25 problems

The Agentic Hive is a formal framework for self-organizing multi-agent systems in which the population of agents undergoes demographic dynamics governed by multi-sector growth theo…

The framework models orchestrated AI agent systems as production economies in the commodity space $\mathcal{H}=L^2([0,T],\mathbb{R}^R)$, with LLM agents as firms, an orchestrator a…

Let $u(\{x_i\},t)$ be the solution of the Hamilton–Jacobi–Bellman equation, let $t_0<t_1<\ldots<t_J$ be a uniform discretization of $[0,t]$ with grid spacing $\delta=t/J$, and let…

Directed-graph extension conjecture. The proposed feedback law can also apply to the more general case of weighted directed graphs.

Let Algorithm … will continue to be a function of the degree of each node. The surrounding analysis establishes finite-time termination in the cases considered, but the general wor…

Let there be multiple moving and possibly camouflaging targets, with the search problem formulated using an objective function such as the expected number of unique targets detecte…

Let $V^{*[2]}(\cdot)$ denote the value function used in the two-agent centralized training phase. Suppose that the condition of the paper's main theorem is satisfied. Two-agent cen…

Let $v_{m,k}(0)$ denote the initial velocity of the $k$-th agent in the $m$-th component, and consider the initial velocity configuration of the nonlinear Cucker--Smale system with…

The paper considers a multi-agent control system in which agents use indirect-design schemes ABSA-1 and ABSA-2 to communicate observations and coordinate control actions, with geom…

Consider a distributed multi-agent control framework in which each subsystem has a central agent, and let $\bar{\mathcal{N}}_i$ denote the subsystem on which agent $i$ computes its…

Consider the systems referred to as the delayed consensus models with proportional and reactive anticipation, denoted by (in the source) systems … . The question concerns whether a…

A configuration consists of a time $t$ together with the positions, directions, and estimates of all drones at that time. A drone is left synchronized at time $t$ if thereafter it…

A configuration consists of a time $t$ together with the positions, directions, and estimates of all drones at that time. A drone is left synchronized at time $t$ if thereafter it…

Let an MPSE problem have pursuers and evaders at positions at time $t$, with $0\leq t<t_c$. Let $\mathcal{B}^t$ be the Apollonius boundary and let $\mathcal{A}_i$ denote the Apollo…

Multidimensional consensus conjecture. Asymptotic global consensus is always found; equivalently,

The vehicle chain consists of identical agents controlled by homogeneous controllers, which may be nonlinear and may use communication; string stability refers to the usual require…

An on-the-fly transport evolves under the primal-dual flow referenced in the source, while a primal flow with a fixed dual function is the analytically established comparison case.…

Joint-connectivity applicability conjecture. The proposed distributed observer and controller also apply to time-varying communication topologies satisfying joint strong connectivi…

Consider the distributed consensus protocol in which the relative velocity magnitude of every agent is … Here $b$ is the decay exponent, and consensus means that the agents' states…

The synchronous heterogeneous Hegselmann–Krause model consists of agents whose opinions evolve synchronously with possibly agent-dependent confidence bounds, so the interaction top…

Vicsek's phase-transition conjecture. The Vicsek model exhibits a second-order phase transition from disordered to ordered motion as a function of the noise and density.

Linearithmic lower-bound conjecture. Any algorithm assuming RP 1–5 requires time

Let $\mathcal{A}_{\rm ave}^\ast$ be the class of distributed averaging algorithms considered in the paper, with time-varying parameters $\{\alpha_k\}$, operating under nearest-neig…

Consider the continuous-time opinion-dynamics system with $n$ agents, and choose the agents' initial opinions independently and randomly according to a bounded probability density…

Let $\tilde s$ be a fixed point of the continuous-time opinion-dynamics system, and let $A$ and $B$ be any two clusters with positions $A$ and $B$ and weights $W_A$ and $W_B$. Stab…