We propose a distributed two-degrees-of-freedom (2DOF) architecture for driving autonomous, possibly heterogeneous, agents to agreement. The scheme mirrors classical servo structures, separating local feedback from network filtering. This separation enables independent network-filter design for prescribed noise attenuation and allows controller heterogeneity to reject local disturbances, including disturbances exciting unstable agreement poles – which is known to be impossible via standard diffusive couplings. The potential of the framework is illustrated via two numerical examples.

We study synchronization of heterogeneous control-affine nonlinear agents interconnected through diffusive (relative-output) measurements. We separate the design into an edge-space step—specifying a stabilizing model evolution for relative outputs—and a lift step—realizing the prescribed edge motion using the agents’ allowable input directions, constrained by the control-affine geometry of the agents. We introduce an admissibility notion that characterizes when an edge-driven diffusive design is feasible. We derive checkable combinatorial certificates that connect graph topology and actuation limits directly to admissibility, so that feasible edge dynamics can be verified in a practical and transparent way. The results are illustrated on synchronization of nonlinear oscillators.

We present a distributed formation control strategy for multi-agent systems based only on rotation symmetry constraints. We propose a potential function that enforces inter-agent rotational symmetries, with its gradient defining the control law driving the agents toward a desired symmetric and planar configuration. We show that only (n-1) edges, the minimal connectivity requirement, are sufficient to implement the control strategy, where n is the number of agents. We further augment the design to address the maneuvering problem, enabling the formation to undergo coordinated translations, rotations, and scalings along a predefined virtual trajectory. Numerical simulations demonstrate the effectiveness and flexibility of the proposed method.

This letter presents a geometric input-output analysis of distance-based formation control, focusing on steady-state signal blocking between actuator and sensor pairs. We characterize steady-state transmission zeros via the zero-frequency residue matrix of the linearized closed-loop dynamics, and show that for connected, flexible frameworks, such zeros occur only on a measure-zero algebraic set. For infinitesimally rigid formations, we derive an explicit geometric condition under which steady-state transmission is lost, showing that zeros occur if and only if the sensor lies on an affine hyperplane determined by the actuator and the formation geometry. Building on this result, we introduce the global transmission polygon, a convex region that provides a constructive sensor-placement rule guaranteeing full-rank steady-state transmission under arbitrary single-node excitations.

This paper addresses the problem of identifying leader nodes in semi-autonomous consensus networks from observed agent dynamics. Using the grounded Laplacian formulation, we derive spectral conditions that ensure the components of the Fiedler vector associated with leader and follower nodes are distinct. Building on the foundation, we emply the notion of relative tempo from prio works as an observable quantity that relates agents' steady-state velocities to the Fiedler vector. This relationship enables the development of a data-driven algorithm that reconstructs the Fiedler vector - and consequently identifies the leader set - using only steady-state velocity measurements, without requiring knowledge of the network topology. The proposed approach is validated through nuerical examples, demonstrating how spectral properties and relative tempo measurements can be combined to reveal hidden leadership structures in consensus networks.

This work introduces a generalization of the leader-first follower (LFF) graph structure for solving the bearing-only formation control problem on directed graphs. The first contribution provides an equilibrium, stability, and convergence analysis for a one-follower, multi-leader system (which is not an LFF graph). We then propose an extension to the LFF structure, termed ordered LFF graphs, that allows for additional forward directed edges to be included. Using the results of the one-follower multi-leader system we show that the ordered LFF graphs can be used to solve the directed bearing-only formation control problem. We also show that these structures offer improved convergence speed as compared to the LFF graphs. Numerical simulations are provided to validate the results.

