Continuous-time Multi-agent Systems Research Articles

Multi-agent flocking control with complex obstacles and adaptive distributed convex optimization

The optimization issue involving flocking control and obstacle avoidance behavior in continuous-time multi-agent systems is the main topic of this work. When an agent encounters an obstacle, a virtual agent is introduced to generate repulsive force, enabling the multi-agent system to navigate around obstacles smoothly. Under the local interaction between agents, a multi-agent flocking control and obstacle avoidance algorithm is proposed with utilizing adaptive distributed convex optimization. This algorithm can minimize the sum of local costs of the system. A symbolic function-based estimation method is introduced to effectively relax the constraints of the cost function. The Lyapunov approach is employed to show the stability of the multi-agent system. With the proposed algorithm, each agent can achieve flocking behavior for convex optimization in complex obstacle environments by interacting with their neighbors, virtual agents, and virtual leaders. Last but not least, simulation examples are given to further illustrate the effectiveness and efficiency of the suggested control algorithm.

Distributed Minimum-Energy Containment Control of Continuous-Time Multi-Agent Systems by Inverse Optimal Control

Dear Editor, This letter focuses on the distributed optimal containment control of continuous-time multi-agent systems (CTMASs) with respect to the minimum-energy performance index over fixed topology. To achieve this, we firstly investigate the optimal containment control problem using the inverse optimal control method, where all states of followers asymptotically converge to the convex hull spanned by the leaders while some quadratic performance indexes get minimized. A sufficient condition for existence of the distributed optimal containment control protocol is derived. By introducing the parametric algebraic Riccati equation (PARE), it is strictly proved that the global performance index can be used to approximate the standard minimum-energy performance index as the parameters tends to infinity. In consequence, the standard minimum-energy cooperative containment control can be solved by local steady state feedback protocols. Finally, numerical examples are given to demonstrate the effectiveness of theoretical results.

Cooperative Containment Control for Multiagent Systems With Reduced-Order Protocols.

This article addresses the problem of containment control for continuous-time multiagent systems. A containment error is first given to show the coordination between the outputs of leaders and followers. Then, an observer is designed based on the neighbor observable convex hull state. Under the assumption that the designed reduced-order observer is subject to external disturbances, a reduced-order protocol is designed to realize the containment coordination. In order to ensure the designed control protocol can achieve the effect of the main theories, a corresponding Sylvester equation is given with a novel approach which proves that the Sylvester equation is solvable. Finally, a numerical example is given to verify the validity of the main results.

Quantized cooperative output regulation of continuous-time multi-agent systems over switching graph

Quantized cooperative output regulation of continuous-time multi-agent systems over switching graph

Event-triggered-based encoding–decoding consensus control of continuous-time multi-agent systems under DoS attacks

The security of multi-agent systems (MASs) is important particularly when considering the potential threat posed by malicious attackers. Specifically, network attacks and information theft caused by attackers have garnered significant attention due to their potential to destroy the consensus of the system. Therefore, this paper presents a novel approach to achieve leader-following consensus control of continuous-time MASs under DoS attacks, leveraging event-triggered encoding and decoding techniques. When the DoS attacks occur, the transmitted information between agents becomes unavailable. To address this challenge, a buffer is introduced to store the latest transmission data and then the stored data can be used when the DoS attacks exist. We also propose an event-triggered encoding–decoding strategy that can be employed for privacy protection in linear continuous-time MASs. The transmitted data is encoded as a codeword before transmitting, and the encoder updates it when event-triggered conditions are met. The receiving end decodes the data upon receipt. Furthermore, a distributed switching controller is designed using the encoded and stored state values to achieve leader-following consensus. The control gain is calculated to obtain sufficient conditions for DoS attacks through the linear matrix inequalities (LMI) and Lyapunov functions. The boundedness of transmitted data and the Zeno phenomenon are also analyzed. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed control algorithm.

