Guaranteed cost finite‐time control for semi‐Markov jump systems with event‐triggered scheme and quantization input

In this paper, the guaranteed cost finite‐time control for semi‐Markov jump systems with unknown transition rates is addressed. An event‐triggered scheme is constructed to automatically monitor the data transmission and the input quantization is involved to reduce the cost of control. Different from the existing general transition rates in the semi‐Markov jump systems, the upper and lower bounds of transition rates are not given in advance but obtained through the stability criteria. The stability criteria are established to verify the stochastic finite‐time boundedness of the closed‐loop event‐triggered system and estimate the performance index of the given cost function. A guaranteed cost optimal controller is also proposed to stabilize the considered system. Finally, the vertical take‐off and landing helicopter model is introduced to verify the effectiveness of the main algorithms.     

Event‐triggered dissipative synchronization for Markovian jump neural networks with general transition probabilities

In this paper, dissipative synchronization problem for the Markovian jump neural networks with time‐varying delay and general transition probabilities is investigated. An event‐triggered communication scheme is introduced to trigger the transmission only when the variation of the sampled vector exceeds a prescribed threshold condition. The transition probabilities of the Markovian jump delayed neural networks are allowed to be known, or uncertain, or unknown. By employing delay system approach, a new model of synchronization error system is proposed. Applying the Lyapunov‐Krasovskii functional and integral inequality combining with reciprocal convex technique, a delay‐dependent criterion is developed to guarantee the stochastic stability of the errors system and achieve strict (Q,S,R)?α dissipativity. The event‐triggered parameters can be derived by solving a set of linear matrix inequalities. A numerical example is presented to illustrate the effectiveness of the proposed design method.     

Filtering of discrete‐time Markov jump linear systems with uncertain transition probabilities

This article addresses the filtering design problem for discrete‐time Markov jump linear systems (MJLS) under the assumption that the transition probabilities are not completely known. We present the methods to determine ??₂‐ and ??_∞‐norm bounded filters for MJLS whose transition probability matrices have uncertainties in a convex polytope and establish an equivalence with the ones with partly unknown elements. The proposed design, based on linear matrix inequalities, allows different assumptions on Markov mode availability to the filter and on system parameter uncertainties to be taken into account. Under mode‐dependent assumption and internal model knowledge, observer‐based filters can be obtained and it is shown theoretically that our method outperforms some available ones in the literature to date. Numerical examples illustrate this claim. Copyright © 2010 John Wiley & Sons, Ltd.     

H∞ stabilization for networked semi‐Markovian jump systems with randomly occurring uncertainties via improved dynamic event‐triggered scheme

This paper aims to solve the H_∞ stabilization problem for networked semi‐Markovian jump systems subject to randomly occurring uncertainties by an improved event‐triggered technique. A new measurement error that is defined as the difference value between the latest transmitted data and the mean value of both current data and latest transmitted data is introduced into the event‐triggered condition. Compared with traditional dynamic event‐triggered scheme, more unexpected data could be avoided to be transmitted, which is demonstrated in the simulation through sufficient comparison experiments. Furthermore, by employing a Lyapunov‐Krasovskii functional method and a free‐weighting matrix method, sufficient conditions are derived to guarantee the stabilization of the closed‐loop semi‐Markovian jump time‐delay system with uncertainties and a prescribed performance index. Then, a codesign method for H_∞ controller gains and event‐triggered parameters is presented. Finally, simulations are given to verify the effectiveness of our improved dynamic event‐triggered scheme.     

Model‐based event‐triggered predictive control for networked systems with communication delays compensation

This paper addresses the model‐based event‐triggered predictive control problem for networked control systems (NCSs). Firstly, we propose a discrete event‐triggered transmission scheme on the sensor node by introducing a quadratic event‐triggering function. Then, on the basis of the aforementioned scheme, a novel class of model‐based event‐triggered predictive control algorithms on the controller node is designed for compensating for the communication delays actively and achieving the desired control performance while using less network resources. Two cases, that is, the value of the communication delay of the first event‐triggered state is less or bigger than the sampling period, are considered separately for certain NCSs, regardless of the communication delays of the subsequent event‐triggered states. The codesign problems of the controller and event‐triggering parameter for the two cases are discussed by using the linear matrix inequality approach and the (switching) Lyapunov functional method. Furthermore, we extended our results to the NCSs with systems uncertainties. Finally, a practical ball and beam system is studied numerically to demonstrate the compensation effect for the communication delays with the proposed novel model‐based event‐triggered predictive control scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Event‐triggered finite‐time reliable control for nonhomogeneous Markovian jump systems

