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In this paper, we consider a mobility system of travelers and providers, and propose a "mobility game" to study when a traveler is matched to a provider. Each traveler seeks to travel using the services of only one provider, who manages one…

In this paper, we introduce an optimal control problem for multi-agent systems with non-local cost which favors simultaneous aggregation of particles. This is done introducing a time-dependent notion of multiplicity whose intrinsic…

In hybrid force-velocity control, the robot can use velocity control in some directions to follow a trajectory, while performing force control in other directions to maintain contacts with the environment regardless of positional errors. We…

In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…

In this survey we consider mathematical models and methods recently developed to control crowd dynamics, with particular emphasis on egressing pedestrians. We focus on two control strategies: The first one consists in using special agents,…

This paper derives a closed-form method for computing hybrid force-velocity control. The key idea is to maximize the kinematic conditioning of the mechanical system, which includes a robot, free objects, a rigid environment and contact…

We analyze the dynamics of multi-agent collective behavior models and their control theoretical properties. We first derive a large population limit to parabolic diffusive equations. We also show that the non-local transport equations…

The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid…

We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…

We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…

To determine an optimal plan for complex tasks, one often deals with dynamic and hierarchical relationships between several entities. Traditionally, such problems are tackled with optimal control, which relies on the optimization of cost…

This paper presents a novel hybrid control protocol for de-conflicting multiple vehicles with constraints on control inputs. We consider turning rate and linear speed constraints to represent fixed-wing or car-like vehicles. A set of…

This paper is devoted to a class of finite horizon deterministic mean field games with Grushin type dynamics, state constraints and nonlocal coupling. First, we consider the optimal control problem that each agent aims to solve when the…

Relying on the careful study of a related problem in the calculus of variations, we study a class of optimal control problems in which the control lies on the acceleration, with state constraints on the position variable. In dimension one,…

In this paper, we develop a control framework for the coordination of multiple robots as they navigate through crowded environments. Our framework comprises of a local model predictive control (MPC) for each robot and a social long…

This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…

Optimal transport (OT) and Schr{\"o}dinger bridge (SB) problems have emerged as powerful frameworks for transferring probability distributions with minimal cost. However, existing approaches typically focus on endpoint matching while…

We model and analyze a herding problem, where the drivers try to steer the evaders' trajectories while the evaders always move away from the drivers. This problem is motivated by the guidance-by-repulsion model [Escobedo, R., Iba\~nez, A.…

This paper focuses on the role of a government of a large population of interacting agents as a mean field optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a PDE of…

In many multi-agent systems of practical interest, such as traffic networks or crowd evacuation, control actions cannot be exerted on all agents. Instead, controllable leaders must indirectly steer uncontrolled followers through local…