Static group synchronization of second-order multi-agent systems via pinning control

This paper investigates the expected static group synchronization problem of the second-order multi-agent systems via pinning control. For directed communication topology with spanning tree, based on Gershgorin disk theorem and the matrix property, a static pinning control protocol with fixed gains is first introduced and some sufficient and necessary static group synchronization criteria are also established. It is worth mentioning that a rigorous proof is also given that only one pinning node is needed to guarantee static group synchronization, which could be inferred that our protocol might be more economical and effective in large scale of multi-agent systems. Then, for weakly connected directed communication topology with nodes of zero in-degree, an adaptive pinning control applied to the node with zero in-degree is also proposed to achieve static group synchronization. Finally, the efficiency of the proposed protocols is verified by two simulation examples.     

Containment control of singular heterogeneous multi-agent systems

In this paper, we first consider the containment control problem of singular heterogeneous multi-agent systems, where all the followers converge to the convex hull spanned by the leaders. To solve this problem, we propose two distributed control laws: one is based on the state feedback control framework, which is suitable for the case that the full state information of each follower is accessible; and the other is based on the output regulation framework, where each follower only can access to its output. Furthermore, the distributed observers are designed for every follower to estimate the convex combination of the leader states which is determined by the communication graph. It should be noted that our results can also regard the non-singular multi-agent systems’ containment control problem as a special case. Finally, simulation results corroborate the effectiveness of our analytical results.     

Containment control of fractional-order multi-agent systems with time-varying delays

In this paper, containment control problems of networked fractional-order multi-agent systems with time-varying delays are studied. The normalized directed graphs are employed to characterize the communication topologies. Two sampled-data based containment control protocols are proposed, which can overcome the time-varying delays and switching topologies. It is interestingly found that the decays of the closed-loop systems correspond to the Mittag-Leffler function and its approximation, which are the extensions of the exponential function and its approximation, respectively. Based on the algebraic graph theory, the properties of row-stochastic matrix, and the relation between the topologies and the matrices, some conditions for containment control are established. For the fixed topology, a necessary and sufficient condition is obtained; and for the switching topology, a sufficient condition is provided. Finally, the theoretical results are illustrated by several numerical simulations.     

Containment control for second-order nonlinear multi-agent systems with aperiodically intermittent position measurements

In some real systems, the intermittent communications and the inaccurate velocity measurements are usually inevitable. To overcome these two communication limitations, this article aims at investigating the containment control problem for a class of second-order multi-agent systems with inherent nonlinear dynamics and aperiodically intermittent position measurements. Under the case that the velocity information is unavailable, a distributed filter is introduced for each second-order follower. Based on the distributed filter, a novel intermittent containment control protocol without velocity measurements is designed. Some sufficient conditions are derived under the common assumption that only relative position measurements between the neighbouring agents are utilized intermittently, and these conditions ensure that the second-order nonlinear multi-agent systems can achieve containment control. Furthermore, some simpler containment conditions are obtained for multi-agent systems with double-integrator dynamics under aperiodically intermittent communications. Finally, numerical simulations are provided to verify the effectiveness of the theoretical results.     

Fractional-order follower observer design for tracking consensus in second-order leader multi-agent systems: Periodic sampled-based event-triggered control

This paper investigates the tracking consensus problem for the second-order leader systems by designing fractional-order observer, where a periodic sampled-based data event-triggered control is employed. In order to track the position information of leader, observers for followers are designed by fractional-order system, where only the relative position information is available. Furthermore, in the process of observers design, a sampled-based event-triggered strategy is proposed so that observers use the event-triggered sampled-data, to reduce the overall load of the network. In our proposed event-triggered strategy, the event detection only works at every sampling time instant which determines whether the sampled-data should be discarded or used. Under this control strategy, the Zeno-behavior is absolutely excluded since the minimum of inter-event times is inherently lower bounded by one sampling period. It is found that the followers can track state of the leader if fractional-order observers are appropriately designed and relevant parameters are properly selected. By using the generalized Nyquist stability criterion, a necessary and sufficient condition for the observer tracking consensus of the second-order leader systems is derived. The results show that the real and imaginary parts of the eigenvalues of the augmented Laplacian matrix, and fractional-order α of observer play a vital role in reaching consensus.     