This article investigates the event‐triggered finite‐time reliable control problem for a class of Markovian jump systems with time‐varying transition probabilities, time‐varying actuator faults, and time‐varying delays. First, a Luenberger observer is constructed to estimate the unmeasured system state. Second, by applying an event‐triggered strategy from observer to controller, the frequency of transmission is reduced. Third, based on linear matrix inequality technique and stochastic finite‐time analysis, event‐triggered observer‐based controllers are designed and sufficient conditions are given, which ensure the finite‐time boundedness of the closed‐loop system in an H_∞ sense. Finally, an example is utilized to show the effectiveness of the proposed controller design approach.     

Event‐triggered control for networked Markovian jump systems

The problem of H_∞ control for networked Markovian jump system under event‐triggered scheme is studied in this paper. In order to reduce the utilization of limited network bandwidth, a dynamic discrete event‐triggered scheme to choose the transmitted data is designed. A Markovian jump time‐delay system model is employed to describe the event‐triggered scheme and the network related behavior, such as transmission delay, data package dropout, and disorder. Furthermore, a sufficient condition is derived to guarantee that the resulting closed‐loop system is stable and has a prescribed performance index. A co‐design method for the H_∞ controller and the event‐triggered scheme is then proposed. The effectiveness and potential of the theoretic results obtained are illustrated by a simulation example. Copyright © 2014 John Wiley & Sons, Ltd.     

Network‐based robust event‐triggered control for continuous‐time uncertain semi‐Markov jump systems

This article investigates the event‐triggered (ET) states feedback robust control problem for a class of continuous‐time networked semi‐Markov jump systems (S‐MJSs). An ET scheme, which depends on semi‐Markov process, is presented to design a suitable controller and save communication resources. To cope with the network transmission delay phenomenon, a time‐delay S‐MJSs model under the ET scheme is introduced to describe this phenomenon. Then, it is assumed that the communication links between event detector and zero‐order holder are imperfect, where the signal quantization and the actuator fault occur simultaneously. The sufficient conditions are derived by means of linear matrix inequalities approach, which guarantees the stochastic stability of the constructed time‐delay S‐MJSs in an optimized performance level. Based on these criteria, the parameters of controller under the ET scheme are readily calculated. Some simulation results with respect to F‐404 aircraft engine system for two kinds of ET parameters are given to validate the proposed method.     

Tracking Control for Stochastic Multi‐Agent Systems Based on Hybrid Event‐Triggered Mechanism

This paper deals with the leader‐following consensus for nonlinear stochastic multi‐agent systems. To save communication resources, a new centralized/distributed hybrid event‐triggered mechanism (HETM) is proposed for nonlinear multi‐agent systems. HETMs can be regarded as a synthesis of continuous event‐triggered mechanism and time‐driven mechanism, which can effectively avoid Zeno behavior. To model the multi‐agent systems under centralized HETM, the switched system method is applied. By utilizing the property of communication topology, low‐dimensional consensus conditions are obtained. For the distributed hybrid event‐triggered mechanism, due to the asynchronous event‐triggered instants, the time‐varying system method is applied. Meanwhile, the effect of network‐induced time‐delay on the consensus is also considered. To further reduce the computational resources by constantly testing whether the broadcast condition has been violated, self‐triggered implementations of the proposed event‐triggered communication protocols are also derived. A numerical example is given to show the effectiveness of the proposed method.     