This paper presents a geometric input-output analysis of hidden modes in distance-based formation control. We study the linearized dynamics under a gradient control law to characterize the system's structural limitations and their dynamic consequences. Our main contribution is a unified geometric framework for uncontrollable modes. We first prove that uncontrollable rigid-body modes are pure rotations about the input node, defining a global rotational subspace ℛ_i. To generalize this, we introduce the local rotational subspace, 𝒯_i, which contains all motions, including deformations, that are locally invisible to the controller at node i. These two geometric objects provide a complete decomposition of the uncontrollable subspace. Finally, we demonstrate the dynamic implications of this structure by proving that the system's ability to recover its shape is determined by an input's alignment with the local component of the standard rotational rigid-body mode, directly linking the geometry of hidden modes to disturbance rejection. We illustrate our results with a case study.

This work develops a symmetry-based framework for formation control on cycle graphs using Dihedral point-group constraints. We show that enforcing inter-agent reflection symmetries, together with anchoring a single designated agent to its prescribed mirror axis, is sufficient to realize every 𝒞_nv-symmetric configuration using only n-1 communication links. The resulting control laws have a matrix-weighted Laplacian structure and guarantee exponential convergence to the desired symmetric configuration. Furthermore, we extend the method to enable coordinated maneuvers along a time-varying reference trajectory. Simulation results are provided to support the theoretical analysis.

This work considers the distance constrained formation control problem with an additional constraint requiring that the formation exhibits a specified spatial symmetry. We employ recent results from the theory of symmetry-forced rigidity to construct an appropriate potential function that leads to a gradient dynamical system driving the agents to the desired formation. We show that only $(1+1/|\Gamma|)n$ edges are sufficient to implement the control strategy when there are $n$ agents and the underlying symmetry group is $\Gamma$. This number is considerably smaller than what is typically required from classic rigidity-theory based strategies ($2n-3$ edges). We also provide an augmented control strategy that ensures the agents can converge to a formation with respect to an arbitrary centroid. Numerous numerical examples are provided to illustrate the main results.

We propose a geometric approach to distance-based formation control modeled on a minimum-norm lifting of Riemannian gradient descent in edge-space to node-space. This yields a unified family of controllers, including the classical gradient controller and its directed variant. For the directed case, we give a simple numerical test for local convergence that applies to any directed graph and target. We show that persistence is neither necessary nor sufficient for local convergence of our directed controller and propose an alternative that is necessary and more easily checked.

We study cluster assignment in homogeneous diffusive multi-agent networks. Given the number of clusters and agents within each cluster, we design the network graph ensuring the system will converge to the prescribed cluster configuration. Using recent results linking clustering and symmetries, we show that it is possible to design an oriented graph for which the action of the automorphism group of the graph has orbits of predetermined sizes, guaranteeing the network will converge to the prescribed cluster configuration. We provide bounds on the number of edges needed to construct these graphs along with a constructive approach for their generation. We also consider the robustness of the clustering process under agent malfunction.

This work deals with the output consensus problems for multi-agent systems over balanced digraphs. While passivity-based approaches are widely used for analyzing undirected consensus protocols, we show that they are generally not applicable to the directed linear consensus protocol. To address this limitation, we propose a general approach that enables a passivity-based analysis for network systems with directed couplings. Then, we mitigate the complexity introduced by nonlinearities and directed interconnections by reformulating the general output consensus problem as a convergence analysis on a submanifold. Within this framework, we further focus on the stabilization problem, a specific form of the output consensus problem, and establish a sufficient passivity-based condition for stabilizing multi-agent systems over balanced digraphs. The results are supported by a numerical example.

This work presents a passivity-based analysis for the nonlinear output agreement problem in network systems over directed graphs. We reformulate the problem as a convergence analysis on the agreement submanifold. First, we establish how passivity properties of individual agents and controllers determine the passivity of their associated system relations. Building on this, we introduce the concept of submanifold-constrained passivity and develop a novel compensation theorem that ensures output convergence to the agreement submanifold. Unlike previous approaches, our approach can analyze the network system with arbitrary digraphs and any passive agents. We apply this framework to analyze the output agreement problem for network systems consisting of nonlinear and passive agents. Numerical examples support our results.

