Related papers: Shaping up crowd of agents through controlling the…
We present an unsupervised approach to analyze crowd at various levels of granularity $-$ individual, group and collective. We also propose a motion model to represent the collective motion of the crowd. The model captures the…
Controlling a large population, in the limit, a continuum, of structurally identical dynamical systems with parametric variations is a pervasive task in diverse applications in science and engineering. However, the severely underactuated…
We study optimal control problems for interacting branching diffusion processes, a class of measure-valued dynamics capturing both spatial motion and branching mechanisms. From the perspective of the dynamic programming principle, we…
In this paper, we consider the coordination control of a group of autonomous mobile agents with multiple leaders. Different interconnection topologies are investigated. At first, a necessary and sufficient condition is proved in the case of…
This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…
We study the optimal control problem of minimizing the convergence time in the discrete Hegselmann--Krause model of opinion dynamics. The underlying model is extended with a set of strategic agents that can freely place their opinion at…
We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear…
The paper considers the problem of a leader that seeks to optimally influence the opinions of agents in a directed network through connecting with a limited number of the agents ("direct followers"), possibly in the presence of a fixed…
A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value…
In optimal control problems of control-affine systems, whose solutions are bang-bang or singular type, verification of optimality using the Hamilton-Jacobi-Bellman (HJB) equation involves the computation of partial derivatives of switching…
This paper is concerned with the problem of designing agents able to dynamically select information from multiple data sources in order to tackle tasks that involve tracking a target behavior while optimizing a reward. We formulate this…
We propose a price impact model where changes in prices are purely driven by the order flow in the market. The stochastic price impact of market orders and the arrival rates of limit and market orders are functions of the market liquidity…
In the typical multiagent formation tracking problem centered on consensus, the prevailing assumption in the literature is that the agents' nonlinear models can be approximated by integrator systems, by their feedback-linearized…
We investigate the long time behavior of weakly dissipative semilinear Hamilton-Jacobi-Bellman (HJB) equations and the turnpike property for the corresponding stochastic control problems. To this aim, we develop a probabilistic approach…
We propose a variant of consensus-based optimization (CBO) algorithms, controlled-CBO, which introduces a feedback control term to improve convergence towards global minimizers of non-convex functions in multiple dimensions. The feedback…
Exploiting the efficiency and stability of Position-Based Dynamics (PBD), we introduce a novel crowd simulation method that runs at interactive rates for hundreds of thousands of agents. Our method enables the detailed modeling of per-agent…
Collective motion is an intriguing phenomenon, especially considering that it arises from a set of simple rules governing local interactions between individuals. In theoretical models, these rules are normally \emph{assumed} to take a…
An exact solution is presented to a model that mimics the crowding effect in financial markets which arises when groups of agents share information. We show that the size distribution of groups of agents has a power law tail with an…
Crowd dynamics and many large biological systems can be described as populations of agents or particles, which can only be observed on aggregate population level. Identifying the dynamics of agents is crucial for understanding these large…
In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localized on a fixed control set. We will assume that there is no…