Static anti‐windup design for a class of Markovian jump systems with partial information on transition rates

This paper investigates the problem of static anti‐windup design for uncertain continuous‐time Markovian jump systems with partially unknown transition rates in the face of actuator saturation. The underlying system is subject to time‐varying and norm‐bounded parameter uncertainties in both the state and input matrices. It is assumed that a set of stabilizing dynamic output‐feedback controllers have been designed for the system in the absence of control saturation. The objective is to design anti‐windup compensation gains for the given controllers such that the system can still be stabilized, irrespective of whether actuator saturation appears or not. To obtain a maximum estimation of the domain of attraction of the resulting closed‐loop system, a convex optimization problem in the linear matrix inequality framework is formulated. Furthermore, the results are extended to the cases of the systems with completely known transition rates and with completely unknown transition rates. Finally, the usefulness of the developed method is demonstrated through simulation examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Observer‐based finite‐time stabilization for extended Markov jump systems

In this paper, we study the problem of observer‐based finite‐time stabilization for a class of extended Markov jump systems with norm‐bounded uncertainties and external disturbances. The stochastic character under consideration is governed by a finite‐state Markov process, but with only partial information on the transition jump rates. Based on the finite‐time stability analysis, sufficient conditions for the existence of the observer‐based controller are derived via a linear matrix inequality approach such that the closed‐loop system trajectory stays within a prescribed bound in a fixed time interval. When these conditions are satisfied, the designed observer‐based controller gain matrices can be obtained by solving a convex optimization problem. Simulation results demonstrate the effectiveness of the approaches proposed in this paper. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Event‐Based Consensus Controller for Linear Multi‐Agent Systems Over Directed Communication Topologies: A Co‐Design Approach

The paper addresses the distributed event‐triggered consensus problem in directed topologies for multi‐agent systems (MAS) with general linear dynamic agents. A co‐design approach is proposed to determine parameters of the consensus controller and its event‐triggered mechanism (ETM), simultaneously. This approach guarantees asymptotic stability along with decreasing data transmission among agents. In the proposed event‐based consensus controller, each agent broadcasts data to the neighbors only at its own triggering instants; this differs from previous studies in which continuous data streams among agents were required. Furthermore, the proposed control law is based on the piecewise constant functions of the measurement values, which are updated at triggering instants. In this case the control scheme decreases the communication network usage, energy consumption, and wear of the actuator. As a result, it facilitates distributed implementation of the proposed consensus controller for real‐world applications. A theorem is proved to outline sufficient conditions to guarantee the asymptotic stability of the closed‐loop system with the event‐based consensus controller. Another theorem is also proved to show the Zeno behavior exclusion. As a case study, the proposed event‐based controller is applied for a diving consensus problem to illustrate the effectiveness of the method.     

Stochastic stability and robust stabilization of semi‐Markov jump linear systems

The semi‐Markov jump linear system (S‐MJLS) is more general than the Markov jump linear system (MJLS) in modeling some practical systems. Unlike the constant transition rates in the MJLS, the transition rates of the S‐MJLS are time varying. This paper focuses on the robust stochastic stability condition and the robust control design problem for the S‐MJLS with norm‐bounded uncertainties. The infinitesimal generator for the constructed Lyapunov function is first derived. Numerically solvable sufficient conditions for the stochastic stability of S‐MJLSs are then established in terms of linear matrix inequalities. To reduce the conservativeness of the stability conditions, we propose to incorporate the upper and lower bounds of the transition rate and meanwhile apply a new partition scheme. The robust state feedback controller is accordingly developed. Simulation studies and comparisons demonstrate the effectiveness and advantages of the proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Distributed Event‐Triggered Consensus for Multiple Underactuated Systems Under Markovian Switching Topologies

This paper presents a distributed consensus algorithm that employs event‐triggered communication for multiple underactuated systems under Markovian switching topologies. Instead of the general stochastic topology, the graph of the entire system is governed by a set of Markov chains to the edges, which can recover the general Markovian switching topologies in line with the practical communication network. By utilizing integral sliding mode control strategy, rigorous analysis of the asymptotic convergence results has been performed through graph theory and Lyapunov stability theory. An event‐triggered communication law is provided for each agent and Zeno behavior of triggering time sequences is excluded. It will yield to the very first application of the multiple underactuated systems, in which the system states could be enforced to track the leader. Finally, the illustrative simulations on six underactuated two‐link manipulators are given to demonstrate the effectiveness of theoretical results.     

