This special session represents the 3rd edition in a distinguished series dedicated to Open Multi-Agent Systems (OMASs), building upon the momentum of previous successful editions:

• 1st ed., Open Multi-agent Sytems: Theory and Applications, 63rd IEEE Conference on Decision and Control (CDC, 2024)

• 2nd ed., Open Multi-Agent Systems: Control, Optimization, and Learning, 64th IEEE Conference on Decision and Control (CDC, 2025)

The organizers are thrilled to host for the first time this special session at the IFAC World Congress, the flagship event of the International Federation of Automatic Control (IFAC). Their goal is to facilitate focused exchange on compelling and emerging challenges in OMASs. Collectively, the organizers have made significant contributions to this field, with extensive publications in leading international journals on topics spanning control, optimization, and learning. They are also active members of both the IFAC and IEEE control communities, dedicated to advancing research and collaboration in this dynamic area.

Both theoretical and application-oriented contributions to OMASs are welcomed to be presented in this special sessions, with topics including, but not limited to, the following:

• Analysis and Control of OMASs

• Privacy, Security and Resiliency in OMASs

• Open Multi-Robot Systems

• Distributed Optimization

• Cooperative Learning and Control

• Online Learning

• Consensus Algorithms

• Distributed Estimation

• Resource Allocation Problems

• Game Theory

• Multi-Dimensional Systems

Coordination control of OMASs involves ensuring that a time-varying number of interconnected systems coordinate their actions according to their objective and the constraints imposed between agents or in the environment. A prominent example is a network of bitcoin miners competing for reward by adding blocks of transactions to the blockchain. These miners can join or leave the network at any time after winning or when the profitability does not justify the costs. Another example concerns decentralized machine learning systems, in which data owners together train a global model without sharing raw data. These devices may connect and disconnect at irregular intervals for privacy reasons or connectivity issues, requiring the learning algorithm to be adaptive and robust. A central aspect of coordination is achieving agreement—commonly referred to as consensus—on certain variables or quantities of interest. Achieving consensus often requires the design and implementation of specialized protocols that address the so-called consensus problem, tail tailored to ensure that, despite the time-varying composition and size of the network, agents can reliably synchronize their states or decisions [1],[4-6],[10],[17]. Consensus protocols are not only pivotal for coordination but also serve as foundational building blocks in a wide range of distributed computation and learning algorithms [2],[8],[12],[15]. They underpin essential tasks such as distributed optimization, resource allocation, and cooperative estimation, making them integral to the advancement of both theoretical and practical aspects of OMASs.

The control and coordination of OMAS enable a wide range of real-world applications, from the deployment of autonomous vehicles in unfamiliar or unknown environments to coordination management in swarm robotics or smart infrastructure, as well as in transport and energy sectors [11]. Beyond engineering, OMAS models also capture complex interactions in social systems, as in opinion dynamics [7],[14], where agents influence each other and react to external factors such as competition from marketers. As many real-world systems are dynamic due to changes in the environment or mission objective, new agents may join or leave the system over time, and the nature of interactions between them may change.

This type of system appears naturally in many applications related to social networks, where the size of the graph evolves according to the arrivals and departures of participants [7],[14]. In this type of context, relationships can also change as interactions between individuals evolve: new friendships are formed to exchange ideas and gain knowledge from others, old friendships are dissolved when they lose interest, or changes/shifts in opinion or alliances transform cooperation into conflict (like/dislike) over time. On the other hand, in opinion dynamics, consumer behavior (follower) is shaped both by the influence of peers (neighbors) and by external entities, such as competing marketers (leaders). If a consumer (follower) becomes a marketer (leader), their influence shifts from passivity to active influence on the opinions of others.

Similarly, OMASs also appear in robotic systems, where mobile robots collaborate to achieve global goals such as transporting goods or checking inventories. In particular, in the case of sensor-based robotic systems, the network topology varies depending on the sensing range of each agent and is therefore adapted according to the inter-agent distances to add newcomers to the system and maintain overall graph connectivity [11]. In addition, since robotic systems are used for more complex and long-term missions, robots need to be deployed for long periods. Thus it is important to take into account robots that leave the network to recharge or due to malfunctions. The topology can also change due to environmental factors, such as antagonistic environments, attacks, or mission updates, leading to malfunctions in robots or robots that initially collaborate to later compete for resources or adapt their behavior to avoid obstacles [13]. Equivalently, when executing tasks in uncertain or unknown environments, it may be necessary for new robots to join the system dynamically, as the task specification or environment evolves.

Most results on coordination control, optimization algorithms, game strategies or learning techniques from the current literature on MASs deal with the case where the number of agents in a system remains the same. With this simpler assumption of a static network, many effective control algorithms, stability guarantees, and network performance to reach an equilibrium point have been proven. However, these results lose their relevance when the network under consideration becomes open and agents intermittently join and leave it. 

The open context of the network can raise many problems in control design and analysis procedures because, due to the nature of agents joining and leaving, the system is constantly changing dimension. Firstly, this change in dimension can lead to a loss of connectivity in the network, particularly when a node occupying an important position leaves the network and renders it disconnected. As a result, agents cease to communicate and the overall system objective is no longer attainable. This behavior can also lead to a sudden increase or decrease in system energy due to spontaneous changes in state size between different modes. It can also prevent the system from reaching equilibrium, making it even divergent and unstable.

