A Max-plus Dual Space Fundamental Solution for a Class of Operator Differential Riccati Equations

DOI10.1137/120879312zbMath1347.49005arXiv1404.7209OpenAlexW2073044650MaRDI QIDQ5252505

William M. McEneaney, Peter M. Dower

Publication date: 2 June 2015

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.7209

zbMATH Keywords

optimal controldynamic programmingsemigroupsfundamental solutioninfinite-dimensional systemsmax-plus methodsLengendre-Fenchel transformoperator differential Riccati equations

Mathematics Subject Classification ID

Numerical methods involving duality (49M29) Dynamic programming in optimal control and differential games (49L20) Control/observation systems governed by partial differential equations (93C20) One-parameter semigroups and linear evolution equations (47D06) General theory of partial differential operators (47F05) Existence theories for problems in abstract spaces (49J27) Existence theories for optimal control problems involving partial differential equations (49J20) Max-plus and related algebras (15A80)

Related Items (6)

Solving Two-Point Boundary Value Problems for a Wave Equation via the Principle of Stationary Action and Optimal Control ⋮ A max-plus primal space fundamental solution for a class of differential Riccati equations ⋮ Staticization, its dynamic program and solution propagation ⋮ The Principle of Least Action and Fundamental Solutions of Mass-Spring and N-Body Two-Point Boundary Value Problems ⋮ Neural network architectures using min-plus algebra for solving certain high-dimensional optimal control problems and Hamilton-Jacobi PDEs ⋮ Verifying fundamental solution groups for lossless wave equations via stationary action and optimal control

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Max-plus methods for nonlinear control and estimation.
• Representation and control of infinite dimensional systems
• Semigroups of linear operators and applications to partial differential equations
• Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations
• A new fundamental solution for differential Riccati equations arising in control
• Convergence of Galerkin approximations for operator Riccati equations - a nonlinear evolution equation approach
• Numerical Approximation for the Infinite-Dimensional Discrete-Time Optimal Linear-Quadratic Regulator Problem
• Optimal Feedback Control of Infinite-Dimensional Parabolic Evolution Systems: Approximation Techniques
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

This page was built for publication: A Max-plus Dual Space Fundamental Solution for a Class of Operator Differential Riccati Equations