Leaderless and leader-following consensus of linear multi-agent systems with distributed event-triggered estimators

This paper considers the event-triggered leaderless and leader-following consensus problems for linear multi-agent systems. By introducing event-triggered estimators, two novel control schemes are proposed. Different from the existing event-triggered controllers, which rely on the Fiedler eigenvalue of Laplacian matrix, the developed controllers only use the information from neighboring agents. Meanwhile, the adaptive trigger parameters are designed in the event-triggered mechanisms to improve the self-regulation ability of the event-triggered estimators. In addition, the leaderless consensus and the leader-following consensus can be achieved under the corresponding control protocols. Finally, two simulation examples are given to illustrate the validity of the proposed control protocols.     

A new Lyapunov functional approach to sampled-data synchronization control for delayed neural networks

This paper discusses the problem of synchronization for delayed neural networks using sampled-data control. We introduce a new Lyapunov functional, called complete sampling-interval-dependent discontinuous Lyapunov functional, which can adequately capture sampling information on both intervals from $r(t?\overline{\tau })$ to $r(t_k?\overline{\tau })$ and from $r(t?\overline{\tau })$ to $r(t_{k+1}?\overline{\tau })$. Based on this Lyapunov functional and an improved integral inequality, less conservative conditions are derived to ensure the stability of the synchronization error system, leading to the fact that the drive neural network is synchronized with the response neural network. The desired sampled-data controller is designed in terms of solutions to linear matrix inequalities. A numerical example is provided to demonstrate that the proposed approaches are effective and superior to some existing ones in the literature.     

Distributed fault detection for nonlinear multi-agent systems under fixed-time observer

This paper mainly investigates the fault detection problem for nonlinear multi-agent systems with actuator faults. For fault detection, a fixed-time observer is proposed by employing auxiliary variable received from neighbor agents. Then, with the aid of the observer, a residual vector is introduced by the auxiliary variable to detect the faults occurring on any followers, and each observer can estimate the whole state of followers. Moreover, the convergence time is dependent on the parameters of the designed observer and independent of initial condition of system state. Finally, the theoretical result is verified by a simulation example.     

Model free adaptive iterative learning control for a class of nonlinear systems with randomly varying iteration lengths

This paper proposes a novel model free adaptive iterative learning control scheme for a class of unknown nonlinear systems with randomly varying iteration lengths. By applying the dynamic linearization technique along the iteration axis, such systems can be transformed into iteration-depended time varying linear systems. Then, an improved model free adaptive iterative learning control scheme can be constructed only using input and output data of the system. From the rigorous theoretical analysis, it is shown that the mathematical expectation of tracking errors converge to zero as iteration increases. This design does not require any dynamic information of the ILC systems and prior information of randomly varying iteration lengths. An illustrative example verifies the effectiveness of the proposed design.     

Sliding-mode consensus algorithms for disturbed second-order multi-agent systems

In this paper, both leaderless and leader-follower consensus problems for a class of disturbed second-order multi-agent systems are studied. Based on integral sliding-mode control, sliding-mode consensus protocols are proposed for leaderless and leader-follower multi-agent systems with disturbances, respectively. Firstly, for leaderless second-order multi-agent systems, a sliding-mode consensus protocol is proposed to make the agents achieve asymptotic consensus. Secondly, for leader-follower second-order multi-agent systems, a finite-time sliding-mode consensus protocol is designed to make the agents achieve consensus in finite time. Both kinds of consensus protocols inherit the anti-disturbance performance and robustness of sliding-mode control and require less communication information. Finally, two numerical simulations are given for leaderless and leader-follower second-order multi-agent systems to validate the efficiency of the proposed consensus protocols.     