Several approaches have been adopted to tackle the above-mentioned problems. Early work on OMASs includes [1],[5],[7]. One way is to define a fixed, but arbitrarily large, dimension of the system from the outset and make a fraction of the agents active, defining the real dimension of the network, while others are inactive [14]. Another way of approaching this problem is to use switched systems, but most existing literature on switched systems assume that all switching modes have the same state dimension (same number of agents), which simplifies analysis and design procedures. A general stability framework for nonlinear OMASs is introduced in [16], modeling the system as a switched system under dimension-varying dynamics and average dwell time, allowing for temporary disconnections. Building on this, some other works also addressed the synchronization problem of OMASs using switched system representation [11],[13]. When no a priori bound is considered on the number of agents as in the previously mentioned approaches, it becomes necessary to develop new mathematical concept and tools to study stability and convergence of open systems. Toward this end, generalized concepts for equilibrium points and distance between points of different dimension have been proposed in [3-5] together with convergence results for contractive and paracontractive systems. By treating agents arrivals and departures as an input to the system, in [9] open systems are described as impulsive systems that change at impulse times. Within the proposed framework, input-to-state stability criteria for the open system are provided.

Therefore, the difficulty of designing distributed algorithms that can be deployed on open networks and provide formal performance guarantees, is mainly due to the lack of formal mathematical tools for analyzing the dynamics of systems with a variable number of components. Thus, it is crucial to study the emerging challenges of OMASs and contribute with novel robust algorithms that make systems resilient to the dynamical changes related to the addition and removal of agents.

[1] Abdelrahim, M., Hendrickx, J.M., and Heemels, W. (2017). Max-consensus in open multi-agent systems with gossip interactions. In Proc. IEEE CDC, 4753– 4758. 

[2] de Galland, C.M., Vizuete, R., Hendrickx, J.M., Frasca, P., and Panteley, E. (2021). Random coordinate descent algorithm for open multi-agent systems with complete topology and homogeneous agents. In Proc. IEEE CDC, 1701–1708. 

[3] Deplano, D., Franceschelli, M., and Giua, A. (2024). Stability of paracontractive open multi-agent systems. In Proc. IEEE CDC, 3031–3036.

[4] Deplano, D., Bastianello, N., Franceschelli, M., and Johansson, K.H. (2025). Optimization and learning in open multi-agent systems. arXiv preprint arXiv:2501.16847.

[5] Franceschelli, M. and Frasca, P. (2020). Stability of open multiagent systems and applications to dynamic consensus. IEEE Trans. on Autom. Control, 66(5), 2326–2331. 

[6] Hadjicostis, C.N. and Dominguez-Garcia, A.D. (2024). Distributed average consensus in open multi-agent systems. In Proc. IEEE CDC, 3037–3042.

[7] Hendrickx, J.M. and Martin, S. (2017). Open multiagent systems: Gossiping with random arrivals and departures. In Proc. IEEE CDC, 763–768. 

[8] Hsieh, Y.G., Iutzeler, F., Malick, J., and Mertikopoulos, P. (2021). Optimization in Open Networks via Dual Averaging. In Proc. IEEE CDC, 514–520.

[9] Mironchenko, A. (2025). Modeling and stability analysis of live systems with time-varying dimension. arXiv preprint arXiv:2501.15991.

[10] Oliva, G., Franceschelli, M., Gasparri, A., and Scala, A. (2023). A sum-of-states preservation framework for open multi-agent systems with nonlinear heterogeneous coupling. IEEE Trans. on Autom. Control, 69(3), 1991– 1998. 

[11] Restrepo, E. and Giordano, P.R. (2024). A distributed strategy for generalized biconnectivity maintenance in open multi-robot systems. In Proc. IEEE CDC, 3043– 3050. 

[12] Sawamura, R., Hayashi, N., and Inuiguchi, M. (2024). A distributed primal-dual push-sum algorithm on open multiagent networks. IEEE Trans. on Autom. Control, 70(2), 1192-1199.

[13] Sekercioglu, P., Fontan, A., and Dimarogonas, D.V. (2025). Stability of open multi-agent systems over dynamic signed graphs. arXiv preprint arXiv:2504.21443. 

[14] Varma, V.S., Morarescu, I.C., and Nesic, D. (2018). Open multi-agent systems with discrete states and stochastic interactions. IEEE Control Systems Letters, 2(3), 375– 380. 

[15] Vizuete, R., de Galland, C.M., Hendrickx, J.M., Frasca, P., and Panteley, E. (2022). Resource allocation in open multi-agent systems: an online optimization analysis. In Proc. IEEE CDC, 5185–5191. 

[16] Xue, M., Tang, Y., Ren, W., and Qian, F. (2022). Stability of multi-dimensional switched systems with an application to open multi-agent systems. Automatica, 146, 110644. 

[17] Zhou, B., Park, J.H., Yang, Y., Jiao, Y., and Hao, R. (2024). Dynamic weighted average consensus of open time-varying multi-agent systems on time scales via sampled-data impulsive communication. IEEE Trans. on Network Science and Engineering, 11(5), 4330-4343.