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 practical finite‐time output feedback stabilization of a class of uncertain nonlinear systems

This paper studies the event‐triggered practical finite‐time output feedback stabilization problem for a class of uncertain nonlinear systems with unknown control gains. First, a reduced‐dimensional observer is employed to implement the reconstruction of the unavailable states. Furthermore, a novel event‐triggered output feedback control strategy is proposed based on the idea of backstepping design and sign function techniques. It is shown that the practical finite‐time stability of the closed‐loop systems is ensured by Lyapunov analysis and related stability criterion. Compared with the existing methods, the main advantage of this strategy is that the observer errors and event‐trigger errors can be processed simultaneously to achieve the practical finite‐time stability. Finally, an example is adopted to demonstrate the validity of the proposed scheme.     

Event‐triggered control for discrete‐time linear systems subject to bounded disturbance

This paper considers event‐triggering controller design for directly observable discrete‐time linear systems subject to bounded disturbances. The main control objective is diminishing the influence aroused by the disturbances despite a reduction of the communication. Criteria are given to design feedback controllers in order to guarantee that systems are uniformly ultimately bounded in an ellipsoidal‐positive invariant set, which is used as an estimate of control performance for disturbance rejection. An optimization for minimizing the ellipsoidal‐positive invariant set is achieved by synthesizing the feedback control gain and the given event‐triggering conditions in LMIs. The effectiveness and applicability of the controller are illustrated by simulations and experimental implementations. Copyright © 2015 John Wiley & Sons, Ltd.     

Event‐triggered constrained control of positive systems with input saturation

This paper addresses the problem of event‐triggered stabilization for positive systems subject to input saturation, where the state variables are in the nonnegative orthant. An event‐triggered linear state feedback law is constructed. By expressing the saturated linear state feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is asymptotically stable with a given set contained in the domain of attraction. On the basis of these conditions, the problem of designing the feedback gain and the event‐triggering strategy for attaining the largest domain of attraction is formulated and solved as an optimization problem with linear matrix inequality constraints. The problem of designing the feedback gain and the event‐triggering strategy for achieving fast transience response with a guaranteed size of the domain of attraction is also formulated and solved as an linear matrix inequality problem. The effectiveness of these results is then illustrated by numerical simulation.     

Event‐triggered approach for finite‐time state estimation of delayed complex dynamical networks with random parameters

This article emphasizes the finite‐time state estimation problem for delayed complex dynamical networks with random parameters. In order to reduce the amount of transmission process, an aperiodic sampled‐data event‐triggered mechanism is introduced to determine whether the measurement output should be released at certain time points which incorporate an appropriate triggering condition and sampling moments. Furthermore, a concept of finite‐time boundedness in the pth moment is proposed to access the performance of state estimator. The objective of this article is to design an event‐triggered state estimator to estimate the states of nodes such that, in the presence of time delays, uncertainties, and randomly changing coupling weights, the estimation error system is finite‐time bounded in the pth moment related to a given constant. Some sufficient conditions in form of linear matrix inequalities and algebraic inequalities are established to guarantee finite‐time boundedness. Finally, a numerical example is presented to show the effectiveness of the theoretical 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.     

Global adaptive finite‐time stabilization for a class of p‐normal nonlinear systems via an event‐triggered strategy

This article addresses the problem of global adaptive finite‐time control for a class of p‐normal nonlinear systems via an event‐triggered strategy. A state feedback controller is first designed for the nominal system by adding a power integrator method. Then, by the skillful design of adaptive dynamic gain mechanism, a novel event‐triggered controller is constructed for uncertain nonlinear system without homogeneous growth condition. It is proved that the global finite‐time stabilization of p‐normal nonlinear systems is guaranteed and the Zeno phenomenon is excluded. Finally, two examples are presented to indicate the effectiveness of the proposed control scheme.     