Distributed strategies for mixed equilibrium problems: Continuous-time theoretical approaches

In this paper, the mixed equilibrium problem is studied by employing a continuous-time multi-agent system, where the objective of agents is to cooperatively find a point from the feasible set such that the sum of bifunctions with a free-variable is nonnegative. Different from existing works on mixed equilibrium problems with only convex set constraints, we consider a more general case where the feasible set is constrained by a set of convex inequalities. Moreover, each agent only has access to the information of its own bifunction and inequality constraint function, as well as the information of a local convex set. To handle this problem, the Karush–Kuhn–Tucker condition that is suitable for continuous-time theoretical approaches is provided, and a continuous-time distributed primal–dual algorithm is proposed. Under mild assumptions on the graph and bifunctions, we prove that the states of all agents asymptotically converge to the common solution of the mixed equilibrium problem. Finally, a simulation example is worked out to demonstrate the effectiveness of our theoretical results.

Iterative learning control for continuous-time multi-agent differential inclusion systems with full learnability

The learnability of systems plays a crucial role in the feasibility of control objective. This study explores the learnability and iterative learning-based consensus control for continuous-time multi-agent differential inclusion systems. Unlike discrete-time systems, analysis for the relationship between output space and realizable output space that used to explore learnability is more tough since involving continuous-time system output. Using measure theory, the systems exhibit full learnability if and only if the input–output coupling matrix is of full-row rank. Considering the possibility of controller power dissipation and demand for improving tracking performance, iterative learning control with state feedback and an efficiency factor is proposed. The consensus performance for the proposed control scheme is strictly explored. Simulation on unmanned vehicles in freeway demonstrates the validity of the theoretical results.

Distributed finite-time optimization algorithms with a modified Newton–Raphson method

In this paper, we propose a distributed finite-time optimization protocol for single-integrator continuous-time multi-agent systems, which utilizes a modified Newton–Raphson method. The inverse of Hessian matrix, sign function and the gradient are adopted for the design of the algorithms. The proposed algorithms make agents converge to the network optimizer under any initial state and finite time, respectively. Lyapunov method and the properties of sign function are employed to verify the convergence of the proposed algorithms. Besides, the adaptive method is also considered to avoid complex parameter conditions and centralized parameters. Finally, numerical simulations are provided to testify the presented results.

Scaled Event-Triggered Resilient Consensus Control of Continuous-Time Multi-Agent Systems Under Byzantine Agents

This paper investigates the scaled event-triggered consensus control for the continuous-time multi-agent system under Byzantine agents. The Byzantine agents do not follow the desired control strategy, which may influence the consensus performance of the multi-agent systems. To realize the scaled consensus under the Byzantine agents, a novel continuous-time scaled event-triggered mean-subsequence-reduced algorithm is constructed. First, a scaled resilient consensus controller is developed, where every cooperative agent removes the most different event-triggered transmitted values from the in-neighbors and obtains the associated scaled resilient consensus control input. Besides, a novel dynamic event-triggered condition is designed based upon the associated discontinuous and non-differentiable Lyapunov function candidate. In addition, two sets of auxiliary variables are introduced into the event-triggered condition, to prevent the usage of the global topology information and to exclude the Zeno behavior simultaneously. The proposed control algorithm can realize the scaled consensus of the continuous-time multi-agent systems, resist the Byzantine agents, and decrease the communication burden simultaneously. The simulation results verify the effectiveness of the proposed algorithm.

A Bi-Event-Triggered Multi-Agent System for Distributed Optimization

In this paper, we propose a continuous-time multi-agent system via event-triggered communication among agents for distributed optimization. We develop a dynamic bi-event triggering rule based on both local decision variables and auxiliary variables to reduce communication costs. We design a bi-event triggered multi-agent system based on the Karush-Kuhn-Tucker conditions, which allows initializing auxiliary variables arbitrarily and hence relaxing the existing zero-sum condition on the initial values of auxiliary variables. We prove the exponential convergence of the multi-agent system to the optimal solution and derive a lower bound of the convergence rate. In addition, we prove the capability of the triggering rule for precluding Zeno behavior. We also elaborate on two numerical examples to illustrate the effectiveness and characteristics of the theoretical results.

Reinforcement learning and cooperative [formula omitted] output regulation of linear continuous-time multi-agent systems

This paper proposes a novel control approach to solve the cooperative H∞ output regulation problem for linear continuous-time multi-agent systems (MASs). Different from existing solutions to cooperative output regulation problems, a distributed feedforward-feedback controller is developed to achieve asymptotic tracking and reject both modeled and unmodeled disturbances. The feedforward control policy is computed via solving regulator equations, and the optimal feedback control policy is obtained through handling a zero-sum game. Instead of relying on the knowledge of system matrices in the state equations of the followers’ dynamics and initial stabilizing feedback control gains, a value iteration (VI) algorithm is proposed to learn the optimal feedback control gain and feedforward control gain using online data. To the best of our knowledge, this paper is the first to show that the proposed VI algorithm can approximate the solution to continuous-time game algebraic Riccati equations with guaranteed convergence. Finally, the numerical analysis is provided to show the effectiveness of the proposed approach.

Unknown input observer based distributed fault detection for nonlinear multi-agent systems with probabilistic time delay

This paper focuses on the fault detection (FD) problem for nonlinear continuous-time multi-agent systems (MASs) with external disturbances and random time-varying delay. The communication topology is assumed to be undirected and connected. Firstly, a stochastic variable satisfying the Bernoulli distribution is utilized to describe the random time-varying delay and transfer the random time-varying delay to a deterministic time-varying delay. To avoid the constraints of the rank conditions for unknown input observer (UIO), the external disturbances and faults from other agents are treated as the unknown inputs which are partitioned into the decoupled part and the non-decoupled part. Sufficient conditions composed of linear matrix inequalities (LMIs) are derived to ensure the stochastic stability of the augmented system with a desired H∞ performance index and extra freedom of design. By utilizing the properties of UIOs properly, the method proposed in this paper can detect multiple faulty nodes simultaneously. Finally, a numerical example demonstrates the effectiveness and feasibility of the proposed approach.

Optimal containment preview control for continuous-time multi-agent systems using internal model principle

ABSTRACT Optimal containment preview analysis and distributed design for multi-agent systems with general continuous-time linear dynamics and directed acyclic communication topology are considered. Firstly, the state augmentation technique and topology reconstruction method are applied to formulate the original problem as a set of internal-model based local optimal output regulation problem. Secondly, the linear superposition principle is employed to obtain the preview feed-forward compensations corresponding to multiple leaders. Thirdly, by expressing each preview compensation term as a form about the current state of the leader, the solvability of the local optimal output regulation problem, as well as the optimal regulation problems, are proved. On this basis, the sufficient conditions and the distributed optimal control strategy are derived, which ensure the convergence of the containment preview problem. Finally, the effectiveness of the distributed design is illustrated by a numerical experiment.

Event-Triggered Formation Control of Multiagent Systems With Linear Continuous-Time Dynamic Models

Event-triggered formation control of linear continuous-time multiagent systems is studied in this article. A complex-valued Laplacian is adopted by the local information of desired formation. For each agent, an event-triggering mechanism based on the neighboring information at event-triggering time instants is presented and continuous communications between neighboring agents are avoided. Furthermore, an event-triggered control strategy using the idea of dynamic state observer is designed. It is shown that any desired formation shape can be achieved. Moreover, the Zeno-behavior is strictly excluded. Finally, effectiveness of the obtained theoretical results is validated by two simulation examples.

