Coverage control in multi-agent systems subject to communication delays

Multi-agent Robots Systems (MARS) can be defined as sets of autonomous robots coordinated through a communication system to achieve cooperative tasks. During the last 20 years, MARS have found a wide range of applications in terrestrial, spatial and oceanic explorations emerging as a new research area (Cao et al. (1997)). Some advantages can be obtained from the collective behavior of MARS. For instance, the kind of tasks that can be accomplished are inherently more complex than those a single robot can accomplish. Also, the system becomes more flexible and fault-tolerant (Yamaguchi (2003)). The range of applications includes toxic residues cleaning, transportation and manipulation of large objects, alertness and exploration, searching and rescue tasks and simulation of biological entities behaviors (Arai et al. (2002)). The study ofMARS extends the classical problems of single robotswith new issues likemotion coordination, task decomposition and task assignment, network communications, searching and mapping, etc. Therefore, the study of MARS encompass distributed systems, artificial intelligence, game theory, biology, ethology, economics, control theory, etc. Motion coordination is an important research area of MARS, specifically formation control (Chen & Wang (2005)). The main goal is to coordinate a group of mobile agents or robots to achieve a desired formation pattern avoiding inter-agent collisions at the same time. The formation strategies are decentralized because it is assumed that every agent measures the position of a certain subset of agents and, eventually, it detects the position of other agents when a minimal allowed distance is violated and collision danger appears. Thus, the main intention is to achieve desired global behaviors through local interactions (Francis et al. (2004)). Also, the decentralized approaches offer greater autonomy for the robots, less computational load in control implementations and its applicability to large scale groups (Do (2007)). According to Desai (2002); Muhammad & Egerstedt (2004), the possible inter-agent communications and the desired relative position of every agent with respect to the others can be represented by a FormationGraph (FG). The application of different FG’s to the same group of robots produces different dynamics on the team behavior. In the literature, some special FG topologies are chosen and the convergence to the desired formation and non-collision is analyzed for any number of robots. A decentralized formation strategy must comply with two fundamental requirements: Global convergence to the desired formation and inter-agent collision avoidance (Cao et al. (1997)). 6

In this dissertation, new algorithms for formation control of multi agent systems (MAS) based on continuum mechanics principles will be suggested. For this purpose, agents of the MAS are considered as particles in a continuum, evolving in R^n, whose desired configuration is required to satisfy an admissible deformation function. Considered is a specific class of mappings that are called homogenous where the Jacobian of the mapping is only a function of time and is not spatially varying. The primary objectives of this dissertation are to develop the necessary theory and its validation on a mobile-agent based swarm test bed that includes two primary tasks: 1) homogenous transformation of MAS and 2) deployment of a random distribution of agents on a desired configuration. Developed will be a framework based on homogenous transformations for the evolution of an MAS in an n-dimensional space (n=1,2, and 3), under1) no inter-agent communication (predefined motion plan), 2) local inter-agent communication, and 3) intelligent perception by agents. In this dissertation, different communication protocols for MAS evolution that are based on certain special features of a homogenous transformation will be developed. It is also aimed to deal with the robustness of tracking of a desired motion by an MAS evolving in R^n. Furthermore, the effect of communication delays in an MAS evolving under consensus algorithms or homogenous maps is investigated. In this regard, the maximum allowable communication delay for MAS evolution is formulated on the basis of eigen-analysis.

Control of time-delay systems represents one important class of control problems. A lot of work has been done in recent years. Much of the research work has been focused on the stability analysis and stabilization of time-delay systems based on the Lyapunov functional and linear matrix inequality (LMI) approaches. While the LMI approach does provide an e±cient tool, the results are mostly only su±cient and only numerical solutions are available. Our research aims to present analytical solutions by some algebraic approaches, which can provide an insightful understanding of control problem of time-delay systems. On the other hand, there has also been significant recent interest in networked multi-agent system (MAS) where unavoidably there exist delays in information acquisition as well as information exchange between agents in addition to possible input/state delays in each agent. This motivates the study of MASs with input and communication delays. The thesis is divided into two parts: Part I is focused on optimal control of single agent systems with multiple input delays; Part II is on distributed consensus control of MAS with communication and input delays. More specifically, in Part I, we shall study the linear quadratic regulation (LQR) and tracking for a single agent with linear dynamics. We first focus on LQR for linear discrete-time systems with multiple delays in a single input channel. By introducing a backward stochastic system, we establish a relationship between the LQR problem for the original system and optimal estimation for a backward stochastic system which can be solved by using projection approach. The explicit optimal controllers are developed for both finite time and infinite time horizon cases. A parallel result for linear continuous-time systems is also established, where the optimal feedback gain is given in terms of the solution of Riccati-type partial differential equations (PDEs).

