On Group Synchronization for Interacting Clusters of Heterogeneous Systems

Solving the Zero-Sum Control Problem for Tidal Turbine System: An Online Reinforcement Learning Approach

A novel completely mode-free integral reinforcement learning (CMFIRL)-based iteration algorithm is proposed in this article to compute the two-player zero-sum games and the Nash equilibrium problems, that is, the optimal control policy pairs, for tidal turbine system based on continuous-time Markov jump linear model with exact transition probability and completely unknown dynamics. First, the tidal turbine system is modeled into Markov jump linear systems, followed by a designed subsystem transformation technique to decouple the jumping modes. Then, a completely mode-free reinforcement learning algorithm is employed to address the game-coupled algebraic Riccati equations without using the information of the system dynamics, in order to reach the Nash equilibrium. The learning algorithm includes one iteration loop by updating the control policy and the disturbance policy simultaneously. Also, the exploration signal is added for motivating the system, and the convergence of the CMFIRL iteration algorithm is rigorously proved. Finally, a simulation example is given to illustrate the effectiveness and applicability of the control design approach.

Distributed robust group output synchronization control for heterogeneous uncertain linear multi-agent systems

This paper investigates the distributed robust group output synchronization problem of heterogeneous uncertain linear leader-follower multi-agent systems (MASs), whose followers have nonidentical and parameter uncertain dynamics. To achieve cooperative tracking with multiple targets, a new group synchronization framework based upon the output regulation technique is established. In the underlying directed communication topology, all nonidentical followers are divided into several subgroups. Meanwhile, each subgroup has its output tracking objective generated by an autonomous exosystem which is seen as the leader of each subgroup. Since not all followers can access their exosystems directly, the distributed exosystem observer based on the algebraic Riccati inequality (ARI) is designed to obtain the information of exosystems. Moreover, to compensate for parameter uncertainties for different group topologies, the p-copy internal model is synthesized into distributed control laws, i.e., dynamic state feedback control protocol under an acyclic directed graph and dynamic output feedback control protocol under a general directed graph. It is shown that group synchronization can be respectively achieved with these controllers under acyclic and general partitions regardless of parameter uncertainties. Finally, some examples are provided to verify the validity of the analytic results.

On Relative-Output Feedback Approach for Group Consensus of Clusters of Multiagent Systems

In this article, the group consensus problem is addressed for a network of multiagent systems (MASs). Unlike in existing literature, where a relative-state feedback-based distributed control input is used to achieve group consensus, this work aims at designing a relative-output-based distributed control law to achieve the same goal. To that effect, the Lyapunov stability theory is used to formulate the sufficient and necessary conditions for the existence of such a feedback controller and then separate conditions have been included for its design. In addition to that, a new linear matrix inequality is explored to choose the intracluster coupling strengths to ensure group consensus. In this article, the relative-output-based control approach is investigated for both the leaderless and the leader-following frameworks of the group consensus problem, and the theoretical findings presented are validated using numerical examples and simulation results.

Robust Cooperative Optimal Sliding-Mode Control for High-Order Nonlinear Systems: Directed Topologies

This article is concerned with the robust cooperative optimal control of nonlinear multiagent systems (MASs) with external disturbances and modeling uncertainties. Using the super-twisting algorithm, a continuous sliding-mode control protocol is presented for high-order nonlinear MASs with multiple inputs. The sliding-mode dynamics is modeled by the Takagi-Sugeno fuzzy approach, and the nominal control protocol that guarantees the robust optimization of the cost function is designed. Directed topologies are allowed using the presented protocol, and many assumptions about topologies are removed. Finally, three numerical examples are reported to demonstrate the effectiveness and improved performance of the presented protocol.

Couple-Group Consensus of Cooperative-Competitive Heterogeneous Multiagent Systems: A Fully Distributed Event-Triggered and Pinning Control Method

This article discusses the couple-group consensus for heterogeneous multiagent systems via event-triggered and pinning control methods. Considering cooperative-competitive interaction among the agents, a novel group consensus protocol is designed. As inducing the time-correlation threshold function, a class of fully distributed event-triggered conditions without depending on any global information is proposed. Utilizing the Lyapunov stability theory, some sufficient conditions are obtained. Under hybrid event triggered and pinning control, pinning control strategies are first introduced. It is shown that under the proposed strategies, all agents can asymptotically achieve pinning couple-group consensus with discontinuous communication in a fully distributed way. Furthermore, the Zeno behavior for each agent is overcome. Finally, the reduction of the systems' controller update frequency and the correctness of our conclusions are illustrated by some simulations.

