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In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…

Probability · Mathematics 2025-05-14 Andrey A. Dorogovtsev , Yuecai Han , Kateryna Hlyniana , Yuhang Li

Active many-body systems composed of many interacting degrees of freedom often operate out of equilibrium, giving rise to non-trivial emergent behaviors which can be functional in both evolved and engineered contexts. This naturally…

Soft Condensed Matter · Physics 2023-11-29 Sumit Sinha , Vishaal Krishnan , L Mahadevan

The realization of efficient micro-machines built from active matter requires precise thermodynamic control far from equilibrium. Despite theoretical progress, the focus on single-parameter driving, coupled with strict theoretical…

Soft Condensed Matter · Physics 2026-03-18 Luke K. Davis

For systems in an externally controllable time-dependent potential, the optimal protocol minimizes the mean work spent in a finite-time transition between two given equilibrium states. For overdamped dynamics which ignores inertia effects,…

Statistical Mechanics · Physics 2008-07-23 Alex Gomez-Marin , Tim Schmiedl , Udo Seifert

Transferring a physical system from an initial to a final state while minimizing energetic losses is an interdisciplinary control problem that bridges stochastic thermodynamics and optimal transport theory. Recent research typically…

Statistical Mechanics · Physics 2026-02-23 Jann van der Meer , Andreas Dechant

We revisit the elementary problem of moving a particle in a harmonic trap in finite time with minimal work cost, and extend it to the case of an active particle. By comparing the Gaussian case of an Active Ornstein-Uhlenbeck particle and…

Statistical Mechanics · Physics 2025-07-16 Janik Schüttler , Rosalba Garcia-Millan , Michael E. Cates , Sarah A. M. Loos

Consecutive traffic signalized intersections can increase vehicle stops, producing vehicle accelerations on arterial roads and potentially increasing vehicle fuel consumption levels. Eco-driving systems are one method to improve vehicle…

Systems and Control · Electrical Eng. & Systems 2020-03-04 Hao Yang , Fawaz Almutairi , Hesham A. Rakha

We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e.…

Optimization and Control · Mathematics 2021-04-13 Manuel Schaller , Friedrich Philipp , Timm Faulwasser , Karl Worthmann , Bernhard Maschke

We consider the problem of finding the energy minimum of a complex quantum Hamiltonian by employing a non-Markovian bath prepared in a low energy state. The energy minimization problem is thus turned into a thermodynamic cooling protocol in…

Quantum Physics · Physics 2024-03-29 Alberto Imparato , Nicholas Chancellor , Gabriele De Chiara

We present a novel particle filtering framework for continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows reformulating the estimation…

Optimization and Control · Mathematics 2021-10-08 Qinsheng Zhang , Amirhossein Taghvaei , Yongxin Chen

Due to their versatility in investigating phenomena in microscopic scales, optical tweezers have been an excellent platform for studying stochastic thermodynamics. In this context, this work presents experimental measurements of the…

Soft Condensed Matter · Physics 2022-09-15 Thalyta Tavares Martins , Lucas Prado Kamizaki , Sérgio Ricardo Muniz

A thermal analogue of the classical brachistochrone problem, which minimizes the connection time between two equilibrium states of harmonically confined Brownian particles, has recently been solved theoretically. Here we report its…

Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…

Statistical Mechanics · Physics 2024-09-18 Julia Sanders , Marco Baldovin , Paolo Muratore-Ginanneschi

Quantifying energy flows at nanometer scales promises to guide future research in a variety of disciplines, from microscopic control and manipulation, to autonomously operating molecular machines. A general understanding of the…

Statistical Mechanics · Physics 2018-11-26 Steven J. Large , Raphaël Chetrite , David A. Sivak

Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…

Systems and Control · Electrical Eng. & Systems 2021-08-24 Prakash Mallick , Zhiyong Chen

The development of efficient artificial nanodevices poses challenges which are of fundamental and technological nature. Recent progress has been made in the context of finite-time thermodynamics. A central question in finite-time…

Statistical Mechanics · Physics 2014-03-18 Mario Einax

We investigate the optimal control of open quantum systems, in particular, the mutual influence of driving and dissipation. A stochastic approach to open-system control is developed, using a generalized version of Krotov's iterative…

Statistical Mechanics · Physics 2015-03-17 Rebecca Schmidt , Antonio Negretti , Joachim Ankerhold , Tommaso Calarco , Jürgen T. Stockburger

Our current transportation system suffers from a number of problems in terms of safety, mobility, and environmental sustainability. The emergence of innovative intelligent transportation systems (ITS) technologies, and in particular…

Systems and Control · Electrical Eng. & Systems 2020-02-06 Zhouqiao Zhao , Guoyuan Wu , Ziran Wang , Matthew J. Barth

We propose a space mapping-based optimization algorithm for microscopic interacting particle dynamics which are inappropriate for direct optimization. This is of relevance for example in applications with bounded domains such that the…

Optimization and Control · Mathematics 2021-02-23 Jennifer Weißen , Simone Göttlich , Claudia Totzeck

For a small system like a colloidal particle or a single biomolecule embedded in a heat bath, the optimal protocol of an external control parameter minimizes the mean work required to drive the system from one given equilibrium state to…

Statistical Mechanics · Physics 2009-11-13 Tim Schmiedl , Udo Seifert
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