Cluster consensus problem of the multi-agent systems with communication delay is studied in this paper. We consider the multi-agent systems with a special Laplacian matrix as its system matrix. For two types of protocols with time-delay, our work shows that the multi-agent systems with communication delays can reach cluster consensus. Some numerical simulations are given to verify the effectiveness of the theoretical results.

This paper presents control algorithms for multiple non-holonomic mobile robots moving in formation. Trajectory tracking based on linear feedback control is combined with inter-agent collision avoidance. Artificial potential functions (APF) are used to generate a repulsive component of the control. Stability analysis is based on a Lyapunov-like function. Then the presented method is extended to include a goal exchange algorithm that makes the convergence of the formation much more rapid and, in addition, reduces the number of collision avoidance interactions. The extended method is theoretically justified using a Lyapunov-like function. The controller is discontinuous but the set of discontinuity points is of zero measure. The novelty of the proposed method lies in integration of the closed-loop control for non-holonomic mobile robots with the distributed goal assignment, which is usually regarded in the literature as part of trajectory planning problem. A Lyapunov-like function joins both trajectory tracking and goal assignment analyses. It is shown that distributed goal exchange supports stability of the closed-loop control system. Moreover, robots are equipped with a reactive collision avoidance mechanism, which often does not exist in the known algorithms. The effectiveness of the presented method is illustrated by numerical simulations carried out on the large formation of robots.

The paper presents a novel approximation method for discrete-time Multi-Agent System (MAS)s with communication delay. The applied approximation method was initially developed for a class of infinite-dimensional homogeneous or-dinary linear Volterra difference systems. First, we extend this approximation to non-homogeneous systems. Second, based on this approximation, we have shown that discrete-time MAS with communication delay and small gains is asymptotically equivalent to a MAS without communication delay. We give an algorithm to compute the delay-free MAS model and we have analysed its properties. Simulations are presented to show the applicability of the proposed approximation approach.

This paper considers the time delay issue in the communication process among multi-agents with directed fixed topology and presents a consensus protocol. Then a sufficient condition for multi-agent system obtaining global asymptotic consistency under directed fixed topological is proved. Furthermore, the upper bound of compactness for the largest time delay is provided and the information consistency idea is applied to the formation control of multi-agent. Finally, some simulations are performed to verify the theoretical results proposed in this paper and the simulation results show that method based on the consistency protocol can be successfully applied to multi-agent networked system with communication delay and the preset formation can be completed well.

The finite-time coverage control problem for networked mobile agents with continuous-time dynamics and unidirectional motion constraint on a closed curve is addressed in this article. The objective is to minimize a coverage cost function in finite time which characterizes the largest arrival time from the multiagent system to any point on the curve. Low gain feedback is employed to design the distributed coverage control laws for the agents with different input constraints due to their limited movement capabilities. An upper bound on each low gain is also provided by showing that the distance between the neighboring agents is always lower and upper bounded. Under the proposed control laws, the networked mobile agents can be driven to the optimal configuration, minimizing the coverage cost function in finite time. Due to the unidirectional motion of the agents, there exists at least one agent which remains static throughout the coverage task. As a result, a less conservative upper bound on the low gains is derived, which provides the possibility of better convergence rates of the proposed coverage control laws.

Distributed control and optimization form the backbone of many critical control systems, with typical examples including sensor networks, power grids, and intelligent transportation systems. As these systems grow in scale and complexity, ensuring the privacy of individual agents becomes increasingly essential. Privacy protection is no longer an optional add-on; it is a crucial element in the design of these systems. Sensitive data, such as states, measurements, and decisions, must be shielded from unauthorized access or malicious attacks, while still allowing the system to function effectively. This special issue aims to explore novel techniques and strategies that protect privacy in distributed control and optimization, showcasing how these approaches can be seamlessly integrated into real-world applications. The diverse contributions in this issue demonstrate the growing importance of privacy in the evolving field of distributed control systems. RNC7747 introduces a privacy-preserving method for coverage control in multi-agent systems with limited communication ranges, ensuring efficient operation without compromising agents' privacy. RNC7798 proposes a privacy-preserving consensus mechanism based on pulse-coupled oscillators, helping maintain privacy while agents coordinate in distributed networks. RNC7778 presents privacy preservation techniques for cloud-based cooperative LQG control systems, enabling privacy protection even when leveraging cloud resources. RNC8051 discusses achieving privacy-preserving average consensus in unreliable network environments, ensuring privacy despite communication challenges. RNC7929 introduces a novel approach to open privacy-preserving consensus via state decomposition, allowing agents to reach consensus while maintaining privacy. RNC7966 investigates leader-follower consensus in multi-agent systems with distributed event-triggered observations, ensuring privacy during agent coordination in real-time systems. RNC7789 discusses the tradeoff between privacy protection strength and control performance in control systems. RNC8029 proposes a new privacy mechanism for distributed average consensus on time-varying directed graphs. RNC7776 investigates event-triggered distributed optimization with differential privacy, reducing communication costs while safeguarding sensitive data. RNC7885 develops an event-triggered privacy-preserving optimization method for directed communication networks, emphasizing privacy during optimization tasks. RNC7791 focuses on robust optimization for virtual power plant scheduling under uncertainty, incorporating privacy preservation into the optimization process. RNC7730 explores prescribed-time distributed optimization with set constraints, offering time guarantees while maintaining privacy in dynamic optimization scenarios. RNC7926 provides a privacy-preserving algorithm for constrained resource allocation with communication delays, crucial for real-time decision-making in distributed systems. RNC7848 presents an adaptive event-triggered control strategy for cyber-physical systems under DoS and deception attacks, ensuring privacy and system security. RNC8068 addresses initial state privacy in nonlinear systems on Riemannian manifolds, offering methods to protect privacy in complex, high-dimensional control systems. RNC7906 focuses on dynamic consensus-based formation control for multi-robot systems, preserving privacy through output masking techniques while achieving coordination. RNC7688 introduces a periodic dynamic encoding mechanism for stealthy attack detection in distributed state estimation, focusing on security and privacy under attack scenarios. RNC70033 tackles robust consensus Kalman filtering for distributed state-saturated systems, incorporating dynamic-disturbed saturation levels and censored measurements to ensure privacy under uncertain conditions. The contributions in this special issue span a broad spectrum of topics related to privacy in distributed control and optimization. As distributed systems continue to evolve, these papers contribute to the ongoing conversation about balancing privacy protection with efficient system operation, highlighting the importance of privacy as a key consideration in the design and optimization of future distributed control systems. The authors declare no conflicts of interest.