Event‐triggered predictive control for networked control systems with network‐induced delays and packet dropouts

This paper presents an event‐triggered predictive control approach to stabilize a networked control system subject to network‐induced delays and packet dropouts, for which the states are not measurable. An observer‐based event generator is first designed according to the deviation between the state estimation at the current time and the one at the last trigger time. A predictive control scheme with a selector is then proposed to compensate the effect of network‐induced delays and packet dropouts. Sufficient conditions for stabilization of the networked control system are derived by solving linear matrix inequalities and the corresponding gains of the controller and the observer are obtained. It is shown that the event‐triggered implementation is able to realize reduction in communication and save bandwidth resources of feedback channel networks. A simulation example of an inverted pendulum model illustrates the efficacy of the proposed scheme.     

Adaptive event‐triggered control for nonlinear discrete‐time systems

This paper focuses on the analysis and the design of event‐triggering scheme for discrete‐time systems. Both static event‐triggering scheme (SETS) and adaptive event‐triggering scheme (AETS) are presented for discrete‐time nonlinear and linear systems. What makes AETS different from SETS is that an auxiliary dynamic variable satisfying a certain difference equation is incorporated into the event‐triggering condition. The sufficient conditions of asymptotic stability of the closed‐loop event‐triggered control systems under both two triggering schemes are given. Especially, for the linear systems case, the minimum time between two consecutive control updates is discussed. Also, the quantitative relation among the system parameters, the preselected triggering parameters in AETS, and a quadratic performance index are established. Finally, the effectiveness and respective advantage of the proposed event‐triggering schemes are illustrated on a practical example. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

Global mean‐square exponential stabilization of stochastic system with time delay via impulsive control

This paper discusses the global mean‐square exponential stabilization problem for a class of nonlinear non‐autonomous stochastic systems with time delay via impulsive controller. By employing the D‐measure of the matrix and establishing a formula for the variation of parameters, some sufficient conditions are proposed for the design of an impulsive controller such that the stochastic impulsive control system with time varying system matrix and time delay is globally mean‐square exponentially stable. Some numerical examples are presented to illustrate the effectiveness of the proposed results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Input‐to‐state stability for discrete‐time nonlinear impulsive systems with delays

This paper aims to study the problem of input‐to‐state stability (ISS) for nonlinear discrete impulsive systems with time delays. Razumikhin‐type theorems, which guarantee ISS – asymptotically ISS and exponentially ISS – for the discrete impulsive ones with external disturbance inputs, are established. As applications, numerical examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Stability and stabilization of nonlinear discrete‐time stochastic systems

This paper mainly studies the locally/globally asymptotic stability and stabilization in probability for nonlinear discrete‐time stochastic systems. Firstly, for more general stochastic difference systems, two very useful results on locally and globally asymptotic stability in probability are obtained, which can be viewed as the discrete versions of continuous‐time Itô systems. Then, for a class of quasi‐linear discrete‐time stochastic control systems, both state‐ and output‐feedback asymptotic stabilization are studied, for which, sufficient conditions are presented in terms of linear matrix inequalities. Two simulation examples are given to illustrate the effectiveness of our main results.     

Dynamic self‐triggered output‐feedback control for nonlinear stochastic systems with time delays

In this paper, the dynamic self‐triggered output‐feedback control problem is investigated for a class of nonlinear stochastic systems with time delays. To reduce the network resource consumption, the dynamic event‐triggered mechanism is implemented in the sensor‐to‐controller channel. Criteria are first established for the closed‐loop system to be stochastically input‐to‐state stable under the event‐triggered mechanism. Furthermore, sufficient conditions are given under which the closed‐loop system with dynamic event‐triggered mechanism is almost surely stable, and the output‐feedback controller as well as the dynamic event‐triggered mechanism are co‐designed. Moreover, a dynamic self‐triggered mechanism is proposed such that the nonlinear stochastic system with the designed output‐feedback controller is stochastically input‐to‐state stable and the Zeno phenomenon is excluded. Finally, a numerical example is provided to illustrate the effectiveness of proposed dynamic self‐triggered output‐feedback control scheme.     

