Event-triggered delayed impulsive control for input-to-state stability of nonlinear impulsive systems

This paper studies the input-to-state stability (ISS) and integral input-to-state stability (iISS) of nonlinear impulsive systems in the framework of event-triggered impulsive control (ETIC), where the stabilizing effect of time delays in impulses is fully considered. Some sufficient conditions which can avoid Zeno behavior and guarantee the ISS/iISS property of impulsive systems are proposed, where external inputs are considered in both the continuous dynamics and impulsive dynamics. A novel event-triggered delayed impulsive control (ETDIC) strategy which establishes a relationship among event-triggered parameters, impulse strength and time delays in impulses is presented. It is shown that time delays in impulses can contribute to the stabilization of impulsive systems in ISS/iISS sense. Finally, the effectiveness of the proposed theoretical results is illustrated by two numerical examples.     

A simple self-triggered sampler for perturbed nonlinear systems

Self-triggered control is a recent design paradigm for resource-constrained networked control systems. By allocating aperiodic sampling instances for a digital control loop, a self-triggered controller is able to utilize network resources more efficiently than conventional sampled-data systems. In this paper we propose a self-triggered sampler for perturbed nonlinear systems ensuring uniformly ultimately boundedness of trajectories. Robustness and time delays are considered. To reduce conservativeness, a disturbance observer for the self-triggered sampler is proposed. The effectiveness of the proposed method is shown by simulation.     

Event-triggered impulsive control of lower-triangular large-scale nonlinear systems based on gain scaling technique

This paper investigates the event-triggered impulsive control problem for a class of large-scale nonlinear systems in lower-triangular form. Based on gain scaling technique and impulsive control theory, a novel decentralized event-triggered impulsive control strategy is first put forward by introducing a static scaling gain, where no control input exists between two consecutive triggering points. Moreover, when the large uncertainties exist in system nonlinearities, we further develop a new control strategy by introducing a time-varying scaling gain. It is proved that the proposed closed-loop control strategies exclude the Zeno behavior without sacrificing the global convergence of system states. Compared with the existing results, it is the first time to apply impulsive control to lower-triangular large-scale nonlinear systems, and the advantages of event-triggered impulsive control and gain scaling technique are subtly combined in the proposed control strategies. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed schemes.     

Hybrid event-triggered and impulsive control for time-delay systems

In this paper, we study the problem of hybrid event-triggered control for a class of nonlinear time-delay systems. Using a Razumikhin-type input-to-state stability result for time-delay systems, we design an event-triggered control algorithm to stabilize the given time-delay system. In order to exclude Zeno behavior, we combine the impulsive control mechanism with our event-triggered strategy. In this sense, the proposed algorithm is a hybrid impulsive and event-triggered strategy. Sufficient conditions for the stabilization of the nonlinear systems with time delay are obtained by using Lyapunov method and Razumikhin technique. Numerical simulations are provided to show the effectiveness of our theoretical results.     

Event-triggered sliding mode control for singular systems with disturbance

This paper investigates the event-triggered sliding mode control (SMC) problem for singular systems with disturbance. Firstly, an event-triggered sliding mode control law is designed to guarantee the reachability of sliding surface. Different from the related methods, in order to deal with the difficulty caused by event-triggered SMC strategy, a novel Lemma is proposed in this paper. Secondly, the admissibility of sliding motion is presented, which is used to solve the controller gain. Then, a positive lower bound of the inter execution time can be guaranteed and the Zeno behavior is avoided. Finally, two simulation examples are presented to show the effectiveness of derived theoretical results.     

Event-triggered dual-mode predictive control for constrained nonlinear systems with continuous/intermittent detection

This paper investigates the problem of event-triggered model predictive control for constrained nonlinear systems. A dual-mode control strategy combined with two different event-triggered mechanisms are introduced to reduce computational and communication loads. For the event-triggered mechanisms, two cases, continuous detection and intermittent detection, are considered, respectively. In order to avoid the transmission of continuous predicted control input trajectories, the actual control signals are generated under a sample-and-hold manner. A decreasing prediction horizon is introduced to reduce the complexity of optimization problems and a tightened state constraint is designed to achieve robust constraint satisfaction. The sufficient conditions are derived to guarantee the feasibility and stability of the closed-loop system. The performance of the proposed strategy is illustrated by a simulation example.     

