Trajectory Control of Scale-Free Dynamical Networks with Exogenous Disturbances

In this paper, the trajectory control of multi-agent dynamical systems with exogenous disturbances is studied. Suppose multiple agents composing of a scale-free network topology, the performance of rejecting disturbances for the low degree node and high degree node is analyzed. Firstly, the consensus of multi-agent systems without disturbances is studied by designing a pinning control strategy on a part of agents, where this pinning control can bring multiple agents' states to an expected consensus track. Then, theinfluence of the disturbances is considered by developing disturbance observers, and disturbance observers based control (DOBC) are developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multi-agent systems with disturbances under the composite controller can be achieved for scale-free network topology. Finally, by analyzing examples of multi-agent systems with scale-free network topology and exogenous disturbances, the verities of the results are proved. Under the DOBC with the designed parameters, the trajectory convergence of multi-agent systems is researched by pinning two class of the nodes. We have found that it has more stronger robustness to exogenous disturbances for the high degree node pinned than that of the lowdegree node pinned.     

Fixed-Time Leader-Following Consensus Tracking Control for Nonliear Multi-Agent Systems under Jointly Connected Graph

This paper researches the fixed-time leader-following consensus problem for nonlinear multi-agent systems (MASs) affected by unknown disturbances under the jointly connected graph. In order to achieve control goal, this paper designs a fixed-time consensus protocol, which can offset the unknown disturbances and the nonlinear item under the jointly connected graph, simultaneously. In this paper, the states of multiple followers can converge to the state of the leader within a fixed time regardless of the initial conditions rather than just converging to a small neighborhood near the leader state. Finally, a simulation example is given to illustrate the theoretical result.     

Event-Triggered Fixed-Time Integral Sliding Mode Control for Nonlinear Multi-Agent Systems with Disturbances

In this paper, the leader-following consensus problem of first-order nonlinear multi-agent systems (FONMASs) with external disturbances is studied. Firstly, a novel distributed fixed-time sliding mode manifold is designed and a new static event-triggered protocol over general directed graph is proposed which can well suppress the external disturbances and make the FONMASs achieve leader-following consensus in fixed-time. Based on fixed-time stability theory and inequality technique, the conditions to be satisfied by the control parameters are obtained and the Zeno behavior can be avoided. In addition, we improve the proposed protocol and propose a new event-triggering strategy for the FONMASs with multiple leaders. The systems can reach the sliding mode surface and achieve containment control in fixed-time if the control parameters are designed carefully. Finally, several numerical simulations are given to show the effectiveness of the proposed protocols.     

Distributed Consensus Tracking Control of Chaotic Multi-Agent Supply Chain Network: A New Fault-Tolerant,Finite-Time,and Chatter-Free Approach

Over the last years, distributed consensus tracking control has received a lot of attention due to its benefits, such as low operational costs, high resilience, flexible scalability, and so on. However, control methods that do not consider faults in actuators and control agents are impractical in most systems. There is no research in the literature investigating the consensus tracking of supply chain networks subject to disturbances and faults in control input. Motivated by this, the current research studies the fault-tolerant, finite-time, and smooth consensus tracking problems for chaotic multi-agent supply chain networks subject to disturbances, uncertainties, and faults in actuators. The chaotic attractors of a supply chain network are shown, and its corresponding multi-agent system is presented. A new control technique is then proposed, which is suitable for distributed consensus tracking of nonlinear uncertain systems. In the proposed scheme, the effects of faults in control actuators and robustness against unknown time-varying disturbances are taken into account. The proposed technique also uses a finite-time super-twisting algorithm that avoids chattering in the system’s response and control input. Lastly, the multi-agent system is considered in the presence of disturbances and actuator faults, and the proposed scheme’s excellent performance is displayed through numerical simulations.     

Consensus protocol for heterogeneous multi-agent systems: A Markov chain approach

This paper deals with the consensus problem for heterogeneous multi-agent systems. Different from most existing consensus protocols, we consider the consensus seeking of two types of agents, namely, active agents and passive agents. The objective is to directly control the active agents such that the states of all the agents would achieve consensus. In order to obtain a computational approach, we subtly introduce an appropriate Markov chain to cast the heterogeneous systems into a unified framework. Such a framework is helpful for tackling the constraints from passive agents. Furthermore, a sufficient and necessary condition is established to guarantee the consensus in heterogeneous multi-agent systems. Finally, simulation results are provided to verify the theoretical analysis and the effectiveness of the proposed protocol.     

H∞ consensus control of a class of second-order multi-agent systems without relative velocity measurement

This paper studies consensus control problems for a class of second-order multi-agent systems without relative velocity measurement. Some dynamic neighbour-based rules are adopted for the agents in the presence of external disturbances. A sufficient condition is derived to make all agents achieve consensus while satisfying desired H_∞ performance. Finally, numerical simulations are provided to show the effectiveness of our theoretical results.     

