Related papers: Stabilized neural Hamilton--Jacobi--Bellman solver…

In recent times, reinforcement learning has produced baffling results when it comes to performing control tasks with highly non-linear systems. The impressive results always outweigh the potential vulnerabilities or uncertainties associated…

We develop a game-theoretic framework for adversarially robust optimal safe predefined-time stabilization of parameter-dependent nonlinear dynamical systems with nonquadratic cost functionals. Our approach ensures that all system…

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…

This paper studies the time-inconsistent MV optimal stopping problem via a game-theoretic approach to find equilibrium strategies. To overcome the mathematical intractability of direct equilibrium analysis, we propose a vanishing…

This paper investigates the stability properties of neural operators through the structured representation offered by the Hybrid B-spline Deep Neural Operator (HBDNO). While existing stability-aware architectures typically enforce…

In this paper we propose a new computational method for designing optimal regulators for high-dimensional nonlinear systems. The proposed approach leverages physics-informed machine learning to solve high-dimensional Hamilton-Jacobi-Bellman…

We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error. A base low-regularity integrator provides a consistent first-order…

This paper proposes an actor-critic algorithm for controlling the temperature of a battery pack using a cooling fluid. This is modeled by a coupled 1D partial differential equation (PDE) with a controlled advection term that determines the…

Neural network approaches that parameterize value functions have succeeded in approximating high-dimensional optimal feedback controllers when the Hamiltonian admits explicit formulas. However, many practical problems, such as the space…

In order to obviate the requirement of drift dynamics in adaptive dynamic programming (ADP), integral reinforcement learning (IRL) has been proposed as an alternate formulation of Bellman equation.However control coupling dynamics is still…

In this note, we study a class of indefinite stochastic McKean-Vlasov linear-quadratic (LQ in short) control problem under the control taking nonnegative values. In contrast to the conventional issue, both the classical dynamic programming…

We address finding the semi-global solutions to optimal feedback control and the Hamilton--Jacobi--Bellman (HJB) equation. Using the solution of an HJB equation, a feedback optimal control law can be implemented in real-time with minimum…

Hard constraints in reinforcement learning (RL) often degrade policy performance. Lagrangian methods offer a way to blend objectives with constraints, but require intricate reward engineering and parameter tuning. In this work, we extend…

There have been attempts in reinforcement learning to exploit a priori knowledge about the structure of the system. This paper proposes a hybrid reinforcement learning controller which dynamically interpolates a model-based linear…

In this paper, we present Deep-MacroFin, a comprehensive framework designed to solve partial differential equations, with a particular focus on models in continuous time economics. This framework leverages deep learning methodologies,…

Model-reference adaptive systems refer to a consortium of techniques that guide plants to track desired reference trajectories. Approaches based on theories like Lyapunov, sliding surfaces, and backstepping are typically employed to advise…

Dynamical systems can be used to model a broad class of physical processes, and conservation laws give rise to system properties like passivity or port-Hamiltonian structure. An important problem in practical applications is to steer…

We consider mean field social optimization in nonlinear diffusion models. By dynamic programming with a representative agent employing cooperative optimizer selection, we derive a new Hamilton--Jacobi--Bellman (HJB) equation to be called…

Reinforcement learning is a powerful paradigm for learning optimal policies from experimental data. However, to find optimal policies, most reinforcement learning algorithms explore all possible actions, which may be harmful for real-world…

Deep learning-based hybrid iterative methods (DL-HIMs) integrate classical numerical solvers with neural operators, utilizing their complementary spectral biases to accelerate convergence. Despite this promise, many DL-HIMs stagnate at…