Distributed impulsive control consensus for a class of unknown nonlinear multi-agent systems based on event-triggered scheme

In this study, we are concerned with the impulsive consensus control problem for a class of nonlinear multi-agent systems (MASs) which have unknown dynamics and directed communication topology. The neural networks (NNs) method is the first utilized to construct distributed event-triggered impulsive consensus protocol. In contrast to the existing impulsive consensus protocol, the consensus protocol proposed in this paper does not need the dynamics of agents, which enhances the system robustness, and realizes distributed event-triggered communication between agents, which can reduce unnecessary consumption of communication resources. Sufficient conditions are derived to ensure the consensus of the controlled MASs and the exclusion of Zeno-behavior. Finally, simulation examples are presented to illustrate the effectiveness of the proposed control protocol.     

Dynamic periodic event-triggered gain-scheduling control co-design for quasi-LPV systems

This paper investigates dynamic periodic event-triggered gain-scheduling control co-design for nonlinear systems subject to disturbances. The considered class of nonlinear systems is such that an equivalent polytopic quasi-LPV model is obtained. Based on the co-design approach, gain-scheduled control law and dynamic event-triggering mechanism (ETM) are jointly designed. The proposed co-design condition is formulated in terms of linear matrix inequality (LMI) conditions which are derived from the Bessel–Legendre inequality and the delay-dependent reciprocally convex combination lemma. As the state information is available to the gain-scheduled controller at specific instants determined by the ETM, it induces the asynchronous phenomenon between the parameters of the controller and the plant’s quasi-LPV model. To reduce the conservativeness induced by this asynchronous phenomenon, an LMI relaxation is proposed. Numerical examples illustrate the advantages of the proposed dynamic periodic event-triggered control co-design approach over its static counterpart.     

Self-triggered impulsive control of nonlinear time delay systems: Application to chemotherapeutic dose-regimen design

This paper proposes a self-triggered impulsive control for nonlinear time-delay systems, where the time instant of the next impulsive input is calculated based on the last measurement and the values of the systems’ parameters. Contrary to event-triggered scheme where the actuation is discrete but a continuous monitoring of the system’s states is necessary, in the self-triggered approach, both sampling and actuation are performed at distinct moments of time. Utilizing Lyapunov–Razumikhin method and by upper-bounding the system’s trajectory, the global asymptotic stability of the system’s equilibrium is verified when the rate of change in the Lyapunov function is exponential. In the general case, the global ultimate boundedness of the system’s trajectory is shown where the ultimate bound can be set arbitrarily small. As an application, for the first time, the problem of dose regimen design is formulated in the sampled data framework. Then, based on the obtained theoretical results, the appropriate regimen is suggested. In particular, time-triggered and self-triggered therapy protocols for docetaxel, a phase specific chemotherapeutic drug which is administered intravenously, are proposed. Clinical constraints such as maximum tolerated dose, discontinuous drug administration, and intermittent measurements are met in the proposed therapy protocols. According to in-silico results, both proposed self-triggered and time-triggered dose regimens outperform the traditional weekly fixed dose administration. Finally, the robustness of the proposed schemes to parameter uncertainties is evaluated through an extensive set of simulations.     

Variable impulsive consensus of nonlinear multi-agent systems

In this paper, the consensus problem for nonlinear multi-agent systems with variable impulsive control method is studied. In order to decrease the communication wastage, a novel distributed impulsive protocol is designed to achieve consensus. Compared with the common impulsive consensus method with fixed impulsive instants, the variable impulsive consensus method proposed in this paper is more flexible and reliable in practical application. Based on Lyapunov stability theory and some inequality techniques, several novel impulsive consensus conditions are obtained to realize the consensus of multi-agent systems. Finally, some necessary simulations are performed to validate the effectiveness of theoretical results.     

Stability analysis of impulsive control systems

This paper studies impulsive control systems. Several stability criteria are established by employing the method of Lyapunov functions. These criteria may be used for impulsive feedback control design. As an application, impulsive control of the Lorenz chaotic system is discussed. Numerical experiments are carried out for the control of the Lorenz system. It is shown that small and frequent impulses need to be used in order to stabilize the Lorenz system.     

Synchronization of quaternion-valued coupled systems with time-varying coupling via event-triggered impulsive control

In this paper, the problem of exponential synchronization of quaternion-valued coupled systems based on event-triggered impulsive control is investigated for the first time. It should be pointed out that the coupling strength is quaternion-valued and time-varying, which makes our model more in line with practical models. First, we prove that event-triggered impulsive control can exclude Zeno behavior. Then, based on the Lyapunov method and the graph theory, some sufficient conditions are derived to ensure that quaternion-valued coupled systems reach synchronization. Furthermore, as an application of our theoretical results, exponential synchronization of quaternion-valued Kuramoto oscillators is studied in detail and a synchronization criterion is presented. Finally, some numerical simulations are given to show the effectiveness of our theoretical results.     