Constrained stabilization problems for discrete‐time linear plants

In this paper we study discrete‐time linear systems with full or partial constraints on both input and state. It is shown that the solvability conditions of stabilization problems are closely related to important concepts, such as the right‐invertibility of the constraints, the location of constraint invariant zeros and the order of constraint infinite zeros. The main results show that for right‐invertible constraints the order of constrained infinite zeros cannot be greater than one in order to achieve global or semi‐global stabilization. This is in contrast to the continuous‐time case. Controllers for both state feedback and measurement feedback are constructed in detail. Issues regarding non‐right invertible constraints are discussed as well. Copyright © 2004 John Wiley & Sons, Ltd.     

Event‐triggered optimal tracking control of nonlinear systems

We propose a novel event‐triggered optimal tracking control algorithm for nonlinear systems with an infinite horizon discounted cost. The problem is formulated by appropriately augmenting the system and the reference dynamics and then using ideas from reinforcement learning to provide a solution. Namely, a critic network is used to estimate the optimal cost while an actor network is used to approximate the optimal event‐triggered controller. Because the actor network updates only when an event occurs, we shall use a zero‐order hold along with appropriate tuning laws to encounter for this behavior. Because we have dynamics that evolve in continuous and discrete time, we write the closed‐loop system as an impulsive model and prove asymptotic stability of the equilibrium point and Zeno behavior exclusion. Simulation results of a helicopter, a one‐link rigid robot under gravitation field, and a controlled Van‐der‐Pol oscillator are presented to show the efficacy of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Fixed‐time sliding mode cooperative control for multiagent networks via event‐triggered strategy

In this article, the problem of event‐triggered‐based fixed‐time sliding mode cooperative control is addressed for a class of leader‐follower multiagent networks with bounded perturbation. First, a terminal integral sliding mode manifold with fast convergent speed is designed. Then, a distributed consensus tracking control strategy based on event‐triggered and sliding mode control is developed that guarantees the multiagent networks achieve consensus within a fixed time which is independent of initial states of agents in comparison with the finite‐time convergence. Furthermore, the update frequency of control law can be considerably reduced and Zeno behavior can be removed by utilizing the proposed event‐triggered control algorithm. Simulation examples are used to show the effectiveness of the new control protocol.     

Input‐to‐state exponents and related ISS for delayed discrete‐time systems with application to impulsive effects

This paper aims to investigate the input‐to‐state exponents (IS‐e) and the related input‐to‐state stability (ISS) for delayed discrete‐time systems (DDSs). By using the method of variation of parameters and introducing notions of uniform and weak uniform M‐matrix, the estimates for 3 kinds of IS‐e are derived for time‐varying DDSs. The exponential ISS conditions with parts suitable for infinite delays are thus established, by which the difference from the time‐invariant case is shown. The exponential stability of a time‐varying DDS with zero external input cannot guarantee its ISS. Moreover, based on the IS‐e estimates for DDSs, the exponential ISS under events criteria for DDSs with impulsive effects are obtained. The results are then applied in 1 example to test synchronization in the sense of ISS for a delayed discrete‐time network, where the impulsive control is designed to stabilize such an asynchronous network to the synchronization.     

Gain scheduled control for discrete‐time systems depending on bounded rate parameters

In this paper we consider a linear, discrete‐time system depending multi‐affinely on uncertain, real time‐varying parameters. A new sufficient condition for the stability of this class of systems, in terms of a feasibility problem involving linear matrix inequalities (LMIs), is obtained under the hypothesis that a bound on the rate of variation of the parameters is known. This condition, obtained by the aid of parameter dependent Lyapunov functions, obviously turns out to be less restrictive than that one obtained via the classical quadratic stability (QS) approach, which guarantees stability in presence of arbitrary time‐varying parameters. An important point is that the methodology proposed in this paper may result in being less conservative than the classical QS approach even in the absence of an explicit bound on the parameters rate of variation. Concerning the synthesis context, the design of a gain scheduled compensator based on the above approach is also proposed. It is shown that, if a suitable LMI problem is feasible, the solution of such problem allows to design an output feedback gain scheduled dynamic compensator in a controller‐observer form stabilizing the class of systems which is dealt with. The stability conditions are then extended to take into account L₂ performance requirements. Some numerical examples are carried out to show the effectiveness and to investigate the computational burden required by the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.