Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximation

DOI10.1051/cocv/2021009OpenAlexW3122712863MaRDI QIDQ4999517

Daniel Walter, Karl Kunisch

Publication date: 7 July 2021

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.08625

zbMATH Keywords

Hamilton-Jacobi-Bellman equationneural networksreinforcement learningoptimal feedback stabilization

Mathematics Subject Classification ID

Computational learning theory (68Q32) Optimal feedback synthesis (49N35) Feedback control (93B52) Stabilization of systems by feedback (93D15) Hamilton-Jacobi equations (35F21)

Related Items (11)

Challenges in optimization with complex PDE-systems. Abstracts from the workshop held February 14--20, 2021 (hybrid meeting) ⋮ An Approximation Scheme for Distributionally Robust PDE-Constrained Optimization ⋮ Data-Driven Tensor Train Gradient Cross Approximation for Hamilton–Jacobi–Bellman Equations ⋮ Optimal polynomial feedback laws for finite horizon control problems ⋮ Relaxation approach for learning neural network regularizers for a class of identification problems ⋮ Approximation of compositional functions with ReLU neural networks ⋮ Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization ⋮ State-dependent Riccati equation feedback stabilization for nonlinear PDEs ⋮ Learning an optimal feedback operator semiglobally stabilizing semilinear parabolic equations ⋮ RICAM, the Johann Radon Institute for Computational and Applied Mathematics ⋮ Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids
• Submersions and preimages of sets of measure zero
• Fundamentality of ridge functions
• Multilayer feedforward networks are universal approximators
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• L\(_2\)-gain and passivity techniques in nonlinear control
• Numerical study of polynomial feedback laws for a bilinear control problem
• Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula
• Feedback stabilization of the two-dimensional Navier-Stokes equations by value function approximation
• Controlled Markov processes and viscosity solutions
• A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
• Constrained Optimization with Low-Rank Tensors and Applications to Parametric Problems with PDEs
• Stabilization by Sparse Controls for a Class of Semilinear Parabolic Equations
• Nonlinear feedback stabilization of a two-dimensional Burgers equation
• Hopf Formula and Multitime Hamilton-Jacobi Equations
• Polynomial Approximation of High-Dimensional Hamilton--Jacobi--Bellman Equations and Applications to Feedback Control of Semilinear Parabolic PDEs
• Adaptive Deep Learning for High-Dimensional Hamilton--Jacobi--Bellman Equations
• Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations
• Semi-Lagrangian Approximation Schemes for Linear and Hamilton—Jacobi Equations
• Infinite-Horizon Bilinear Optimal Control Problems: Sensitivity Analysis and Polynomial Feedback Laws

This page was built for publication: Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximation