Related papers: Optimal Control Problems in Transport Dynamics
The issues in air traffic control have so far been addressed with the intent to improve resource utilization and achieve an optimized solution with respect to fuel comsumption of aircrafts, efficient usage of the available airspace with…
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,…
The study of population dynamics originated with early sociological works but has since extended into many fields, including biology, epidemiology, evolutionary game theory, and economics. Most studies on population dynamics focus on the…
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…
Efficient motion planning algorithms are of central importance for deploying robots in the real world. Unfortunately, these algorithms often drastically reduce the dimensionality of the problem for the sake of feasibility, thereby foregoing…
We investigate how to control optimally a traffic flow through a junction on the line by acting only on speed reduction or traffic light at the junction. We show the existence of an optimal control and, under structure assumptions, provide…
We address the problem of controlling the density of a large ensemble of follower agents by acting on a group of leader agents that interact with them. Using coupled partial integro-differential equations to describe leader and follower…
In this work, we consider the two dimensional tidal dynamics equations in a bounded domain and address some optimal control problems like total energy minimization, minimization of dissipation of energy of the flow, etc. We also examine an…
State-dependent networked dynamical systems are ones where the interconnections between agents change as a function of the states of the agents. Such systems are highly nonlinear, and a cohesive strategy for their control is lacking in the…
We consider a probabilistic model for large-scale task allocation problems for multi-agent systems, aiming to determine an optimal deployment strategy that minimizes the overall transport cost. Specifically, we assign transportation agents…
We propose a new method for trajectory planning to solve the data harvesting problem. In a two-dimensional mission space, $N$ mobile agents are tasked with the collection of data generated at $M$ stationary sources and delivery to a base…
Motivated by the fact that intelligent traffic control systems have become inevitable demand to cope with the risk of traffic congestion in urban areas, this paper develops a distributed control strategy for urban traffic networks. Since…
We propose an optimal solution to a deterministic dynamic assignment problem by leveraging connections to the theory of discrete optimal transport to convert the combinatorial assignment problem into a tractable linear program. We seek to…
We consider a stochastic impulse control problem that is motivated by applications such as the optimal exploitation of a natural resource. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a…
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…
Modeling and control of agent-based models is twice cursed by the dimensionality of the problem, as both the number of agents and their state space dimension can be large. Even though the computational barrier posed by a large ensemble of…
This paper studies the problem of optimal flow control in dynamic inventory systems. A dynamic optimal distribution problem, including time-varying supply and demand, capacity constraints on the transportation lines, and convex flow cost…
Consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources distribution in a given box. We…
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…
We consider the optimal control problem of steering an agent population to a desired distribution over an infinite horizon. This is an optimal transport problem over a dynamical system, which is challenging due to its high computational…