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Equivalence between Nonlinear H ∞ Control Problems and Existence of Viscosity Solutions of Hamilton—Jacobi—Isaacs Equations rid="*" id="*" This wor ...

Equivalence between Nonlinear H ∞ Control Problems and Existence of Viscosity Solutions of... In this paper we extend to completely general nonlinear systems the result stating that the $ {{\cal H}}_\infty $ suboptimal control problem is solved if and only if the corresponding Hamilton—Jacobi—Isaacs (HJI) equation has a nonnegative (super)solution. This is well known for linear systems, using the Riccati equation instead of the HJI equation. We do this using the theory of differential games and viscosity solutions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Equivalence between Nonlinear H ∞ Control Problems and Existence of Viscosity Solutions of Hamilton—Jacobi—Isaacs Equations rid="*" id="*" This wor ...

Soravia, P.
Applied Mathematics and Optimization , Volume 39 (1) – Jun 1, 2007
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Publisher
Springer Journals
Copyright
Copyright © Inc. by 1999 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s002459900096
Publisher site
See Article on Publisher Site

Abstract

In this paper we extend to completely general nonlinear systems the result stating that the $ {{\cal H}}_\infty $ suboptimal control problem is solved if and only if the corresponding Hamilton—Jacobi—Isaacs (HJI) equation has a nonnegative (super)solution. This is well known for linear systems, using the Riccati equation instead of the HJI equation. We do this using the theory of differential games and viscosity solutions.

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Jun 1, 2007

There are no references for this article.