Incentive design constitutes a foundational paradigm for influencing the behavior of strategic agents, wherein a system planner (principal) publicly commits to an incentive mechanism designed to align individual objectives with collective social welfare. This paper introduces the Regret-Minimizing Adaptive Incentive Design (RAID) problem, which aims to synthesize incentive laws under information asymmetry and achieve asymptotically minimal regret compared to an oracle with full information. To this end, we develop the RAID algorithm, which employs a switching policy alternating between probing (exploration) and estimate-based incentivization (exploitation). The associated type estimator relies only on the weakest excitation condition required for strong consistency in least squares estimation, substantially relaxing the persistence-of-excitation assumptions previously used in adaptive incentive design. In addition, we establish the strong consistency of the proposed type estimator and prove that the incentive obtained asymptotically minimizes the planner's average regret almost surely. Numerical experiments illustrate the convergence rate of the proposed methodology.

Graphs provide a natural framework to describe processes shaped by pairwise interactions among agents. But many dynamical systems involve interactions within groups of three or more agents. Here, we develop the “ℓ-hyperedge approximation,” an analytical framework for stochastic processes on regular hypergraphs, in which each individual belongs to k groups of size ℓ. The framework accommodates both higher-order interactions that determine payoffs and higher-order processes for updating states in response to payoffs. For evolutionary games on hypergraphs, our analysis generalizes the classical b/c > k rule for cooperation to the ℓ-player donation game; and it yields critical benefit-to-cost ratios for the nonlinear ℓ-player public goods game, which remains bounded as the degree grows. Applied to neutral complex contagions, where inheritance of states occurs within hyperedges rather than along parent–offspring edges, the framework gives a closed-form fixation probability, showing how a single complexity parameter governs the spread of rare types. Coupling the two processes produces a unified stochastic model of payoff-biased complex contagions in structured populations. Together, these results extend pair approximation from graphs to hypergraphs, accommodating multiway interactions and group-level inheritance with no pairwise analog.

This work describes a collective decision-making dynamical process in a multiagent system under the assumption of cooperative higher-order interactions within the community, modeled as a hypernetwork. The nonlinear interconnected system is characterized by saturated nonlinearities that describe how agents transmit their opinion state to their neighbors in the hypernetwork, and by a bifurcation parameter representing the community's social effort. We show that the presence of higherorder interactions leads to the unfolding of a pitchfork bifurcation, introducing an interval for the social effort parameter in which the system exhibits bistability. With equilibrium points representing collective decisions, this implies that, depending on the initial conditions, the community will either remain in a deadlock state (with the origin as the equilibrium point) or reach a nontrivial decision. A numerical example is given to illustrate the results.

In this article we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We use this to predict the evolution of the distribution of agents by first computing the moment trajectories and then use this to reconstruct the distribution of the agents. In the latter an inverse problem is solved in order to reconstruct a nominal distribution and to recover the macroscale properties of the group of agents. The proposed method is applicable for several types of multiagent systems, e.g., leader-follower systems. We derive error bounds for the moment trajectories and describe how to take these error bounds into account for computing the moment dynamics. The convergence of the moment dynamics is also analyzed for cases with monomial moments. To illustrate the theory, two numerical examples are given. In the first we consider a multiagent system with interactions and compare the proposed method for several types of moments. In the second example we apply the framework to a leader-follower problem for modeling a pedestrian crowd.

This paper addresses formation control of reduced attitudes in which a continuous control protocol is proposed for achieving and stabilizing all regular polyhedra (also known as Platonic solids) under a unified framework. The protocol contains only relative reduced attitude measurements and does not depend on any particular parametrization as is usually used in the literature. A key feature of the control proposed is that it is intrinsic in the sense that it does not need to incorporate any information of the desired formation. Instead, the achieved formation pattern is totally attributed to the geometric properties of the space and the designed inter-agent connection topology. Using a novel coordinates transformation, asymptotic stability of the desired formations is proven by studying stability of a constrained nonlinear system. In addition, a methodology to investigate stability of such constrained systems is also presented.

This paper proposes a privacy-preserving algorithm to solve the average-consensus problem based on Shamir’s secret sharing scheme, in which a network of agents reach an agreement on their states without exposing their individual states until an agreement is reached. Unlike other methods, the proposed algorithm renders the network resistant to the collusion of any given number of neighbors (even with all neighbors’ colluding). Another virtue of this work is that such a method can protect the network consensus procedure from eavesdropping.