This study investigates the state synchronization of linear time-invariant (LTI) agents within a networked environment characterized by intermittent and asynchronous communication, alongside heterogeneous time-varying transmission delays. These delays are not assumed to be known a-priori but only time-stamped. A hybrid controller, augmented with a special kind of predictor, is proposed to compensate for the delays and guarantee synchronization. Notably, synchronization is achieved under comparable conditions to the delay-free case, provided that transmission delays are smaller than the corresponding sampling interval. This is independent of the agents’ dynamics and requires no additional knowledge of the underlying communication topology. An algorithm is presented for implementing the required predictor buffer with a size of one, offering a straightforward and scalable implementation.

This article investigates the bearing‐based formation control problem for second‐order multiagent systems (SMS) in the presence of the bounded disturbances in their models. The main contributions of this article are listed as follows: (1) We extend the bearing formation control to SMS. (2) We propose two novel robust distributed bearing formation control laws. In the first control law, the bearing measurement in the global inertial frame is required. This control law guarantees that the inter‐agent bearings converge to the desired bearings. The second control law requires obtaining the local bearing measurements and relative orientation measurements. This control law guarantees that the inter‐agent bearings converge to the desired bearings and the orientation of each agent converges to a common orientation. Some simulations are conducted, and simulation results verify the effectiveness of the proposed control laws.

This paper studies state synchronization of homogeneous LTI agents to a trajectory generated by a given exosystem under both spatial and temporal communication constraints. In particular, communication between the agents is assumed to be intermittent and asynchronous, i.e. effectively acting on a time-varying graph at irregular sampling instances. The paper extends our previous state-feedback result to the output feedback setting. This naturally requires the introduction of local state observers, which complement local continuous-time emulators of unconstrained closed-loop dynamics. The observer interaction with emulators is not unique and we propose an architecture that greatly streamlines the analysis of the closed-loop system and simplifies the implementation of the scheme. As a result, the synchronization is proved under mild persistency of connectivity assumption on spacial connectivity under arbitrary uniformly bounded sampling intervals.

This article studies two distributed bearing-based event-triggered schemes to achieve formation stabilization. We focus on systems with double-integrator dynamics with bearings sensing capabilities. Firstly, we propose a bearing-only event-triggered condition (ETC) that is edge-dependent which drives the control updates of the agents using only information dependent on relative sensed quantities. Secondly, along with bearing measurements we make use of local agent state measurements to arrive at an ETC that uses this collective measurement to drive the sensing and control updates of an agent. In doing so, we propose a new control law that renders the final formation stationary. Simulations are provided to verify the validity of the proposed algorithms.

This paper studies the prescribed-time relative motion control problem of spacecraft formation flying under input saturation. Using prescribed-time theory, a prescribed-time sliding mode is designed such that the states on the sliding mode converge to the equilibrium in the prescribed time. Based on the prescribed-time sliding mode, a prescribed-time relative motion tracking controller is developed, which guarantees fast formation maneuvers with feasible fuel consumption and strong robustness under input saturation. Furthermore, a simulation example is carried out to verify the effectiveness of the proposed controller.

This letter provides a characterization of linear passivizing input-output transformations for MIMO systems with known passivity indices. Building on recent results for SISO systems, we show that any transformation mapping an I/O (rho,nu) -passive MIMO system to an I/O (rho(& lowast;),nu*)-passive system can be expressed as the product of three matrices - two depending on the original and desired passivity indices, and a matrix satisfying a matrix inequality. This parameterization enables formulation of optimal passivation problems that we explore as an application example.

Passivity theory is one of the cornerstones of control theory providing a systematic way to study the stability of interconnected systems. It is well known that many systems are not passive, and must be passivized in order to be included in the framework of passivity theory. Input-output (loop) transformations are the most general tool for passivizing systems. In this paper, we propose a characterization of all possible input-output transformations that map a system with given shortage of passivity to a system with prescribed excess of passivity. We do so by using the connection between passivity theory and cones for SISO systems.