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We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear…

Optimization and Control · Mathematics 2016-02-22 Alessandro Alla , Maurizio Falcone , Dante Kalise

This paper introduces the Hamilton-Jacobi-Bellman Proximal Policy Optimization (HJBPPO) algorithm into reinforcement learning. The Hamilton-Jacobi-Bellman (HJB) equation is used in control theory to evaluate the optimality of the value…

Machine Learning · Computer Science 2023-02-02 Amartya Mukherjee , Jun Liu

Many optimal control problems are formulated as two point boundary value problems (TPBVPs) with conditions of optimality derived from the Hamilton-Jacobi-Bellman (HJB) equations. In most cases, it is challenging to solve HJBs due to the…

Optimization and Control · Mathematics 2019-07-25 Sixiong You , Ran Dai , Ping Lu

We treat infinite horizon optimal control problems by solving the associated stationary Hamilton-Jacobi-Bellman (HJB) equation numerically to compute the value function and an optimal feedback law. The dynamical systems under consideration…

Optimization and Control · Mathematics 2021-05-19 Mathias Oster , Leon Sallandt , Reinhold Schneider

This paper investigates the convergence properties of the upwind difference scheme for the Hamilton--Jacobi--Bellman (HJB) equation, a central partial differential equation in optimal control theory. First, assuming the existence of a…

Numerical Analysis · Mathematics 2026-02-05 Daisuke Inoue , Yuji Ito , Takahito Kashiwabara , Norikazu Saito , Hiroaki Yoshida

In optimal control problems of control-affine systems, whose solutions are bang-bang or singular type, verification of optimality using the Hamilton-Jacobi-Bellman (HJB) equation involves the computation of partial derivatives of switching…

Optimization and Control · Mathematics 2020-09-15 Victor Riquelme

In this paper, we investigate the distributed optimal control problem for a kind of nonlinear multi-agent systems. In particular,both the state and the system dynamic structures of each agent are private and can only be shared among…

Optimization and Control · Mathematics 2026-04-08 Ruixue Li , Wenjing Yang , Zhaorong Zhang , Xun Li , Juanjuan Xu

Convex Q-learning is a recent approach to reinforcement learning, motivated by the possibility of a firmer theory for convergence, and the possibility of making use of greater a priori knowledge regarding policy or value function structure.…

Optimization and Control · Mathematics 2022-10-18 Fan Lu , Joel Mathias , Sean Meyn , Karanjit Kalsi

We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…

Optimization and Control · Mathematics 2013-09-10 Vladimir Gaitsgory , Ludmila Manic

The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined…

Quantum Physics · Physics 2011-10-05 Srinivas Sridharan , Matthew R. James

For an infinite-horizon control problem, the optimal control can be represented by the stable manifold of the characteristic Hamiltonian system of Hamilton-Jacobi-Bellman (HJB) equation in a semiglobal domain. In this paper, we first…

Optimization and Control · Mathematics 2024-05-14 Guoyuan Chen

We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton-Jacobi-Bellman…

Quantum Physics · Physics 2007-05-23 J. Gough , V. P. Belavkin , O. G. Smolyanov

We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which…

Optimization and Control · Mathematics 2023-06-21 Marc Chen , Mohammad Shirazi , Peter A. Forsyth , Yuying Li

This paper studies the optimal dividend problem with a bounded payout rate in a partially observed regime-switching diffusion model, where, in practice, the market regime is unobserved and key model parameters are unknown. To address this…

Optimization and Control · Mathematics 2026-01-29 Zhongqin Gao , Yan Lv , Jingmin He

We study the policy iteration algorithm (PIA) for entropy-regularized stochastic control problems on an infinite time horizon with a large discount rate, focusing on two main scenarios. First, we analyze PIA with bounded coefficients where…

Optimization and Control · Mathematics 2025-05-28 Hung Vinh Tran , Zhenhua Wang , Yuming Paul Zhang

Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional…

Machine Learning · Computer Science 2023-12-12 Paula Chen , Tingwei Meng , Zongren Zou , Jérôme Darbon , George Em Karniadakis

We consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control. Using a result of existence and uniqueness of a sufficiently regular mild solution of the associated…

Probability · Mathematics 2021-03-22 F. Gozzi , F. Masiero

In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to…

Machine Learning · Computer Science 2026-01-16 Patrick Cheridito , Jean-Loup Dupret , Donatien Hainaut

We study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the…

Optimization and Control · Mathematics 2022-11-17 Yumiharu Nakano

The purpose of this note is to propose a new approach for the probabilistic interpretation of Hamilton-Jacobi-Bellman equations associated with stochastic recursive optimal control problems, utilizing the representation theorem for…

Probability · Mathematics 2017-05-03 Lishun Xiao , Shengjun Fan , Dejian Tian