Cluster-Delay Mean Square Consensus of Stochastic Multi-Agent Systems with Impulse Time Windows

This paper investigates the cluster-delay mean square consensus problem of a class of first-order nonlinear stochastic multi-agent systems with impulse time windows. Specifically, on the one hand, we have applied a discrete control mechanism (i.e., impulsive control) into the system instead of a continuous one, which has the advantages of low control cost, high convergence speed; on the other hand, we considered the existence of impulse time windows when modeling the system, that is, a single impulse appears randomly within a time window rather than an ideal fixed position. In addition, this paper also considers the influence of stochastic disturbances caused by fluctuations in the external environment. Then, based on algebraic graph theory and Lyapunov stability theory, some sufficiency conditions that the system must meet to reach the consensus state are given. Finally, we designed a simulation example to verify the feasibility of the obtained results.     

Improved Nonlinear Extended State Observer-Based Sliding-Mode Rotary Control for the Rotation System of a Hydraulic Roofbolter

This paper develops a sliding-mode control with an improved nonlinear extended state observer (SMC-INESO) for the rotation system of a hydraulic roofbolter with dead-zones, uncertain gain, and disturbances, with the purpose of improving tracking performance. Firstly, the rotation system is modeled to compensate for dead-zone nonlinearity. Then, we present an improved nonlinear extended state observer to estimate disturbances of the rotation system in real time. Moreover, a proportional-integral-differential sliding-mode surface is introduced and an improved sliding-mode reaching law is designed. Based on this, a sliding-mode control law is developed. In order to eliminate the influence of estimation error and uncertain gain, we design two adaptation laws based on the sliding-mode surface and the estimated states. Finally, the effectiveness of the proposed SMC-INESO is verified through comparative simulation studies.     

Nonlinear consensus protocols for multi-agent systems based on centre manifold reduction

Nonlinear consensus protocols for dynamic directed networks of multi-agent systems with fixed and switching topologies are investigated separately in this paper. Based on the centre manifold reduction technique, nonlinear consensus protocols are presented. We prove that a group of agents can reach a β-consensus, the value of which is the group decision value varying from the minimum and the maximum values of the initial states of the agents. Moreover, we derive the conditions to guarantee that all the agents reach a β--consensus on a desired group decision value. Finally, a simulation study concerning the vertical alignment manoeuvere of a team of unmanned air vehicles is performed. Simulation results show that the nonlinear consensus protocols proposed are more effective than the linear protocols for the formation control of the agents and they are an improvement over existing protocols.     

Cyclic dominance in adaptive networks

The Rock-Paper-Scissors (RPS) game is a paradigmatic model for cyclic dominance in biological systems. Here we consider this game in the social context of competition between opinions in a networked society. In our model, every agent has an opinion which is drawn from the three choices: rock, paper or scissors. In every timestep a link is selected randomly and the game is played between the nodes connected by the link. The loser either adopts the opinion of the winner or rewires the link. These rules define an adaptive network on which the agents’ opinions coevolve with the network topology of social contacts. We show analytically and numerically that nonequilibrium phase transitions occur as a function of the rewiring strength. The transitions separate four distinct phases which differ in the observed dynamics of opinions and topology. In particular, there is one phase where the population settles to an arbitrary consensus opinion. We present a detailed analysis of the corresponding transitions revealing an apparently paradoxical behavior. The system approaches consensus states where they are unstable, whereas other dynamics prevail when the consensus states are stable.     

Consensus protocol for multi-agent continuous systems

Based on the algebraic graph theory, the networked multi-agent continuous systems are investigated. Firstly, the digraph （directed graph） represents the topology of a networked system, and then a consensus convergence criterion of system is proposed. Secondly, the issue of stability of multi-agent systems and the consensus convergence problem of information states are all analysed. Furthermore, the consensus equilibrium point of system is proved to be global and asymptotically reach the convex combination of initial states. Finally, two examples are taken to show the effectiveness of the results obtained in this paper.     

Social dynamics with peer support on heterogeneous networks

Human behavior often exhibits a scheme in which individuals adopt indifferent, neutral, or radical positions on a given topic. The mechanisms leading to community formation are strongly related with social pressure and the topology of the contact network. Here, we discuss an approach to model social behavior which accounts for the protection by alike peers proportional to their relative abundance in the closest neighborhood. We explore the ensuing non-linear dynamics emphasizing the role of the specific structure of the social network, modeled by scale-free graphs. We find that both coexistence of opinions and consensus on the default position are possible stationary states of the model. In particular, we show how these states critically depend on the heterogeneity of the social network and the specific distribution of external control elements.     

