Impulse Interval Research Articles

New Stability Criterion for Positive Impulsive Fuzzy Systems by Applying Polynomial Impulse-Time-Dependent Method.

The problems of exponential stability and L1 -gain for positive impulsive Takagi-Sugeno (T-S) fuzzy systems are further studied in this article. Different from the Lyapunov function in the literature, where the Lyapunov matrices are time-invariant or only linearly dependent on the impulse interval, in this article, a novel polynomial impulse-dependent (ID) copositive Lyapunov function (CLF) is constructed by using the polynomial impulse time function. In addition, the binomial coefficients are applied to derive new finite linear programming conditions. Less conservative results are obtained since the polynomial ID CLF contains more impulse interval information. Three examples demonstrate the influence of the polynomial degree on the results and the effectiveness of the developed new results.

Sliding-mode-based impulsive control for a class of time-delay systems with input disturbance

This paper addresses the impulsive stabilization problem for a class of time-delay systems in the presence of input disturbances. A novel impulsive control law is constructed, which is based on the discrete-time equivalent control design technique. The sliding-mode-based impulsive control law allows counteracting the disturbance effect using its previous step value. To adapt in real time to the variation in sampling periods, the sliding function is designed as a function of impulse interval. Piecewise Lyapunov functions based on the partition on the maximum impulse interval are introduced to deal with the time-varying structure of the sliding function. Sufficient conditions for exponential input-to-state stability (EISS) of the impulsively controlled systems are derived, in which the EISS gain characterizes the attenuation ability of the proposed impulsive control law on the disturbance estimation error. The disturbance attenuation performance of the proposed impulsive control strategy is demonstrated through the time-delay Chua’s circuit.

Variable Gain Impulsive Synchronization for Discrete-Time Delayed Neural Networks and Its Application in Digital Secure Communication.

This article revisits the problems of impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks (DDNNs) in the presence of disturbance in the input channel. A new Lyapunov approach based on double Lyapunov functionals is introduced for analyzing exponential input-to-state stability (EISS) of discrete impulsive delayed systems. In the framework of double Lyapunov functionals, a pair of timer-dependent Lyapunov functionals are constructed for impulsive DDNNs. The pair of Lyapunov functionals can introduce more degrees of freedom that not only can be exploited to reduce the conservatism of the previous methods, but also make it possible to design variable gain impulsive controllers. New design criteria for impulsive stabilization and impulsive synchronization are derived in terms of linear matrix inequalities. Numerical results show that compared with the constant gain design technique, the proposed variable gain design technique can accept larger impulse intervals and equip the impulsive controllers with a stronger disturbance attenuation ability. Applications to digital signal encryption and image encryption are provided which validate the effectiveness of the theoretical results.

Stability of stochastic systems with semi-Markovian switching and impulses

The aim of this paper is to investigate the stochastic asymptotic stability of semi-Markov switched systems with mixed impulses. A novel definition of average impulse gain is given to estimate the intensity of the mixed impulses. Based on the multiple Lyapunov function approach and average impulse interval method, we provide sufficient conditions on the stochastic asymptotic stability for the semi-Markov switched system with impulses. Moreover, the influence of impulses on the system is estimated by applying the average impulse gain and average impulse interval method, which are not only suitable for synchronous impulses but also for asynchronous impulses. The theoretical results are demonstrated by two examples.

Event-triggered impulsive quasi-synchronization for BAM neural networks with reliable redundant channel

This work addresses the quasi-synchronization of delay master–slave BAM neural networks. To improve the utilization of channel bandwidth, a dynamic event-triggered impulsive mechanism is employed, in which data is transmitted only when a preset event-triggered mechanism or a forced impulse interval is satisfied. In addition, to guarantee the reliability of information transmission, a reliable redundant channel for BAM neural networks is adopted, whose transmission scheduling strategy is designed on the basis of the packet dropouts rate of the main communication channels. Further, an algorithm is employed to reduce the quasi-synchronization range of the error systems and the controllers are obtained. At last, a simulation result is shown to illustrate the effectiveness of the presented strategy.

Synchronization of time-delayed complex networks with delay-partitioning: A Chua’s circuit networks application

This article addresses the almost surely global exponential synchronization (ASGES) for complex networks in the delay-partitioning framework. Under impulsive control, by dividing impulse intervals and time delay, the information of the impulse intervals can be more fully utilized. Firstly, a novel type of Lyapunov functional is introduced by applying a practical switching law, which combines mode-dependent average dwell-time (MDADT) and transition probability (TP). The use of the partition method makes the relationship between the undelayed state and the delayed state can be better handled, delay-dependent stability criteria are established with less conservatism. Secondly, under the action of impulsive control and fault-tolerant control, a controller synthesis algorithm is provided. Moreover, a corollary extends the results to intermittent control. Finally, an example of Chua’s circuit networks is provided to illustrate the effectiveness of proposed method, which can obtain larger allowable time-delay.

