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Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case.…

Optimization and Control · Mathematics 2020-05-19 Sudeep Kundu , Karl Kunisch

This paper introduces a reinforcement learning-based tracking control approach for a class of nonlinear systems using neural networks. In this approach, adversarial attacks were considered both in the actuator and on the outputs. This…

Systems and Control · Electrical Eng. & Systems 2022-09-20 Farshad Rahimi , Sepideh Ziaei

We address the crucial yet underexplored stability properties of the Hamilton--Jacobi--Bellman (HJB) equation in model-free reinforcement learning contexts, specifically for Lipschitz continuous optimal control problems. We bridge the gap…

Optimization and Control · Mathematics 2024-04-23 Namkyeong Cho , Yeoneung Kim

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

Feedback controllers for port-Hamiltonian systems reveal an intrinsic inverse optimality property since each passivating state feedback controller is optimal with respect to some specific performance index. Due to the nonlinear…

Optimization and Control · Mathematics 2020-07-20 Lukas Kölsch , Pol Jané Soneira , Felix Strehle , Sören Hohmann

In this paper, near optimal tracking of a class of nonlinear systems is addressed. Adaptive (approximate) dynamic programming approach is used to calculate the optimal control in closed form. ADP (Adaptive (approximate) dynamic programming)…

Optimization and Control · Mathematics 2021-09-22 Farshid Asadi , Ali Heydari

The paper deals with a class of time-inconsistent control problems for McKean-Vlasov dynamics. By solving a backward time-inconsistent Hamilton-Jacobi-Bellman (HJB for short) equation coupled with a forward distribution-dependent stochastic…

Optimization and Control · Mathematics 2020-02-18 Hongwei Mei , Chao Zhu

This paper proposes a general incremental policy iteration adaptive dynamic programming (ADP) algorithm for model-free robust optimal control of unknown nonlinear systems. The approach integrates recursive least squares estimation with…

Optimization and Control · Mathematics 2025-09-01 Qingkai Meng , Fenglan Wang , Lin Zhao

The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…

Optimization and Control · Mathematics 2024-04-23 Michael Herty , Hicham Kouhkouh

This paper proposes an off-policy risk-sensitive reinforcement learning based control framework for stabilization of a continuous-time nonlinear system that subjects to additive disturbances, input saturation, and state constraints. By…

Systems and Control · Electrical Eng. & Systems 2022-04-21 Cong Li , Qingchen Liu , Zhehua Zhou , Martin Buss , Fangzhou Liu

This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is…

Optimization and Control · Mathematics 2016-11-17 Yoke Peng Leong , Matanya B. Horowitz , Joel W. Burdick

This paper studies the robust optimal control design for uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (robust-ADP). The objective is to fill up a gap in the past literature of ADP where dynamic…

Dynamical Systems · Mathematics 2013-03-12 Yu Jiang , Zhong-Ping Jiang

This paper presents an optimal dynamic control framework for bounded Jacobian nonlinear discrete-time (DT) systems with nonlinear observations affected by both state and process noise. Rather than directly stabilizing the uncertain system,…

Systems and Control · Electrical Eng. & Systems 2025-05-01 Mohammad Khajenejad

This paper introduces a novel approach to evaluating the asymptotic stability of equilibrium points in both continuous-time (CT) and discrete-time (DT) nonlinear autonomous systems. By utilizing indirect Lyapunov methods and linearizing…

Systems and Control · Electrical Eng. & Systems 2025-08-08 Sadredin Hokmi , Mohammad Khajenejad

This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the…

Systems and Control · Electrical Eng. & Systems 2025-09-03 Kamal Fenza , Moussa Labbadi , Mohamed Ouzahra

We examine the problem of two-point boundary optimal control of nonlinear systems over finite-horizon time periods with unknown model dynamics by employing reinforcement learning. We use techniques from singular perturbation theory to…

Optimization and Control · Mathematics 2023-06-12 Vasanth Reddy , Hoda Eldardiry , Almuatazbellah Boker

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

Optimal feedback control with implicit Hamiltonians poses a fundamental challenge for learning-based value function methods due to the absence of closed-form optimal control laws. Recent work~\cite{gelphman2025end} introduced an implicit…

Optimization and Control · Mathematics 2026-04-28 Eric Gelphman , Deepanshu Verma , Nicole Tianjiao Yang , Stanley Osher , Samy Wu Fung

The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the…

Optimization and Control · Mathematics 2025-06-23 Zhe Jiao , Wantao Jia , Weiqiu Zhu

In this paper, we propose Q-learning algorithms for continuous-time deterministic optimal control problems with Lipschitz continuous controls. Our method is based on a new class of Hamilton-Jacobi-Bellman (HJB) equations derived from…

Machine Learning · Computer Science 2020-10-28 Jeongho Kim , Jaeuk Shin , Insoon Yang