冠状动脉系统高阶滑模自适应混沌同步设计

针对冠状动脉系统混沌同步问题, 系统模型受到有界但未知的不确定干扰条件下, 利用几何齐次性理论和积分滑模面设计高阶滑模自适应控制器, 使响应系统在有限时间内跟踪驱动系统, 该方法无需提前预知扰动边界. 采用Lyapunov理论对闭环系统进行分析并证明该控制器保证该系统能够在有限时间内镇定, 从仿真实验结果可以看出所设计的控制器在不确定干扰的情况下系统具有良好鲁棒性和未知参数的自适应性, 为能够有效治疗心肌梗死等冠状动脉疾病提供了一定的理论依据.     

Tracking consensus for nonlinear heterogeneous multi-agent systems subject to unknown disturbances via sliding mode control

We investigate the tracking control for a class of nonlinear heterogeneous leader-follower multi-agent systems(MAS)with unknown external disturbances. Firstly, the neighbor-based distributed finite-time observers are proposed for the followers to estimate the position and velocity of the leader. Then, two novel distributed adaptive control laws are designed by means of linear sliding mode(LSM) as well as nonsingular terminal sliding mode(NTSM), respectively. One can prove that the tracking consensus can be achieved asymptotically under LSM and the tracking error can converge to a quite small neighborhood of the origin in finite time by NTSM in spite of uncertainties and disturbances. Finally, a simulation example is given to verify the effectiveness of the obtained theoretical results.     

Leader-following consensus problem with a varying-velocity leader and time-varying delays

In this paper, we study a leader-following consensus problem for a multi-agent system with a varying-velocity leader and time-varying delays. Here, the interaction graph among the followers is switching and balanced. At first, we propose a neighbor-based rule for every agent to track a leader whose states may not be measured. In addition, we consider the convergence analysis of this multi-agent system under two different conditions: the connection between the followers and the leader is time-invariant and time-varying. For the first case, a novel decomposition method is introduced to facilitate the convergence analysis. By utilizing a Lyapunov–Krasovskii functional, we obtain sufficient conditions for uniformly ultimately boundedness of the tracking errors. Finally, two simulations are also presented to illustrate our theoretical results.     

Error correction in ensemble registers for quantum repeaters and quantum computers

We propose to use a collective excitation blockade mechanism to identify errors that occur due to disturbances of single atoms in ensemble quantum registers where qubits are stored in the collective population of different internal atomic states. A simple error correction procedure and a simple decoherence-free encoding of ensemble qubits in the hyperfine states of alkali-metal atoms are presented.     

Full-order and reduced-order observer-based synchronization for chaotic systems with unknown disturbances and parameters

The Letter deals with the problem of synchronization of chaotic dynamic system with unknown disturbances and parameters based on observer. First, under some assumptions for drive system, a kind of full-order observer-based synchronization method is summarized. The response system is a robust adaptive full-order observer with adaptation laws for the unknown disturbances and parameters. Second, under the same assumptions, a reduced-order observer-based response system which can synchronize part states of drive system is developed. By choosing a special reduced-order gain matrix, the reduced-order observer-based response system is able to eliminate the influence of the unknown disturbances and parameters directly, so it is unnecessary for one to design the adaptation laws of them. Finally, some numerical simulations for Lorenz chaotic system are design and the simulation results are analyzed in detail.     

Controlling chaos based on an adaptive nonlinear compensator mechanism

The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory. By using a designed nonlinear compensator mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example. From the Lyapunov stability theory, sufficient conditions for choosing control parameters to guarantee chaos control are derived. Several experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.     

Three-State Opinion Model on Complex Topologies

We investigate opinion diffusion on complex networks and the interplay between the existence of neutral opinion states and non-trivial network structures. For this purpose, we apply a three-state opinion model based on magnetic-like interactions to modular complex networks, both synthetic and real networks extracted from Twitter. The model allows for tuning the contribution of neutral agents using a neutrality parameter. We also consider social agitation, encoded as a temperature, that accounts for random opinion changes that are beyond the agent neighborhood opinion state. Using this model, we study which topological features influence the formation of consensus, bipartidism, or fragmentation of opinions in three parties, and how the neutrality parameter and the temperature interplay with the network structure.     

Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain Disturbances

In this paper, a robust trajectory tracking control method with state constraints and uncertain disturbances on the ground of adaptive dynamic programming (ADP) is proposed for nonlinear systems. Firstly, the augmented system consists of the tracking error and the reference trajectory, and the tracking control problems with uncertain disturbances is described as the problem of robust control adjustment. In addition, considering the nominal system of the augmented system, the guaranteed cost tracking control problem is transformed into the optimal control problem by using the discount coefficient in the nominal system. A new safe Hamilton–Jacobi–Bellman (HJB) equation is proposed by combining the cost function with the control barrier function (CBF), so that the behavior of violating the safety regulations for the system states will be punished. In order to solve the new safe HJB equation, a critic neural network (NN) is used to approximate the solution of the safe HJB equation. According to the Lyapunov stability theory, in the case of state constraints and uncertain disturbances, the system states and the parameters of the critic neural network are guaranteed to be uniformly ultimately bounded (UUB). At the end of this paper, the feasibility of the proposed method is verified by a simulation example.