Integral sliding mode control design for uncertain impulsive systems with delayed impulses

This paper addresses the integral sliding mode control (ISMC) problem of uncertain impulsive systems with delayed impulses. Firstly, an integral sliding surface with embedded impulse information is constructed, which is able to counteract the intermittent impact of delayed impulses. Then an ISMC law is designed to guarantee the finite-time reachability of the predefined sliding surface without special restriction on system dynamics. Secondly, two different types of linear control laws with switching gains are proposed to robustly stabilize the sliding mode dynamics. The first type is independent of the size of impulse delays, and is used to tackle the impulses with unknown bounded delays. The second type aims at providing impulse-delay-dependent stabilization algorithms under the assumption that the delays are smaller than the impulse intervals. In the situation where the upper bounds of the uncertainties are characterized by two unknown constants, an adaptive ISMC law is proposed to ensure the existence of sliding mode. Switching Lyapunov functions and the state augmentation technique are introduced to exploit the positive/negative effects of delayed impulses. Several tractable conditions for designing the switching gains and the sliding surfaces are derived in terms of linear matrix inequalities. Finally, three numerical examples are presented to show the effectiveness of the proposed control algorithms and highlight their merits.

Exponential stability of nonlinear systems via event-triggered impulsive control based on partial states

In the framework of partial unknown states, this paper studies the exponential stability problem of nonlinear systems. A novel event-triggered mechanism (ETM) just involving partial known states is designed to guarantee the exponential stability of considered system, where forced impulse with great freedom degree is introduced in ETM. What's more, the information of known states of the system is fetched and applied to supplement the unknown part at impulse instants. With the help of matrix analysis technique, some linear matrix inequalities (LMI) based sufficient conditions are presented from the perspective of the quantity of known and unknown states. Besides, our proposed conditions establish the relationship of event-triggered parameters, impulse interval, and impulse strength. Finally, expository examples and their numerical modeling are appeared to prove the availability of main results.

Synchronization of coupled switched neural networks subject to hybrid stochastic disturbances

In this paper, the theoretical analysis on exponential synchronization of a class of coupled switched neural networks suffering from stochastic disturbances and impulses is presented. A control law is developed and two sets of sufficient conditions are derived for the synchronization of coupled switched neural networks. First, for desynchronizing stochastic impulses, the synchronization of coupled switched neural networks is analyzed by Lyapunov function method, the comparison principle and a impulsive delay differential inequality. Then, for general stochastic impulses, by partitioning impulse interval and using the convex combination technique, a set of sufficient condition on the basis of linear matrix inequalities (LMIs) is derived for the synchronization of coupled switched neural networks. Eventually, two numerical examples and a practical application are elaborated to illustrate the effectiveness of the theoretical results.

Synchronization of neural networks involving unmeasurable states and impulsive disturbances by observer and feedback control

In this article, the problem of synchronization for neural networks is studied by way of the feedback control based on the state estimation even thought the existence of delayed impulsive disturbances which produce negative impacts on the control. Meanwhile, two cases are fully addressed, where drive neural networks and response neural networks involve unmeasurable states respectively. The key matters, which we settle, are the construction of the observer and the design of feedback control based on the state estimation, in the presence of delayed impulsive disturbances and unmeasurable states. By utilizing the linear matrix inequality (LMI) and the delayed impulsive differential inequality, certain adequate qualifications are gotten to ensure synchronization. Moreover, note that our proposed conditions not only drop the limitation of impulse intervals and impulse sizes, but also realize the coexistence of delayed impulses and macroscale impulses. Finally, expository examples and their numerical modeling are appeared to prove the availability of main results.

Designing Distributed Impulsive Controller for Networked Singularly Perturbed Systems

This paper develops a novel synthesis approach for synchronization of a network of singularly perturbed systems (SPSs) with a small singular perturbation parameter (SPP) <inline-formula><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> via distributed impulsive control. First, a decoupling method in the setting of directed networks is employed to decompose networked SPSs related to complex eigenvalues of the Laplacian matrix. Then, based on an improved piecewise continuous Lyapunov function, an <inline-formula><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula>-dependent synchronization criterion is established. The relationship among the impulse interval, the impulse gain matrix and <inline-formula><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> is revealed. By employing the newly-obtained synchronization criterion, sufficient conditions on the existence of an <inline-formula><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula>-dependent impulse gain matrix are derived. Finally, an example is simulated to verify the effectiveness of the theoretical results.