Predictor-Based Neural Dynamic Surface Control for Bipartite Tracking of a Class of Nonlinear Multiagent Systems

This article is concerned with bipartite tracking for a class of nonlinear multiagent systems under a signed directed graph, where the followers are with unknown virtual control gains. In the predictor-based neural dynamic surface control (NDSC) framework, a bipartite tracking control strategy is proposed by the introduction of predictors and the minimal number of learning parameters (MNLPs) technology along with the graph theory. Different from the traditional NDSC, the predictor-based NDSC utilizes prediction errors to update the neural network for improving system transient performance. The MNLPs technology is employed to avoid the problem of "explosion of learning parameters". It is proved that all closed-loop signals steered by the proposed control strategy are bounded, and the system achieves bipartite consensus. Simulation results verify the efficiency and effectiveness of the strategy.

Semi-global cluster synchronization for nonlinear systems under fixed and switching topologies

In this paper, the cluster synchronization problem for heterogeneous nonlinear systems with input saturation is studied under both fixed and switching topologies. The distributed feedback controllers are first designed by low gain technique to deal with the input saturation. Sufficient conditions for reaching semi-global cluster synchronization are derived by utilizing the algebraic graph theory, Lyapunov method, and low gain technique. It is shown that the semi-global cluster synchronization problem can be solved by using the proposed synchronization protocols on some preconditions for both fixed and switching topologies. Moreover, under the switching topology, the lower bound of the total activation time for the derived topology with a directed spanning tree is explicitly specified. Finally, some examples are presented to demonstrate the effectiveness of the proposed theories.

Cluster Consensus of Multiagent Systems With Weighted Antagonistic Interactions

This article addresses the problem of cluster consensus for multiagent systems (MASs) associated with weighted antagonistic interactions. Compared with some existing results, a general communication topology among agents is introduced in this article, where there is no need to confine directed cycles to the root of a spanning tree. By taking into consideration the structures of directed cycles and multiple paths, the judgment of structural balance is simplified significantly. A novel cluster consensus protocol is also proposed for structurally unbalanced digraphs. Moreover, two necessary and sufficient conditions are derived, by which cluster consensus can be achieved in an MAS if and only if its communication topology contains a directed spanning tree. Then, by employing an algebra theorem, a sufficient criterion for the unstable system under a directed cycle is obtained, whether the number of agents on this cycle is odd or even. Some illustrative examples are given to demonstrate the effectiveness of theoretical results.

Distributed Stabilization of Multiple Heterogeneous Agents in the Strong-Weak Competition Network: A Switched System Approach

The distributed stabilization problem is studied in this article for a group of heterogeneous second-order agents in the strong-weak competition network containing three kinds of relationships among agents: 1) cooperation; 2) strong competition; and 3) weak competition. The entire network satisfies the structural balance condition which can be partitioned into two subnetworks, while the strong and weak competitions are alternate actions on the agents from different subnetworks. To stabilize such heterogeneous networked systems in a distributed way, the switched system approach is developed and utilized in this article, where it is revealed that distributed stabilization can be achieved provided that the ratio on the activating periods of strong and weak competition is chosen appropriately. As an extension, a periodical switching law is taken into account to simplify the design process, where the periodical competition function is introduced correspondingly and several effective sufficient conditions are attained. Finally, the derived analytical results are demonstrated by performing numerical simulations.

Semiglobal Cluster Consensus for Heterogeneous Systems With Input Saturation

In this article, the semiglobal cluster consensus problem is investigated for heterogeneous generic linear systems with input saturation. A general case in a leaderless framework is studied first, and then in order to broaden the scope of application, we consider a special case in which the leader nodes are pinned intermittently. To tackle the above problems, we propose a linear control scheme by using the low-gain feedback technique under the assumptions that each node is asymptotically null controllable and the underlying topology of each cluster (the extended cluster under the intermittent pinning control) has a directed spanning tree. The Lyapunov-based method and the low-gain feedback technique are developed for convergence analysis. It is shown that for both cases, the convergence rate is explicitly specified, which depends on the low-gain parameter and system matrices. Finally, two numerical examples are provided to verify the effectiveness of the theoretical findings.

Distributed Q -Learning-Based Online Optimization Algorithm for Unit Commitment and Dispatch in Smart Grid

Economic dispatch (ED) and unit commitment (UC) problems need to be revisited in order to make a transition from a traditional power system to a smart grid. In this paper, we formulate the ED and UC problems into a unified form, which is also capable of characterizing the infinite horizon UC problem. Based on the formulation, a centralized Q -learning-based optimization algorithm is proposed. The proposed algorithm runs in an online manner and requires no prior information on the mathematical formulation of the actual cost functions, thus being capable of dealing with situations for which such cost functions are too difficult to obtain. Then, the distributed counterpart of the centralized algorithm is developed by relaxing the demand for global information and balancing exploration and exploitation cooperatively in a distributed way. Theoretical analysis of the proposed algorithms is also provided. Finally, several case studies are presented to demonstrate the effectiveness of the proposed algorithms.