Resource limited event-triggered model predictive control for continuous-time nonlinear systems based on first-order hold

This paper investigates a resources-limited situation in the event-triggered model predictive control (ETMPC) for continuous-time nonlinear system with first-order hold fashion. In consideration of limited bandwidth in data transmission through wireless network under actual operation, our strategy divides the prediction horizon, and applies linear interpolation instead of zero-order hold fashion to obtain a better system performance, so that the reduction of resources and the optimization of strategy can be guaranteed. Furthermore, in actual industry processes, quadratic cost function cannot be implemented in all operations, then general cost function is adopted in this paper. Based on the first-order hold method and general cost function, the feasibility of the ETMPC algorithm and the stability of dynamical systems are analyzed. At last, a practical example is given to show the advantages of our method.     

Event-triggered feedback stabilization of switched linear systems using dynamic quantized input

This paper is concerned with the co-design of event-triggered sampling, dynamic input quantization and constrained switching for a switched linear system. The mismatch between the plant and its corresponding controller is considered. This behavior is raised by switching within the event-triggered sampling interval. Accordingly, novel update laws of dynamic quantization parameter are designed separately for matched sampling intervals (without switching) and mismatched sampling intervals (with a switch). We technically transform the total variation (increment or decrement) of Lyapunov functions in one sampling interval into the discrete-time update of quantization parameter. Based on this transformation, a hybrid quantized control policy is developed. This policy, in conjunction with the average dwell-time switching law and the constructed event-triggered condition, can ensure the exponential stabilization of the switched system with finite-level quantized input. Besides, the event-triggered scheme is proved to be Zeno-free. The effectiveness of the developed method is verified by a simulation example.     

Optimal control of impulsive hybrid systems

In this paper, we deal with optimization techniques for a class of hybrid systems that comprise continuous controllable dynamics and impulses (jumps) in the state. Using the mathematical techniques of distributional derivatives and impulse differential equations, we rewrite the original hybrid control system as a system with autonomous location transitions. For the obtained auxiliary dynamical system and the corresponding optimal control problem (OCP), we apply the Lagrange approach and derive the reduced gradient formulas. Moreover, we formulate necessary optimality conditions for the above hybrid OCPs, and discuss the newly elaborated Pontryagin-type Maximum Principle for impulsive OCPs. As in the case of the conventional OCPs, the proposed first order optimization techniques provide a basis for constructive computational algorithms.     

Self-triggered filter design for a class of nonlinear stochastic systems with Markovian jumping parameters

This paper is concerned with the self-triggered filtering problem for a class of Markovian jumping nonlinear stochastic systems. The event-triggered mechanism (ETM) is employed between the sensor and the filter to reduce unnecessary measurement transmission. Governed by the ETM, the measurement is transmitted to the filter as long as a predefined condition is satisfied. The purpose of the addressed problem is to synthesize a filter such that the dynamics of the filtering error is bounded in probability (BIP). A sufficient condition is first given to ensure the boundedness in probability of the filtering error dynamics, and the characterization of the desired filter gains is then realized by means of the feasibility of certain matrix inequalities. Furthermore, a self-triggered mechanism is designed to guarantee the filtering error dynamics to be BSP with excluded Zeno phenomenon. In the end, numerical simulation is carried out to illustrate the usefulness of the proposed self-triggered filtering algorithm.     

Impulsive control for differential systems with delay

This paper deals with the impulsive control for a class of differential systems with delay. Using Lyapunov functions and the comparison principle, we present some sufficient conditions for the asymptotic stability and exponential stability of impulsive control systems with delay. Moreover, we give an estimate of the upper bound of impulse interval. The results in this paper extend and improve the earlier publications. Copyright © 2012 John Wiley & Sons, Ltd.     

Lyapunov stability for impulsive control affine systems

This article studies several notions of Lyapunov stability for impulsive control affine systems in the setting of nonautonomous dynamical systems. It presents some relations between the stability of an impulsive control affine system and the stability of its adjacent control system. Stability of compact sets and their components are specially investigated. Lyapunov functionals are employed to characterize each type of stability of closed sets.     

Stability and boundedness of nonlinear impulsive systems in terms of two measures via perturbing Lyapunov functions

This paper develops the concepts of stability, practical stability and boundedness in terms of two measures for nonlinear impulsive differential systems using the method of perturbing Lyapunov functions. The notion of perturbing Lyapunov functions enables us to discuss stability properties of solutions of nonlinear impulsive differential systems in terms of two measures under much weaker assumptions. The novel results offer a way to unify a variety of stability results found in the relative literature.