Robust exponential stability of discrete-time uncertain impulsive stochastic neural networks with delayed impulses

This paper is devoted to the study of the robust exponential stability (RES) of discrete-time uncertain impulsive stochastic neural networks (DTUISNNs) with delayed impulses. Using Lyapunov function methods and Razumikhin techniques, a number of sufficient conditions for mean square (RES-ms) robust exponential stability are derived. The obtained results show that the hybrid dynamic is RES-ms with regard to lower boundary of impulse interval if the discrete-time stochastic neural networks (DTSNNs) is RES-ms and that the impulsive effects are instable. Conversely, if DTSNNs is not RES-ms, impulsive effects can induce unstable neural networks (NNs) to stabilize again concerning an upper bound of the impulsive interval. The results obtained in this study have a broader scope of application than some previously existing findings. Two numerical examples were presented to verify the availability and advantages of the results.

Orbital Interception Pursuit Strategy for Random Evasion Using Deep Reinforcement Learning

Aiming at the interception problem of noncooperative evader spacecraft adopting random maneuver strategy in one-to-one orbital pursuit–evasion problem, an interception strategy with decision-making training mechanism for the pursuer based on deep reinforcement learning is proposed. Its core purpose is to improve the success rate of interception in the environment with high uncertainty. First of all, a multi-impulse orbit transfer model of pursuer and evader is established, and a modular deep reinforcement learning training method is built. Second, an effective reward mechanism is proposed to train the pursuer to choose the impulse direction and impulse interval of the orbit transfer and to learn the successful interception strategy with the optimal fuel and time. Finally, with the evader taking a random maneuver decision in each episode of training, the trained decision-making strategy is applied to the pursuer, the corresponding interception success rate of which is further analyzed. The results show that the pursuer trained can obtain universal and variable interception strategy. In each round of pursuit–evasion, with random maneuver strategy of the evader, the pursuer can adopt similar optimal decisions to deal with high-dimensional environments and thoroughly random state space, maintaining high interception success rate.

Impulsive Boundedness for Nonautonomous Dynamic Complex Networks with Constraint Nonlinearity

This paper discusses time-scale type global boundedness of nonautonomous complex networks (NCNs) under impulsive control. By using constraint nonlinearity of NCNs, properties of exponential function and impulsive inequalities, we establish new sufficient conditions for global boundedness and asymptotic stability of NCNs on time scales, and the upper bound of the system can be calculated easily. It is shown that the constraint nonlinearity and impulse interval length will affect the estimation of state bound of NCNs under different network size. It provides a unified criteria for global boundedness of NCNs on continuous, discrete and mixed-time domains and hence improves corresponding existing ones. The nonlinear constraints studied in this paper are widely applied to Lurie systems, ball motion models and so on. Numerical examples are given to illustrate the correctness of the results. Finally, the theoretical results are applied to Lurie systems and bounded driving of unmanned vehicles.

Stabilization Analysis and Impulsive Controller Design for Positive Interval Type-2 Polynomial Fuzzy Systems

This article investigates the polynomial fuzzy impulsive control problem for positive nonlinear systems subject to parameter uncertainties. The positive nonlinear systems are represented as positive interval type-2 (IT2) polynomial fuzzy-model-based systems, while the parameter uncertainties are captured by the IT2 membership functions (MFs). Considering that the controller being designed needs to be implementable and practical, in addition to ensuring the positivity and stability of the system, there are still some potential requirements for the controller, such as lower implementation cost and control cost. To reduce the implementation cost, the IT2 polynomial fuzzy impulsive controller is designed under the imperfect premise matching concept that the premise MFs and the number of rules of fuzzy controller are different from those of fuzzy model. To reduce the control cost, the impulsive controller that can tolerate larger impulse control interval (ICI) is designed by the following two novel methods. The first one is the proposed impulse-time-dependent discretized polynomial copositive Lyapunov function whose Lyapunov variable is designed as the interpolation polynomial function of time. The second one is the advanced IT2 membership-function-dependent (IT2MFD) analysis method which is improved by a novel footprint of uncertainty partitioning method proposed by this paper, so that this advanced IT2MFD method can alleviate the negative impact of parameter uncertainties on the ICI. Finally, a simulation example using lipoprotein metabolism and potassium ion transfer model as the nonlinear system to be controlled is used to verify the effectiveness of the proposed impulsive control methods.

Input-to-State Stabilization of Nonlinear Impulsive Delayed Systems: An Observer-Based Control Approach

This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous disturbances. Since the information of plant's states, time delays, and exogenous disturbances is often hard to be obtained, the key design challenge, which we resolve, is the construction of a state observer-based controller. For this purpose, we firstly propose a corresponding observer which is independent of time delays and exogenous disturbances to reconstruct (or estimate) the plant's states. And then based on the observations, we establish an observer-based control design for the plant to achieve the input-to-state stability (ISS) and integral-ISS (iISS) properties. With the help of the comparison principle and average impulse interval approach, some sufficient conditions are presented, and moreover, two different linear matrix inequalities (LMIs) based criteria are proposed to design the gain matrices. Finally, two numerical examples and their simulations are given to show the effectiveness of our theoretical results.

Performance analysis of impulsive station-keeping strategies for cis-lunar orbits with the ephemeris model

Future long-term lunar missions, such as cis-lunar space stations and communication/navigation constellations, have been proposed by different space agencies. For such long-term missions, reliable station-keeping strategies are of great importance to counteract unfavourable effects of perturbations, navigation errors, etc. In this study, representative cis-lunar orbits with favourable characteristics, including near rectilinear halo orbits (NRHOs), distant retrograde orbits (DROs), and halo orbits, are considered as nominal orbits of long-term lunar missions for station-keeping analysis. Both the target point method and the discrete linear quadrant regulator (DLQR) control are applied to these nominal orbits in the ephemeris model. Under some practical constraints caused by the navigation and orbital control systems, Monte-Carlo simulations are carried out to evaluate performances of the station-keeping strategies. Then, effects of solar radiation pressure (SRP) and nonspherical lunar gravity on the station-keeping performances are demonstrated by Monte-Carlo simulations with low-fidelity nominal orbits constructed in ephemeris models without SRP or nonspherical lunar gravity. Finally, comparisons between different impulse intervals are made to find the balance between the station-keeping cost and position deviation. It is found that the stability index of the nominal orbit has no direct effect on the station-keeping cost, but plays an important role in the selection of the impulse interval. The DROs and NRHOs allow a much longer impulse interval than the unstable halo orbits. The results can provide useful references for selections of the nominal orbit and station-keeping strategy in future long-term lunar missions.

Global [formula omitted]-synchronization for nonlinear complex networks with unbounded multiple time delays and uncertainties via impulsive control

The global μ-synchronization problem of nonlinear drive–response complex networks with uncertainties is investigated in this paper. Unbounded multiple time delays, such as internal delays, coupling delays, and sampling delays in impulse instants are considered in our complex network model. The difficulties caused by these multiple time delays are overcome by introducing a generalized impulsive delayed comparison principle. A delayed impulsive controller is designed, and some novel synchronization criteria are derived in order to make drive–response complex networks achieve μ-synchronization. Compared with the existing related works, there is no restriction about impulse intervals and delays, as well as, the external coupling matrix is no longer needed to satisfy the dissipative coupling condition. Finally, two numerical simulations are shown to present the correctness of our theoretical results.

Pinning impulsive synchronization of two-layer heterogeneous delayed networks

This article mainly investigates pinning impulsive synchronization of the two-layer delayed network with unidirectional interlayer coupling and transmission delays. The intralayer topologies of different layers are independent each other, and the nodal dynamics in each layer are different as well. Using the Lyapunov stability theory and the auxiliary system method, several pinning impulsive strategies for guaranteeing interlayer generalized synchronization of two-layer delayed networks are put forward. When the impulse interval is fixed as a constant value, the smallest number of pinned nodes and largest impulse interval needed theoretically for ensuring interlayer generalized synchronization are obtained. Specially, when the impulse strengths, the impulse interval, and the number of pinned nodes are respectively set to constant values independent of the impulsive instant, the influences of these parameters on the synchronized region are further discussed. Furthermore, it is found that the relatively small interlayer transmission delay is beneficial to interlayer generalized synchronization. Numerical simulations are presented to verify the effectiveness and correctness of the proposed schemes.

A refined discretized timer-dependent Lyapunov functional for impulsive delay systems

A new type of discretized Lyapunov functional is introduced for stability and hybrid L2×l2-gain analysis of linear impulsive delay systems. This functional consists of three parts. The first part is the conventional discretized functional for delay-independent stability analysis. The second part is the looped-functionals-like functional for exploiting the internal structure inside impulse intervals, in which the decision matrix functions are approximated by piecewise linear matrix functions. The third part is a discretized adjustive factor, which makes the proposed Lyapunov functional continuous along the system trajectories. Thanks to this continuity, the resultant criteria for exponential stability and finite hybrid L2×l2-gain are expressed in terms of a combination of the continuous and discrete parts of the system. It is shown through numerical examples that the accuracy of the stability test increases with the increase of the partition number on impulse intervals, and the convergence rate is faster than that of the previous discretized functionals-based approach.