Event‐Triggered Iterative Learning Control for Multi‐Agent Systems with Quantization

The emergence of networked control systems urges the digital control design to integrate communication constraints efficiently. In order to accommodate this requirement, this paper investigates the joint design of tracking problem for multi‐agent system (MAS) in the presence of resource‐limited communication channel and quantization. An event‐triggered robust learning control with quantization is firstly proposed and employed for MAS in this paper. The new event‐triggered distributed robust learning control system with the introduction of logarithmic quantization guarantees the asymptotic tracking property on the finite interval. Convergence analysis is given based on the Lyapunov direct method. Finally, numerical simulations are given to illustrate the efficacy of the event‐triggered approach compared with time‐triggered controllers.     

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

In this paper, the exponential mean‐square stability of neutral switching Markovian jump systems with generally incomplete transition probabilities is investigated. The model discussed in this paper concludes both deterministic switching signals and Markovian jumping signals. The transition rates of the jumping process are assumed to be partly available, that is, some elements have been exactly known, some have been merely known with lower and upper bounds, and others may have no information to use. Based on the Lyapunov‐Krasovskii functional method, sufficient conditions on the exponential mean‐square stability of the considered system are derived in terms of liner matrix inequalities. A numerical example is provided to show the feasibility and effectiveness of the proposed results.     

Event‐triggered adaptive backstepping control for parametric strict‐feedback nonlinear systems

This paper proposes a novel adaptive backstepping control method for parametric strict‐feedback nonlinear systems with event‐sampled state and input vectors via impulsive dynamical systems tools. In the design procedure, both the parameter estimator and the controller are aperiodically updated only at the event‐sampled instants. An adaptive event sampling condition is designed to determine the event sampling instants. A positive lower bound on the minimal intersample time is provided to avoid Zeno behavior. The closed‐loop stability of the adaptive event‐triggered control system is rigorously proved via Lyapunov analysis for both the continuous and jump dynamics. Compared with the periodic updates in the traditional adaptive backstepping design, the proposed method can reduce the computation and the transmission cost. The effectiveness of the proposed method is illustrated using 2 simulation examples.     

Event‐Triggered Control for Multi‐Agent Systems with General Directed Topology and Time Delays

Recent years have witnessed a growing interest in event‐triggered strategies for coordination and cooperative control of multi‐agent systems. However, the most previous works and developments focus on the interactive network that has no communication delays. This paper deals with the consensus problem of an agent system with event‐triggered control strategy under communication time delays. We first propose a time delays system model, then present a novel event triggering function that not only avoids continuous communication but also excludes the Zeno behavior. Furthermore, we provide the consensus analysis using an inequality technique instead of the traditional linear matrix inequality method, and we demonstrate that the inter‐event times for each agent are strictly positive, which implies that the Zeno behavior can be excluded. Finally, simulation results show the effectiveness of the proposed approach and illustrate the correctness of the theoretical results.     

Event‐triggered fault detection for switched systems with time‐varying sojourn probabilities

In this paper, a codesign strategy of an event‐triggered scheme and a fault detection filter (FDF) is developed for the networked switched systems with delayed measurements. A novel switching rule is proposed to better describe the switching behavior in a real system, under which the probability staying in each subsystem is time varying and results in a piecewise continuous system dynamics. An event‐triggered strategy based on the relative error with respect to the delayed measurement signal is established to reduce the communication burden. Our attention is concentrated on the construction of an event‐triggered fault detection technique for the proposed switched system with delayed measurements. Combining the stochastic analysis techniques and the average dwell time (ADT) method, a sufficient condition is obtained to guarantee the finite‐time boundedness of the generated residual system, the sensitivity of the residual signal to faults, and the disturbance attenuation of the switched system to external disturbances. Based on the established condition, a codesign strategy is developed to get the event‐triggered threshold and the FDF gain. Finally, two simulation results verify the effectiveness of the proposed design method.     

Adaptive event‐triggered global fast finite‐time control for a class of uncertain nonlinear systems

This article designs an adaptive event‐triggered controller to solve the problem of global finite‐time stabilization for a class of uncertain nonlinear systems. By using the symbol function technique, the event‐triggered error is completely compensated, the adaptive technique and the back‐stepping method are simultaneously applied to the controller design, and the new way of designing controller is completed on the basis of fast finite‐time stability theory. Subsequently, taking Lyapunov stability theorem into account, the system stability is proved, and the system is demonstrated by contradiction to be non‐zeno. Finally, giving a simulation example to display the feasibility of this method.