Secure consensus with partial public protocols

Existing consensus designs require that the information of local control laws is open access. This is undesirable whenever the privacy of local interactions is concerned. In this paper, a different framework of the consensus protocol design with the consideration of authority management of accessing local controllers is provided, by using an edge-based implementation. In the scenario of the proposed designs, each local controller is realized by a parallel connection of a public element and a private element. The public elements are uniform and open access. However, the private elements are allowed to be significant nonuniform and are only known by the pairs of agents who share them. For both continuous-time multi-agent systems and their sampled-data counterparts, we provide the design criterions for the partial public protocols under both static and dynamic public elements, respectively. By exploring the edge sensitivity design approach, it is shown that the consensus can be achieved under the proposed protocols if the private control laws satisfy certain constraints dependent on the public ones and the network topologies. Numerical examples are also provided to illustrate the proposed design criterions.

Consensus error analysis for linear continuous-time multi-agent systems with additive noises

This paper investigates the distributed consensus problem for linear continuous-time multi-agent systems subject to additive process noises. Due to the existence of noises, the asymptotic consensus cannot be achieved. Hence, a distributed consensus protocol is proposed such that all the agents can achieve consensus to some degree. Furthermore, based on Lyapunov theory, we characterize the consensus error under undirected and directed topologies. Numerical examples are presented to verify the effectiveness of two results.

Practical consensus for heterophilous multiagent networks with constrained states

This paper studies practical consensus problems for continuous-time multiagent systems with heterophilous dynamics. Agents in the network tend to cease communication when they are close enough to each other inspired by the heterophily principle in social and opinion dynamics. We propose two types of state constraints on dynamical agents, in which the hard constraint refers to exogenous restrictions that rule the entire evolution of the agent behavior and the soft constraint turns out to be endogenous and only the ultimate equilibria of the agents are restricted. Sufficient conditions have been established to achieve practical consensus for both types of constrained systems. Numerical simulations show that the practical consensus time grows logarithmically, revealing a rapid convergence with respect to disagreement of initial conditions.

Event-Triggered privacy-preserving average consensus for continuous-time multi-agent network systems

This paper deals with the privacy-preserving average consensus problem for continuous-time multi-agent network systems (MANSs) based on the event-triggered strategy. A novel event-triggered privacy-preserving consensus algorithm is designed to achieve the average consensus of MANSs while avoiding the disclosure of the agents’ initial states. Different from the approaches incorporating stochastic noises, an output mask function in the proposed algorithm is developed to make initial state of each agent indiscernible by the others. Particularly, under the output mask function, all agents can exactly tend to the average value of initial states rather than the mean square value. Under the proposed algorithm, detailed theoretical proof about average consensus and privacy of the MANSs are conducted. Moreover, the proposed algorithm is extended to nonlinear continuous-time MANSs, and the corresponding results are also derived. A numerical simulation eventually is performed to demonstrate the validity of our results.

Flocking of Multi-Agent Systems with Nonuniform and Nonconvex Input Constraints

This paper investigates the nonuniform and nonconvex input constrained flocking control problem of continuous-time multi-agent systems. A distributed flocking control algorithm is proposed for each agent using the local information from its neighbor agents subject to nonuniform and nonconvex control constraints. Based on a constraint scaling factor and a specific coordinate transformation, a Lyapunov function is constructed to address the nonlinearities caused by input constraints. It is proved that all agents from an explicitly specified region of initial states eventually converge to a common point with the same velocity, while each agent's inputs remain within its own constrained nonconvex set. A simulation example is given to demonstrate the effectiveness of the theoretical results.

Continuous-time distributed optimization with strictly pseudoconvex objective functions

In this paper, the distributed optimization problem is investigated by employing a continuous-time multi-agent system. The objective of agents is to cooperatively minimize the sum of local objective functions subject to a convex set. Unlike most of the existing works on distributed convex optimization, here we consider the case where the objective function is pseudoconvex. In order to solve this problem, we propose a continuous-time distributed project gradient algorithm. When running the presented algorithm, each agent uses only its own objective function and its own state information and the relative state information between itself and its adjacent agents to update its state value. The communication topology is represented by a time-varying digraph. Under mild assumptions on the graph and the objective function, it shows that the multi-agent system asymptotically reaches consensus and the consensus state is the solution to the optimization problem. Finally, several simulations are carried out to verify the correctness of our theoretical achievements.