation rates. The new conditions are based on the Lyapunov theory and are expressed through Linear Matrix Inequalities. An alternative parameter-dependent Lyapunov-Krasovskii functional is employed and its time-derivative is handled using recent integral inequalities for quadratic functions proposed in the literature. As main results, a novel sufficient stability condition for delay-dependent systems as well as a new sufficient condition to design gain-scheduled state-feedback controllers are stated. In the new proposed methodology, the Lyapunov matrices and the system matrices are put separated making it suitable for supporting in a new way the design of the stabilization controller. An example, based on a model of a real-world problem, is provided to illustrate the effectiveness of the proposed method.     

Stabilization of networked periodic piecewise linear systems under asynchronous switching with packet dropouts

In this paper, the networked stabilization of discrete-time periodic piecewise linear systems under transmission package dropouts is investigated. The transmission package dropouts result in the loss of control input and the asynchronous switching between the subsystems and the associated controllers. Before studying the networked control, the sufficient conditions of exponential stability and stabilization of discrete-time periodic piecewise linear systems are proposed via the constructed dwell-time dependent Lyapunov function with time-varying Lyapunov matrix at first. Then to tackle the bounded time-varying packet dropouts issue of switching signal in the networked control, a continuous unified time-varying Lyapunov function is employed for both the synchronous and asynchronous subintervals of subsystems, the corresponding stabilization conditions are developed. The state-feedback stabilizing controller can be directly designed by solving linear matrix inequalities (LMIs) instead of iterative optimization used in continuous-time periodic piecewise linear systems. The effectiveness of the obtained theoretical results is illustrated by numerical examples.     

New results on reachable sets bounding for delayed positive singular systems with bounded disturbances

This paper addresses the reachable sets bounding problem for time-delay positive singular systems subject to bounded disturbances. The time delays in the considered systems are assumed to be time-varying. Both invariant and time-varying singular systems are investigated in this paper. Existence conditions of componentwise ultimate bounds of the state vector of considered systems are derived and given in terms of the spectral abscissa of the system matrices, which are easy to be checked. The obtained results are demonstrated by two numerical examples.     

Event-triggered finite-time fault detection for delayed networked systems with conic-type nonlinearity and deception attacks

The paper is concerned with the finite-time fault detection (FTFD) problem for a class of delayed networked systems subject to conic-type nonlinearity and randomly occurring deception attacks (RODAs) via dynamic event-triggered mechanism (DETM). The nonlinear function with the conic-type constraint is limited to a known hypersphere with uncertain center. Moreover, a variable governed by Bernoulli distribution is introduced to characterize the RODAs phenomenon. In order to reduce unnecessary communication transmissions, a DETM is considered in the design of finite-time fault detection filter (FTFDF) for the addressed networked systems with time-delays. This paper focuses on the design of an FTFDF via the DETM to ensure the finite-time stochastic stability of error dynamics system with satisfactory the prescribed $H_{\infty }$ performance. Moreover, the desired FTFDF parameter matrices are obtained by solving linear matrix inequalities. In the end, a simulation example is employed to illustrate the validity of the proposed FTFD method.     

H∞ control for network-based systems with time-varying delay and packet disordering

The H_∞ control problem is investigated in this paper for a class of networked control systems (NCS) with time-varying delay and packet disordering. A new model is proposed to describe the packet disordering phenomenon and then converted into a parameter-uncertain system with multi-step delay. Based on the obtained system model, a sufficient condition for robust stability of the NCS is derived. Furthermore, an optimization problem with linear matrix inequalities (LMIs) constraints is formulated to design the state feedback H_∞ controller such that the closed-loop NCS is robust stable and has an optimal H_∞ disturbance attenuation level. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.