| Title: |
Kullback–Leibler-Quadratic Optimal Control |
| Authors: |
Cammardella, Neil; Bušić, Ana; Meyn, Sean |
| Contributors: |
University of Florida Gainesville (UF); Dynamics of Geometric Networks (DYOGENE); Département d'informatique - ENS-PSL (DI-ENS); École normale supérieure - Paris (ENS-PSL); Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL); Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de Paris; Institut National de Recherche en Informatique et en Automatique (Inria); Apprentissage, graphes et optimisation distribuée (ARGO); Laboratory of Information, Network and Communication Sciences (LINCS); Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Mines-Télécom Paris (IMT)-Sorbonne Université (SU); ANR-22-PETA-0004,AI-NRGY,Distributed AI-based architecture of future energy systems integrating very large amounts of distributed sources(2022) |
| Source: |
ISSN: 0363-0129. |
| Publisher Information: |
CCSD; Society for Industrial and Applied Mathematics |
| Publication Year: |
2023 |
| Subject Terms: |
Mean field games; Distributed control; Markov decision processes; Demand Dispatc; AMS: 90C40; 93E20; 90C46 93E35; 60J20; [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY] |
| Description: |
International audience ; This paper presents approaches to mean-field control, motivated by distributed control of multiagent systems. Control solutions are based on a convex optimization problem, whose domain is a convex set of probability mass functions (pmfs). The main contributions follow: (1) Kullback–Leibler-quadratic (KLQ) optimal control is a special case in which the objective function is composed of a control cost in the form of Kullback–Leibler divergence between a candidate pmf and the nominal, plus a quadratic cost on the sequence of marginals. Theory in this paper extends prior work on deterministic control systems, establishing that the optimal solution is an exponential tilting of the nominal pmf. Transform techniques are introduced to reduce complexity of the KLQ solution, motivated by the need to consider time horizons that are much longer than the intersampling times required for reliable control. (2) Infinite-horizon KLQ leads to a state feedback control solution with attractive properties. It can be expressed as state feedback, in which the state is the sequence of marginal pmfs, or an open loop solution is obtained that is more easily computed. (3) Numerical experiments are surveyed in an application of distributed control of residential loads to provide grid services, similar to utility-scale battery storage. The results show that KLQ optimal control enables the aggregate power consumption of a collection of flexible loads to track a time-varying reference signal, while simultaneously ensuring each individual load satisfies its own quality of service constraints. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/arxiv/2004.01798; ARXIV: 2004.01798 |
| DOI: |
10.1137/21M1433654 |
| Availability: |
https://inria.hal.science/hal-04476982; https://doi.org/10.1137/21M1433654 |
| Accession Number: |
edsbas.B2EB4A3A |
| Database: |
BASE |