Fault-Tolerant Consensus Tracking Control for Linear Multiagent Systems Under Switching Directed Network

In this paper, for linear leader-follower networks with multiple heterogeneous actuator faults, including partial loss of effectiveness fault and actuator bias fault, a cooperative fault-tolerant control (CFTC) approach is developed. Assume that the interaction network topology among all nodes is a switching directed graph. To address the difficulty of designing the distributed compensation control laws under the time-varying asymmetrical network structure, a novel distributed-reference-observer-based fault-tolerant tracking control approach is established, under which the global tracking errors are proved to be asymptotically convergent in the presence of actuator failures. First, by constructing a group of distributed reference observers based on neighborhood state information, all followers can estimate the leader's state trajectories directly. Second, a decentralized adaptive fault-tolerant tracking controller via local estimation is designed to achieve the global synchronization. Furthermore, the reliable coordination problem under switching directed topology with intermittent communications is solved by utilizing the presented CFTC approach. Finally, the effectiveness of the proposed coordination control protocol is illustrated by its applications to a networked aircraft system.

Consensus Tracking for Heterogeneous Interdependent Group Systems

This paper is concerned with the consensus tracking problem for heterogeneous interdependent group systems with fixed communication topologies. First, the interdependent model of the heterogeneous system is built from the perspective of the difference of the individual characteristic and the difference of the subgroup topology structure. A class of distributed consensus tracking control protocol is proposed for realizing the consensus tracking of the heterogeneous interdependent group system via using local information. Then, for fixed communication topologies, some corresponding sufficient conditions are given to ensure the achievement of the consensus tracking. Two parameters are defined, which denote, respectively, the proportion of interdependence individual and the redundancy of interdependence. The effects of these parameters are analyzed on the consensus tracking of group systems. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Prespecified-Time Cluster Synchronization of Complex Networks via a Smooth Control Approach

Most existing finite-/fixed-time synchronization control schemes are nonsmooth or discontinuous, and the settling time is estimated with conservatism. It is due to the utilization of signum function or fraction power state feedback. This brief considers the problem of prespecified-time cluster synchronization of complex networks with a smooth control protocol. The synchronization time is independent of any control parameters or any systems' initial conditions, which is actually uniformly prescribed according to task requirements without any estimations. Moreover, the cluster synchronization can maintain after the specified time, and the smooth control input can always keep uniformly bounded in an infinite time interval as well. Finally, one numerical example is provided to illustrate the effectiveness of the proposed protocol and design method.

Finite-Time Coordination Behavior of Multiple Euler-Lagrange Systems in Cooperation-Competition Networks

In this paper, the finite-time coordination behavior of multiple Euler-Lagrange systems in cooperation-competition networks is investigated, where the coupling weights can be either positive or negative. Then, two auxiliary variables about the information exchange among agents are designed, and the finite-time distributed protocol is proposed based on the auxiliary variables and the property of the Euler-Lagrange system. By combining the approach of adding a power integrator with the homogeneous domination method, it is shown that finite-time bipartite consensus can be achieved if the cooperation-competition network is structurally balanced and the parameters of the distributed protocol are chosen appropriately; otherwise, finite-time distributed stabilization can be achieved. Furthermore, from the perspective of network decomposition, the finite-time coordination behavior is further considered, and some sufficient conditions about the cooperation subnetwork and the competition subnetwork are obtained. As an extension, finite-time coordination behavior only with partial state information of the neighbors is discussed, and some similar results are obtained. Finally, four numerical examples are shown for illustration.

Symmetry induced group consensus

There has been substantial work studying consensus problems for which there is a single common final state, although there are many real-world complex networks for which the complete consensus may be undesirable. More recently, the concept of group consensus whereby subsets of nodes are chosen to reach a common final state distinct from others has been developed, but the methods tend to be independent of the underlying network topology. Here, an alternative type of group consensus is achieved for which nodes that are "symmetric" achieve a common final state. The dynamic behavior may be distinct between nodes that are not symmetric. We show how group consensus for heterogeneous linear agents can be achieved via a simple coupling protocol that exploits the topology of the network. We see that group consensus is possible on both stable and unstable trajectories. We observe and characterize the phenomenon of "isolated group consensus," where one or more clusters may achieve group consensus while the other clusters do not.