Distributed control of cluster lag consensus for first-order multi-agent systems on QUAD vector fields

This paper addresses the problem of cluster lag consensus for first-order multi-agent systems which can be formulated as moving agents in a capacity-limited network. A distributed control protocol is developed based on local information, and the robustness of the protocol is analyzed by using tools of Frobenius norm, Lyapunov functional and matrix theory. It is shown that when the root agents of the clusters are influenced by the active leader and the intra-coupling among agents is stronger enough, the multi-agent system will reach cluster lag consensus. Moreover, cluster lag consensus for multi-agent systems with a time-varying communication topology and heterogeneous multi-agent systems with a directed topology are studied. Finally, the effectiveness of the proposed protocol is demonstrated by some numerical simulations.     

A BP-PID controller-based multi-model control system for lateral stability of distributed drive electric vehicle

The lateral stability is the crucial feature in a distributed drive electronic vehicle (DDEV). A high speed DDEV in a sharp turn may lose the lateral stability when it encounters fast varied road adhesion coefficients. To solve this problem, a BP-PID controller-based multi-model control system (MMCS) is designed for DDEV via direct yaw-moment control (DYC) in this paper. Firstly, according to the varied road adhesion coefficients, the working circumstance of DDEV is summarized as seven kinds of typical types. A sub-model set is established to accurately describe the operating mode of the working circumstance. Secondly, based on the sub-model set, a nonlinear sub-controller set is constructed with seven off-line tuning BP-PID controllers and an on-line tuning one. The off-line tuning controller can fast calculate the required direct yaw-moment, and the on-line tuning controller is aimed to achieve a high control accuracy. Thirdly, a controller switching policy is composed of an error judgement policy and a model matching policy. Such switching policy is utilized to precisely identify the working circumstance of DDEV and implement switching control. Finally, simulation experiments prove that the designed MMCS shows a significant control performance and guarantees the lateral stability of DDEV under varied road adhesion coefficients.     

Consensus analysis for multi-agent systems via periodic event-triggered algorithms with quantized information

In this article, a novel distributed event-triggered control protocol for the consensus of second-order multi-agent systems with undirected topology is studied. Based on the proposed control protocol, the event-triggered condition is evaluated only at every sampling instant. The control input for each agent will be updated with local information if and only if its condition is violated. Both ideal and quantized relative state measurements are considered under this framework. Some sufficient conditions for achieving consensus are derived using spectral properties of edge Laplacian matrix and the discrete-time Lyapunov function method. Finally, numerical examples are given to demonstrate the effectiveness of our theoretical results.     

Intermittent control strategy for synchronization of fractional-order neural networks via piecewise Lyapunov function method

In this paper, the synchronization problem of fractional-order neural networks (FNNs) with chaotic dynamics is investigated via the intermittent control strategy. Two types of intermittent control methods, the aperiodic one and the periodic one, are applied to achieve the synchronization of the considered systems. Based on the dynamic characteristics of the intermittent control systems, the piecewise Lyapunov function method is employed to derive the synchronization criteria with less conservatism. The results under the aperiodically intermittent control show more generality than the ones via the periodically intermittent control. For each of the aperiodic and periodic cases, a simple controller design process is presented to show how to design the corresponding intermittent controller. Finally, two numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.     

Viable immersion and invariance control for a class of nonlinear systems and its application to aero-engines

This paper presents a novel approach to stabilize a class of nonlinear systems with state constraints. The motivation behind this study is the need to develop a stabilizing state feedback controller that does not require the knowledge of Lyapunov function and can regulate the states to the equilibrium while meeting the constraints. By using an integration of two relatively new tools: immersion and invariance (I&I) theory and viability theory, a sufficient condition for stability and stabilizability of a general nonlinear affine system with state constraints is derived; Then, the related results are exploited to stabilize a class of nonlinear system in feedback form and with state constraints represented by inequalities and the viable I&I stabilizing state feedback controller is obtained constructively. Further, an application to a nonlinear aero-engine model with the temperature constraint is given to illustrate the applicability and the effectiveness of the proposed method. Finally, a comparative simulation is presented, highlighting the advantages of the viable I&I controller.     

