PDE Control

PDE control focuses on designing controllers to manipulate the behavior of systems described by partial differential equations (PDEs), aiming for stability and desired performance. Current research emphasizes data-driven approaches, particularly employing deep reinforcement learning (DRL) and neural operators (NOs) to approximate complex control laws, often within a reduced-order modeling framework to handle high dimensionality. These methods offer potential for improved efficiency and robustness compared to traditional model-based techniques, impacting diverse fields requiring precise control of spatially distributed systems, such as fluid dynamics and materials science. The development of benchmark environments and open-source tools is facilitating broader exploration and comparison of these novel algorithms.

Papers

November 6, 2024

Interpretable and Efficient Data-driven Discovery and Control of Distributed Systems
Florian Wolf, Nicolò Botteghi, Urban Fasel, Andrea Manzoni
Reinforcement Learning External Control Nonlinear Dynamic Data Driven Discovery PDE Control Control Paradigm

May 18, 2024

PDE Control Gym: A Benchmark for Data-Driven Boundary Control of Partial Differential Equations
Luke Bhan, Yuexin Bian, Miroslav Krstic, Yuanyuan Shi
New Benchmark Partial Differential Equation PDE Control PDE Backstepping Boundary Control

March 22, 2024

Parametric PDE Control with Deep Reinforcement Learning and Differentiable L0-Sparse Polynomial Policies
Nicolò Botteghi, Urban Fasel
Deep Reinforcement Learning Optimal Control Linear Policy PDE Control Interpretable Control

March 1, 2024

Policy Optimization for PDE Control with a Warm Start
Xiangyuan Zhang, Saviz Mowlavi, Mouhacine Benosman, Tamer Başar
Policy OpTimization Reduced Order Model Reduction Warm Start PDE Control

January 18, 2024

Approximation of Solution Operators for High-dimensional PDEs
Nathan Gaby, Xiaojing Ye
Average Approximation Reduced Order High Dimensional Partial Differential Equation Solution Operator PDE Control

January 15, 2024

Adaptive Neural-Operator Backstepping Control of a Benchmark Hyperbolic PDE
Maxence Lamarque, Luke Bhan, Yuanyuan Shi, Miroslav Krstic
Lyapunov Function Adaptive Control PDE Control

November 30, 2023

Controlgym: Large-Scale Control Environments for Benchmarking Reinforcement Learning Algorithms
Xiangyuan Zhang, Weichao Mao, Saviz Mowlavi, Mouhacine Benosman, Tamer Başar
Learning Based Reinforcement Learning Benchmark Continuous Environment Real World Control PDE Control

August 21, 2023

Deep Learning of Delay-Compensated Backstepping for Reaction-Diffusion PDEs
Shanshan Wang, Mamadou Diagne, Miroslav Krstić
Deep Learning Reaction Diffusion Delay Resilient PDE System PDE Control Backstepping Control

July 21, 2023

Neural Operators for PDE Backstepping Control of First-Order Hyperbolic PIDE with Recycle and Delay
Jie Qi, Jing Zhang, Miroslav Krstic
Neural Operator Advanced Textile Recycling Account Time Delay Hyperbolic Model Parabolic Partial Differential Equation PDE Backstepping PDE Control

PDE Control

Papers

Interpretable and Efficient Data-driven Discovery and Control of Distributed Systems

PDE Control Gym: A Benchmark for Data-Driven Boundary Control of Partial Differential Equations

Parametric PDE Control with Deep Reinforcement Learning and Differentiable L0-Sparse Polynomial Policies

Policy Optimization for PDE Control with a Warm Start

Approximation of Solution Operators for High-dimensional PDEs

Adaptive Neural-Operator Backstepping Control of a Benchmark Hyperbolic PDE

Controlgym: Large-Scale Control Environments for Benchmarking Reinforcement Learning Algorithms

Deep Learning of Delay-Compensated Backstepping for Reaction-Diffusion PDEs

Neural Operators for PDE Backstepping Control of First-Order Hyperbolic PIDE with Recycle and Delay