Adaptive Sliding Mode Consensus Tracking for Second-Order Nonlinear Multiagent Systems With Actuator Faults

This paper investigates the consensus tracking problem of second-order nonlinear multiagent systems (MAS) with disturbance and actuator fault by the sliding mode control method. The communication topology of the MAS is directed and only part of the followers have access to the leader's information. First, a discontinuous sliding mode tracking protocol is studied for consensus tracking of the MAS. Second, to address the shortcoming of chattering and difficulty of setting the control gain in the discontinuous protocol, a continuous sliding mode tracking protocol with an adaptive mechanism is developed. The adaptive mechanism will adjust the gain of the control automatically and enable the tracking protocol to work well without prior knowledge of the MAS. Third, the performance of the adaptive sliding mode protocol for consensus tracking of the MAS in the presence of actuator faults of biased fault and partial loss of effectiveness fault is further investigated. Finally, numerical simulations are performed to illustrate the efficiency of the theoretical results.

Dynamic Coverage Control in a Time-Varying Environment Using Bayesian Prediction

This paper investigates the dynamic coverage control problem for a group of agents with unknown density function. A cost function, depending on a certain metric and the density function, is defined to describe the performance of coverage network. Since the optimal deployment of agents is closely depending on the density function, we employ the Bayesian prediction approaches to estimate the density function. Moreover, a novel coverage-control-customized algorithm is proposed to acquire the Bayesian parameters. The merits of this Bayesian-based spatial estimation algorithm are the consideration of measurement noise and the capability of dealing time-varying density function. However, the estimated density function from Bayesian framework follows normal distribution, which leads the cost function to a stochastic process. To deal with this type of cost function, a discrete control scheme is proposed to steer the agents approaching to a near-optimal deployment. The mean-square stability of the proposed coverage system is further analyzed. Finally, numerical simulations are provided to verify the effectiveness of the proposed approaches.

Event-triggered containment control for second-order multi-agent systems with sampled position data

This paper is concerned with the problem of event-triggered containment control for second-order multi-agent systems with sampled position data. First, a distributed event-triggered containment control protocol is designed, which utilizes the sampled position data only and allows the event-triggering condition to be intermittently examined at constant sampling instants. Then, based on the algebraic graph theory and matrix theory, a sufficient condition on the communication topology, the controller gains, and the sampling period is derived so as to achieve containment control. Finally, a numerical example is provided to verify the theoretical results.

Neural Adaptive Sliding-Mode Control of a Vehicle Platoon Using Output Feedback

This paper investigates the output feedback control problem of a vehicle platoon with a constant time headway (CTH) policy, where each vehicle can communicate with its consecutive vehicles. Firstly, based on the integrated-sliding-mode (ISM) technique, a neural adaptive sliding-mode control algorithm is developed to ensure that the vehicle platoon is moving with the CTH policy and full state measurement. Then, to further decrease the measurement complexity and reduce the communication load, an output feedback control protocol is proposed with only position information, in which a higher order sliding-mode observer is designed to estimate the other required information (velocities and accelerations). In order to avoid collisions among the vehicles, the string stability of the whole vehicle platoon is proven through the stability theorem. Finally, numerical simulation results are provided to verify its effectiveness and advantages over the traditional sliding-mode control method in vehicle platoons.

Distributed Consensus Optimization in Multiagent Networks With Time-Varying Directed Topologies and Quantized Communication

This paper considers solving a class of optimization problems which are modeled as the sum of all agents' convex cost functions and each agent is only accessible to its individual function. Communication between agents in multiagent networks is assumed to be limited: each agent can only interact information with its neighbors by using time-varying communication channels with limited capacities. A technique which overcomes the limitation is to implement a quantization process to the interacted information. The quantized information is first encoded as a binary sequence at the side of each agent before sending. After the binary sequence is received by the neighboring agent, corresponding decoding scheme is utilized to resume the original information with a certain degree of error which is caused by the quantization process. With the availability of each agent's encoding states (associated with its out-channels) and decoding states (associated with its in-channels), we devise a set of distributed optimization algorithms that generate two iterative sequences, one of which converges to the optimal solution and the other of which reaches to the optimal value. We prove that if the parameters satisfy some mild conditions, the quantization errors are bounded and the consensus optimization can be achieved. How to minimize the number of quantization level of each connected communication channel in fixed networks is also explored thoroughly. It is found that, by properly choosing system parameters, one bit information exchange suffices to ensure consensus optimization. Finally, we present two numerical simulation experiments to illustrate the efficacy of the algorithms as well as to validate the theoretical findings.