Adaptive synchronization of multi-agent systems via variable impulsive control

This paper mainly focuses on the adaptive synchronization problem of multi-agent systems via distributed impulsive control method. Different from the existing investigations of impulsive synchronization with fixed time impulsive inputs, the proposed distributed variable impulsive protocol allows that the impulsive inputs are chosen within a time period (namely impulsive time window) which can be described by the distances of the left (right) endpoints or the centers between two adjacent impulsive time windows. Obviously, this kind of flexible control scheme is more effective in practical systems (especially for the complex environment with physical restrictions). Moreover, the proposed adaptive control technique is helpful to solve the problem with uncertain system parameters. By means of Lyapunov stability theory, impulsive differential equations and adaptive control technique, three sufficient impulsive consensus conditions are given to realize the synchronization of a class of multi-agent nonlinear systems. Finally, two numerical simulations are provided to illustrate the validity of the theoretical analysis.     

Novel event-triggered filter design for nonlinear networked control systems

This paper investigates the problem of event-triggered filter design for nonlinear networked control systems (NCSs) in the framework of interval type-2 (IT2) fuzzy systems. A novel IT2 fuzzy filter for ensuring asymptotic stability and H_∞ performance of filtering error system is proposed, where the premise variables are different from those of the fuzzy model. Attention is focused on solving the problem of event-triggered filter design subject to parameter uncertainties, data quantization, and communication delay in a unified frame. It is shown that the proposed event-triggered filter design communication mechanism for IT2 fuzzy NCSs has the advantage of the existing event-triggered approaches to reduce the utilization of limited network resources and provides flexibility in balancing the tracking error and the utilization of network resources. Finally, simulation example is given to validate the advantages of the presented results.     

Iterative learning control for fractional-order multi-agent systems

In this paper, we apply iterative learning control to both linear and nonlinear fractional-order multi-agent systems to solve consensus tacking problem. Both fixed and iteration-varying communicating graphs are addressed in this paper. For linear systems, a PD^α-type update law with initial state learning mechanism is introduced by virtue of the memory property of fractional-order derivative. For nonlinear systems, a D^α-type update law with forgetting factor and initial state learning is designed. Sufficient conditions for both linear and nonlinear systems are established to guarantee all agents achieving the asymptotic output consensus. Simulation examples are provided to verify the proposed schemes.     

Periodic event-triggered resilient control for cyber-physical systems under denial-of-service attacks

This paper studies the problem of designing a resilient control strategy for cyber-physical systems (CPSs) under denial-of-service (DoS) attacks. By constructing an H_∞ observer-based periodic event-triggered control (PETC) framework, the relationship between the event-triggering mechanism and the prediction error is obtained. Then, inspired by the maximum transmission interval, the input-to-state stability of the closed-loop system is proved. Compared with the existing methods, a Zeno-free periodic PETC scheme is designed for a continuous-time CPS with the external disturbance and measurement noise. In particular, the objective of maximizing the frequency and duration of the DoS attacks is achieved without losing robustness. Finally, two examples are given to verify the effectiveness of the proposed approach.     

A new class of fixed-time bipartite consensus protocols for multi-agent systems with antagonistic interactions

In this paper, we study the fixed-time consensus problem for multi-agent systems with structurally balanced signed graph. A new class of fixed-time nonlinear consensus protocols is designed by employing the neighbor’s information. By using Lyapunov stability method, states of all agents can be guaranteed to reach agreement in a fixed time under our presented protocols, and the consensus values are the same in modulus but different in sign. Moreover, it is shown that the settling time is not dependent on the initial conditions, and it makes a good convenience to estimate the convergence time by just knowing the graph topology and the information flow of the multi-agent systems. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed consensus protocols.