A sparse collocation method for solving time-dependent HJB equations using multivariate \(B\)-splines

DOI10.1016/j.automatica.2014.07.012zbMath1297.49053OpenAlexW2143340660MaRDI QIDQ466457

Kalmanje Krishnakumar, Cornelis C. de Visser, Nithin Govindarajan

Publication date: 27 October 2014

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.automatica.2014.07.012

zbMATH Keywords

Hamilton-Jacobi-Bellman equationoptimal feedback controlcollocation methodsplinesadaptive dynamic programming

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Quadratic programming (90C20) Dynamic programming (90C39)

Related Items

Model reduction of parabolic PDEs using multivariate splines ⋮ Guaranteed cost spacecraft attitude stabilization under actuator misalignments using linear partial differential equations

Uses Software

• ToolboxLS

Cites Work

• Unnamed Item
• Unnamed Item
• Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
• An adaptive least-squares collocation radial basis function method for the HJB equation
• Differential constraints for bounded recursive identification with multivariate splines
• A radial basis collocation method for Hamilton-Jacobi-Bellman equations
• A neural network solution for fixed-final time optimal control of nonlinear systems
• A new approach to linear regression with multivariate splines
• Online actor-critic algorithm to solve the continuous-time infinite horizon optimal control problem
• The method of weighted residuals and variational principles. With application in fluid mechanics, heat and mass transfer
• Numerical solution of Hamilton-Jacobi-Bellman equations by an upwind finite volume method
• Level set methods and dynamic implicit surfaces
• An adaptive domain decomposition method for the Hamilton-Jacobi-Bellman equation
• Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach
• Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
• Bivariate Splines of Various Degrees for Numerical Solution of Partial Differential Equations
• Spline Functions on Triangulations
• An Approximation Theory of Optimal Control for Trainable Manipulators
• Trivariate spline approximations of 3D Navier-Stokes equations
• Approximate Dynamic Programming
• Collocation at Gaussian Points
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations