Impulsive Control Algorithm Research Articles

Quasi-Synchronization of Discrete-Time-Delayed Heterogeneous-Coupled Neural Networks via Hybrid Impulsive Control.

This article explores the quasi-synchronization of discrete-time-delayed heterogeneous-coupled neural networks (CNNs) via hybrid impulsive control. By introducing an exponential decay function, two non-negative regions are introduced that are named time-triggering and event-triggering regions, respectively. The hybrid impulsive control is modeled by the dynamical location of Lyapunov functional in two regions. When the Lyapunov functional locates in the time-triggering region, the isolated neuron node releases impulses to corresponding nodes in a periodical manner. Whereas, when the trajectory locates in the event-triggering region, the event-triggered mechanism (ETM) is activated, and there are no impulses. Under the proposed hybrid impulsive control algorithm, sufficient conditions are derived for quasi-synchronization with a definite error convergence level. Compared with pure time-triggered impulsive control (TTIC), the proposed hybrid impulsive control method can effectively reduce the times of impulses and save communication resources on the premise of ensuring performance. Finally, an illustrative example is given to verify the validity of the proposed method.

Bipartite event-triggered impulsive output consensus for switching multi-agent systems with dynamic leader

This paper studies the output consensus of heterogeneous switching linear multi-agent systems (LMASs). The considered switching topology in a signed graph is jointly connected. An event-triggered impulsive control algorithm is proposed, in which the event-triggered time sequence is allowed to be different from the impulsive sequence. Specifically, the leader’s control inputs in the LMASs model are allowed to be designed for the followers. In a fully distributed manner, a general compensator consisting of an impulsive and dynamic event-triggered mechanism is proposed to estimate the state of the leader. Based on the designed compensator and observer, a distributed control law is proposed to realize the bipartite output consensus by using an iterative method. Under the event triggering strategy, the combined measurement method is used, so that each agent only needs to update input information at the moment of its event triggering. Finally, our theoretical results are demonstrated through a numerical example.

Distributed Impulsive Control for Signed Networks of Coupled Harmonic Oscillators With Sampled Positions

This article considers the distributed impulsive control problem for a signed network composed by coupled harmonic oscillators based on relative position data, where the topology graph can be either structurally balanced or unbalanced, consisting of positive and negative links. First, an impulsive control algorithm is proposed for the network by utilizing both current and previous sampled positions. A necessary and sufficient condition is established such that the impulsive-controlled network can exhibit convergent behaviors, including bipartite synchronization, interval bipartite synchronization, and global stabilization. Second, some discussions are further provided to analyze two additional impulsive control algorithms designed with either current or previous sampled positions, in which it is shown that the former algorithm cannot lead to the convergent behaviors of the network, while the latter algorithm can solve the distributed impulsive control problem of the network under some appropriate conditions. Finally, simulation examples are given to illustrate the theoretical analysis.

Chaos Suppression in a Gompertz-like Discrete System of Fractional Order

In this paper, we introduce the fractional-order variant of a Gompertz-like discrete system. The chaotic behavior is suppressed with an impulsive control algorithm. The numerical integration and the Lyapunov exponent are obtained by means of the discrete fractional calculus. To verify numerically the obtained results, beside the Lyapunov exponent, the tools offered by the 0-1 test are used.

Distributed leaderless impulsive consensus of non-linear multi-agent systems with input saturation

This paper aims to propose dynamic consensus protocols for a class of non-linear saturated multi-agent systems. Due to the existence of non-linear dynamics of each agent, the system does not satisfy the condition named asymptotically null controllable with bounded controls (ANCBC). As a result, the widely-adopted method of low-gain feedback to solve consensus control problems for linear multi-agent systems with input saturation cannot be used. To step back, even if the system is linear and meets the ANCBC condition, the existing low-gain method or that combined with adaptive method can only make the system eventually reach zero consensus, which is unable to bring the system to dynamic consensus. In addition, from the view of energy conservation, this study proposes the impulsive control method to reduce the energy consumption of the controller. By taking advantages of the stability theory of impulsive systems, as well as the properties of Laplacian matrix and convex hull, corresponding distributed dynamic consensus protocols are proposed. Still, the shape reference set is introduced to assess the attraction domain of the leaderless MASs. Finally, the performance of the proposed anti-saturation impulsive control algorithm is demonstrated by extensive numerical experiments.

Chaos control in the fractional order logistic map via impulses

In this paper the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of fractional order is considered in terms of Caputo delta fractional difference. Every $\Delta$ steps, the state variable is instantly modified with the same impulse value, chosen from a bifurcation diagram versus impulse. It is shown that the solution of the impulsive control is bounded. The numerical results are verified via time series, histograms, and the 0-1 test. Several examples are considered

Dynamic consensus of nonlinear time-delay multi-agent systems with input saturation: an impulsive control algorithm

This paper aims to solve the dynamic consensus problem for a class of nonlinear multi-agent systems with input saturation and time delay. Due to the existing nonlinearity of the system, the low-gain feedback method widely used to handle saturation in multi-agent systems is no longer applicable. Moreover, to reduce both the communication and control energy consumption, an impulsive control algorithm is designed. Based on the stability theory of impulsive systems, as well as the property of the Laplacian matrix and convex hull, the set invariance conditions in the format of LMI are obtained. In addition, an optimization method is proposed for simultaneously designing the control parameters and assessing the attraction domain. Finally, the performance of the proposed consensus algorithms is demonstrated by two numerical experiments.

Formation Design of Distributed Telescopes in Earth Orbit for Astrophysics Applications

This paper presents a new formation design that enables deployment of large distributed telescopes aligned with inertial targets in Earth orbit. To minimize propellant consumption, the proposed design uses a two-phase operations concept including observations and formation reconfigurations. During observations, a quasi-continuous control system negates the relative acceleration perpendicular to the line of sight, allowing the interspacecraft separation to passively drift. After each observation, a formation reconfiguration is performed to ensure proper alignment with the target at the start of the next observation. Absolute and relative orbits that minimize the total delta-v cost of a specified mission profile are derived in closed-form including effects of perturbations such as Earth oblateness. Additionally, a new stochastic model predictive control architecture is proposed that uses an optimal impulsive control algorithm to efficiently control the formation. The performance and value of the proposed formation design are demonstrated through high-fidelity simulations of a reference mission to image the exoplanet AEgir using a small starshade and telescope. The results of these simulations demonstrate both that the proposed formation design globally minimizes the delta-v cost of the mission and that the mission is feasible with current propulsion technologies.

Quasi-Synchronization of Delayed Memristive Neural Networks via a Hybrid Impulsive Control

This paper investigates the quasi-synchronization of delayed memristive neural networks (MNNs) via a novel hybrid impulsive control algorithm which combines time-triggered and event-triggered impulsive control. The relationship between a predesigned non-negative auxiliary function and a given exponentially decreasing threshold function is used to describe the switching. Under this novel controller, sufficient conditions for the quasi-synchronization are derived by the impulsive differential inequality. In addition, by choosing appropriate parameters or initial conditions such that the initial value of the non-negative auxiliary function is less than that of the event-triggered function, the quasi-synchronization can be realized theoretically as long as the event-triggered impulsive intensity is less than 1. This greatly reduces the conservatism of the existing quasi-synchronization results. Furthermore, the event-triggered rules can avoid the Zeno behavior as long as the event-triggered impulsive intensity is less than 1. This hybrid mechanism can reduce the amount of impulsive control and lessen the network communication. Finally, one example is given to illustrate the validness of the obtained results.

Switching and impulsive control algorithms for nonlinear hybrid dynamical systems

Control algorithms are developed for physical processes modeled as hybrid dynamical systems (HDSs). In this framework, a HDS is a nonlinear switched system of ordinary differential equations (ODEs) coupled with impulsive equations. Switching and impulsive control is applied with two performance goals in mind: First, a high-frequency switching control method is provided to drive a HDS state to the origin while only requiring the HDS state intermittently. Attractivity of the origin is proved under a shell bisection algorithm; a high-frequency switching control rule is designed for this purpose. Second, a state-dependent switching control strategy is derived for when the transient behavior of the HDS is of interest. Finite-time stabilization is guaranteed under a so-called minimum rule algorithm; for each HDS mode, the state space is divided into different control regions and a switching control rule is constructed to switch between controllers whenever a boundary is reached. The theoretical tools used in this article include the Campbell–Baker–Hausdorff formula, multiple Lyapunov functions, and average dwell-time conditions.

Distributed impulsive control for islanded microgrids with variable communication delays

This study develops a new droop-based secondary distributed control strategy with hybrid dynamical form for the islanded microgrids (MGs). Two impulsive control algorithms containing time-varying delays are designed, under which the frequency and voltage restoration and active power sharing accuracy of all distributed generators can be realised with an exponential convergence speed. Compared to the traditional continuous or discrete-time distributed algorithms, the designed impulsive controllers formulate the controlled MG to be a hybrid dynamics, which are more general and applicable for practical power systems. Moreover, some delay-dependent sufficient conditions on the requirements for sparse communication network and impulsive time intervals are derived, in which the time delays do not need to be less than the length of the impulsive intervals. Simulation results on the control parameter analysis, and communication network topologies validates the developed theories.

Impulsive coordination of nonlinear multi-agent systems with multiple leaders and stochastic disturbance

This paper studies the coordination of nonlinear multi-agent systems with multiple leaders and stochastic disturbance. Two impulsive control algorithms are proposed to make all agents to track the convex set determined by the multiple leaders under both fixed and switching topologies. Based on Lyapunov function and comparison principle of impulsive systems, some results on the convergence of the controlled systems are obtained. Finally, some numerical simulations demonstrate the validity of the proposed control algorithms.

Pinning impulsive control algorithms for complex network

In this paper, we further investigate the synchronization of complex dynamical network via pinning control in which a selection of nodes are controlled at discrete times. Different from most existing work, the pinning control algorithms utilize only the impulsive signals at discrete time instants, which may greatly improve the communication channel efficiency and reduce control cost. Two classes of algorithms are designed, one for strongly connected complex network and another for non-strongly connected complex network. It is suggested that in the strongly connected network with suitable coupling strength, a single controller at any one of the network's nodes can always pin the network to its homogeneous solution. In the non-strongly connected case, the location and minimum number of nodes needed to pin the network are determined by the Frobenius normal form of the coupling matrix. In addition, the coupling matrix is not necessarily symmetric or irreducible. Illustrative examples are then given to validate the proposed pinning impulsive control algorithms.