Related papers: Kinetic description of optimal control problems an…
In this paper, we present a critical collection of essential mathematical tools and techniques for the analysis of Boltzmann-type kinetic equations, which in recent years have established themselves as a flexible and powerful paradigm to…
This paper investigates the social optimality of linear quadratic mean field control systems with unmodeled dynamics. The objective of agents is to optimize the social cost, which is the sum of costs of all agents. By variational analysis…
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…
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 survey some recent developments on the mathematical modeling of opinion dynamics. After an introduction on opinion modeling through interacting multi-agent systems described by partial differential equations of kinetic type, we focus our…
This paper focuses on a model for opinion dynamics, where the influence weights of agents evolve in time. We formulate a control problem of consensus type, in which the objective is to drive all agents to a final target point under suitable…
We present a formulation of an optimal control problem for a two-dimensional diffusion process governed by a Fokker-Planck equation to achieve a nonequilibrium steady state with a desired circulation while accelerating convergence toward…
We consider the problem of controlling the group behavior of a large number of dynamic systems that are constantly interacting with each other. These systems are assumed to have identical dynamics (e.g., birds flock, robot swarm) and their…
We exhibit optimal control strategies for a simple toy problem in which the underlying dynamics depend on a parameter that is initially unknown and must be learned. We consider a cost function posed over a finite time interval, in contrast…
We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem…
We discuss kinetic-based particle optimization methods and variable-sample strategies for problems where the cost function represents the expected value of a random mapping. Kinetic-based optimization methods rely on a consensus mechanism…
We present a dynamic programming-based solution to a stochastic optimal control problem up to a hitting time for a discrete-time Markov control process. Firstly, we determine an optimal control policy to steer the process toward a compact…
The article poses a general model for optimal control subject to information constraints, motivated in part by recent work of Sims and others on information-constrained decision-making by economic agents. In the average-cost optimal control…
We present the analysis of the stationary equilibria and their stability in case of an opinion formation process in presence of binary opposite opinions evolving according to majority-like rules on social networks. The starting point is a…
We study the synthesis of optimal control policies for large-scale multi-agent systems. The optimal control design induces a parsimonious control intervention by means of l-1, sparsity-promoting control penalizations. We study instantaneous…
We present a control framework for stochastic compartmental models in epidemiology. In this framework, rather than directly controlling the stochastic system, we perform optimal control of an associated Fokker-Planck equation, with the goal…
This paper concerns an optimal control problem $(P)$ related to a nonlinear Fokker-Planck equation. The problem is deeply related to a stochastic optimal control problem $(P_S)$ for a McKean-Vlasov equation. The existence of an optimal…
We design receding horizon control strategies for stochastic discrete-time linear systems with additive (possibly) unbounded disturbances, while obeying hard bounds on the control inputs. We pose the problem of selecting an appropriate…
We study a continuous-time version of the Hegselmann-Krause model describing the opinion dynamics of interacting agents subject to random perturbations. Mathematically speaking, the opinion of agents is modelled by an interacting particle…
This paper presents a data-driven method to find a closed-loop optimal controller, which minimizes a specified infinite-horizon cost function for systems with unknown dynamics. Suppose the closed-loop optimal controller can be parameterized…