Empirically derived continuum models of collective behavior among large populations dynamic agents are a subject intense study in several fields, including biology, engineering, and finance. We formulate mean-field game model whose mimics an empirically nonlocal homogeneous flocking for with gradient self-propulsion dynamics. The framework provides non-cooperative optimal control description the population distributed setting. In this description, each agent's state is driven by optimally...

We present a novel trajectory optimization framework to address the issue of robustness, scalability and efficiency in optimal control reinforcement learning.Based on prior work Cooperative Stochastic Differential Game (CSDG) theory, our method performs local using cooperative controllers.The resulting is called Game-Differential Dynamic Programming (CG-DDP).Compared related methods, CG-DDP exhibits improved performance terms robustness efficiency.The proposed also applied data-driven...

Mean field games (MFG) have emerged as a viable tool in the analysis of large-scale self-organizing networked systems. In particular, MFGs provide game-theoretic optimal control interpretation emergent behavior noncooperative agents. The purpose this paper is to study MFG models which individual agents obey multidimensional nonlinear Langevin dynamics, and analyze closed-loop stability fixed points corresponding coupled forward-backward partial differential equation (PDE) such models,...

We present the infinite dimensional approach to control of a general class doubly stochastic or otherwise known Q-mark Markov Jump Diffusion (Q-MJD) processes. The governing dynamics for probability density function (PDF) this Q-MJD processes is Partial Integro Differential Equation (PIDE). Minimum Principle (MP) applied these PIDE dynamics. qualitatively compare MP and Dynamic Programming (DPP) frameworks as developed sampling based algorithms illustrate how presented framework multi...

In this paper we investigate whether the linearly solvable stochastic optimal control framework generalizes to case of differential equations in infinite dimensional spaces. particular, show that connection between relative entropy-free energy relation and dynamic programming principles caries over Our analysis is based on a generalization Feynman-Kac lemma for certain classes diffusions Hilbert space-valued Q-Wiener processes. We observe utilized information theoretic representation allows...

The Hamilton Jacobi Bellman (HJB) PDE for the stochastic optimal control (SOC) problem diffusion SDE dynamics which have affine controls and state multiplicative noise is a second order fully nonlinear PDE. previously known linearly solvable framework as well first forward backward SDEs (FBSDEs) frameworks therefore characteristic inadequacy to support sampling algorithms this SOC problem. We present of FBSDEs solving in paper. derive Feynman Kac representation HJB corresponding diffusions...

Large-size populations consisting of a continuum identical and non-cooperative agents with stochastic dynamics are useful in modeling various biological engineered systems. This paper addresses the control problem designing optimal state-feedback controllers which guarantee closed-loop stability stationary density such nonlinear Langevin dynamics, under action their individual steady state controls. We represent corresponding coupled forward-backward PDEs as decoupled Schr\"odinger...

Control of continuous time dynamics with multiplicative noise is a classic topic in stochastic optimal control. This work addresses the problem designing infinite horizon controls stability guarantees for large populations identical, non-cooperative and non-networked agents multi-dimensional nonlinear excited by noise. For agent belonging to class reversible diffusion processes, we provide constraints on state control cost functions which guarantee closed-loop system under action individual...

Control of continuous time dynamics with multiplicative noise is a classic topic in stochastic optimal control. This work addresses the problem designing infinite horizon controls stability guarantees for \textit{a single agent or large population systems} identical, non-cooperative and non-networked agents, multi-dimensional nonlinear excited by noise. For belonging to class reversible diffusion processes, we provide constraints on state control cost functions which guarantee closed-loop...