This paper concerns the problem of formation‐containment control for general‐linear multi‐agent systems (MASs) with both communication delays and switching interaction topologies. On the one hand, the leaders can communicate with each other to form the desired formation and on the other, the followers need to enter the convex envelope spanned by the multiple leaders. Firstly, by using the neighbouring relative information, formation‐containment protocols are designed for each leader and follower, where an edge‐based state observer is incorporated into the formation‐containment controller to evaluate the whole leaders' state. Secondly, according to the linear matrix inequality technology, an algorithm is given to determine the unknown feedback matrixes in the protocol. Then, based on Lyapunov theory, the formation‐containment error is proved to be convergent and formation feasibility conditions are also presented for the MASs to achieve formation‐containment. Finally, a simulation on several MASs is provided to demonstrate the theoretical results.

In this article, we investigate the distributed resilient control problem for a class of cyber-physical systems with communication delays under denial-of-service (DoS) attacks. In contrast to the previous DoS attacks results based on multiagent systems (MASs), a new distributed resilient control approach is proposed for more general heterogeneous linear MASs with nonuniform communication delays. Two types of sampled-based observers are, respectively, proposed. Namely, adaptive distributed observers are designed by introducing a buffer mechanism to eliminate the heterogeneous behavior caused by communication delays while adaptive distributed resilient observers are designed by introducing resilient mechanisms to resist the DoS attacks. Furthermore, a time-varying sampling period sequence is provided to prevent the attacker from identifying the sampling period of the system. Based on the developed resilient observers, a controller is developed. It is proved that the considered problem can be solved by the developed method. Finally, a numerical example is given to illustrate the effectiveness of the obtained result.

Time-varying group formation tracking control for second-order multi-agent systems with communication delays and multiple leaders

Cooperative path planning for unmanned aerial vehicle (UAV) swarms has attracted considerable research attention, yet it remains challenging in complex, uncertain environments. To tackle this problem, we model the cooperative path planning task as a heterogeneous decentralized Markov Decision Process (MDP), emphasizing the symmetry-inspired role assignment between leader and wingmen UAVs, which ensures balanced and coordinated behaviors in dynamic settings. We address the problem using a Multi-Agent Soft Actor-Critic (MASAC) framework enhanced with a symmetry-aware reward mechanism designed to optimize multiple cooperative objectives: simultaneous arrival, formation topology preservation, dynamic obstacle avoidance, trajectory smoothness, and inter-agent collision avoidance. This design promotes behavioral symmetry among agents, enhancing both coordination efficiency and system robustness. Simulation results demonstrate that our method achieves efficient swarm coordination and reliable obstacle avoidance. Quantitative evaluations show that our MASAC-CA algorithm achieves a Mission Success Rate (MSR) of 99.0% with 2–5 wingmen, representing approximately 13% improvement over baseline MASAC, while maintaining Formation Keeping Rates (FKR) of 59.68–26.29% across different swarm sizes. The method also reduces collisions to near zero in cluttered environments while keeping flight duration, path length, and energy consumption at levels comparable to baseline algorithms. Finally, the proposed model’s robustness and effectiveness are validated in complex uncertain environments, underscoring the value of symmetry principles in multi-agent system design.

Output-constrained fixed-time coordinated control for multi-agent systems with event-triggered and delayed communication

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