Related papers: Approximation of deterministic mean field type con…
This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a…
When the interactions of agents on a network are assumed to follow the Deffuant opinion dynamics model, the outcomes are known to depend on the structure of the underlying network. This behavior cannot be captured by existing mean-field…
This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior…
The Markov chain approximation of a one-dimensional symmetric diffusion is investigated in this paper. Given an irreducible reflecting diffusion on a closed interval with scale function $s$ and speed measure $m$, the approximating Markov…
This paper studies optimal control under the average-reward/cost criterion for deterministic linear systems. We derive the value function and optimal policy, and propose an approximate solution using Model Predictive Control to enable…
Historically, traffic modelling approaches have taken either a particle-like (microscopic) approach, or a gas-like (meso- or macroscopic) approach. Until recently with the introduction of mean-field games to the controls community, there…
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…
We revisit closed-loop performance guarantees for Model Predictive Control in the deterministic and stochastic cases, which extend to novel performance results applicable to receding horizon control of Partially Observable Markov Decision…
We consider a class of discrete time Markov chains with state space [0,1] and the following dynamics. At each time step, first the direction of the next transition is chosen at random with probability depending on the current location. Then…
The exact treatment of Markovian models of complex systems requires knowledge of probability distributions exponentially large in the number of components $n$. Mean-field approximations provide an effective reduction in complexity of the…
In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
The theory of first-order mean field type differential games examines the systems of infinitely many identical agents interacting via some external media under assumption that each agent is controlled by two players. We study the…
We present a data-driven model predictive control scheme for chance-constrained Markovian switching systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are…
The purpose of this paper is to explore the necessary conditions for optimality of mean-field forward-backward delay control systems. A new estimate is proved, which is a powerfultool to deal with the optimal control problems of mean-field…
In this paper, the problem of non-fragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli…
This paper presents a Distributed Stochastic Model Predictive Control algorithm for networks of linear systems with multiplicative uncertainties and local chance constraints on the states and control inputs. The chance constraints are…
Mean field control provides a robust framework for coordinating large-scale populations with complex interactions and has wide applications across diverse fields. However, the inherent nonlinearity and the presence of unknown system…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is…