In this dissertation, we study two problems within the field of the multi-agent systems theory. One is the formation control for multiple reducedattitudes, which are extensively utilized in many pointing applications and under-actuated scenarios for attitude maneuvers. In contrast to most existing methodologies on the formation control, the proposed method does notneed to contain any formation errors in the protocol. Instead, the constructedformation is attributed to geometric properties of the configuration space andthe designed connection topology. We refer to this type of formation controlas intrinsic formation control. Besides, the control protocols proposed in thiswork are designed directly in space S^2 , avoiding to use any attitude parameterizations. Moreover, along the studies, some elementary tools for reducedattitudes control are developed.

Another problem is a moment-based methodology to modeling and ana-lyzing collective behavior of a group of agents. The theory is applicable fora wide range of applications, such as multi-agent systems with interactionsas well as with leaders and/or control input, and the use of this frameworkcan considerably reduce the computational burden for controlling and ana-lyzing such systems. We therefore propose to develop and use this theory forthe multi-agent applications such as crowd dynamics, opinion dynamics andother macroscopic problems.

Particularly, in paper A a continuous control law is provided for a reduced attitude system, by which a regular tetrahedron formation can achieveasymptotic stability under a quite large family of gain functions in the con-trol. Then, with a further restriction on the control gain, almost global stability of the tetrahedron formation is also obtained. In this work, we introducea novel coordinates transformation that represents the relative reduced atti-tudes between the agents. The proposed method is an intrinsic formationcontrol that does not need to involve any information of the desired formation beforehand. Another virtue of the method proposed is that only relativeattitude measurement is required.

Paper B further concerns the formation control of all regular polyhedralconfigurations (also called Platonic solids) for reduced attitudes. Accord-ing to the symmetries possessed by regular polyhedra, a unified frameworkis proposed for their formations. Via using the coordinates transformationpreviously proposed, it is shown that stability of the desired formations canbe provided by stabilizing a constrained nonlinear system. Then, a method-ology to investigate the stability of this type of constrained systems is alsopresented.

In paper C, we introduce an approach for modeling collective behaviorof a group of agents using moments. We represent the swarming via their dis-tribution and derive a method to estimate the dynamics of the moments. We use this to predict the evolution of the distribution of agents by first computing the moment trajectories and then use this to reconstruct the distributionof the agents. In the latter an inverse problem is solved in order to reconstructa nominal distribution and to recover the macro-scale properties of the groupof agents. The proposed method is applicable for several types of multi-agent systems, including leader-follower systems.

Paper D considers the problem of tracking and encircling a moving target by agents in the 3-dimensional space. In this work, we show that similardesign techniques proposed for reduced attitudes formations can also be applied to the formation control for point mass systems. Therein, a group ofagents are driven to some desired formation on a spherical surface and simultaneously the center of this spherical formation is kept coinciding withthe target to be tracked. By properly designing communication topology, theagents constitute a cyclic formation along the equator of an encircling sphere.

In Paper E, a methodology based on differential geometry techniquesis proposed to investigate exponential stability of a formation for reducedattitudes. By such a method, there is no need in finding any relative coordinates, which is typically needed but shown to be difficult when the formationproblem is evolving in a non-Euclidean space. In the paper, the desired formation is treated as an embedding submanifold in (S^2)^N and by using therotation symmetries owned by the attitude dynamics its stability is directlyexamined. Moreover, such a method turns out to be coordinates free, namely,exponential stability of a formation can be completely determined by just investigating any one equilibrium which can result in the formation under anylocal chart of (S^2 )^N . This greatly simplifies the stability analysis for theformation problems.

In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the occupation measure of the group of agents by their moments and show how the dynamics of the moments can be modeled. Then approximate trajectories of the moments can be computed and an inverse problem is solved to recover macro-scale properties of the group of agents. To illustrate the theory, a numerical example with interactions between the agents is given.

In this work, a methodology based on differential geometry techniques is proposed to investigate exponential stability of a formation for reduced attitudes. By the proposed method, there is no need in finding any relative coordinates, which is typically needed but shown to be difficult when the formation problem is evolving in a non-Euclidean space. In this paper, the desired formation is treated as an embedding submanifold in (S-2)(N) and by using the rotation symmetries owned by the attitude dynamics its stability is directly examined. Moreover, such a method turns out to be coordinates free, namely, exponential stability of a formation can be completely determined by just investigating any one equilibrium which can result in the formation under any local chart of (S-2)(N). This greatly simplifies the stability analysis for the formation problems.

The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed controllers using the vectorized signum function are proposed, which guarantee almost global and local convergence, respectively. Filippov solutions and non-smooth analysis techniques are adopted to handle the discontinuities. Sufficient conditions are provided to guarantee finite-time convergence and boundedness of the solutions. Simulation examples are provided to verify the performances of the control protocols designed in this paper.