# Equivalence between Nonlinear H ∞ Control Problems and Existence of Viscosity Solutions of Hamilton—Jacobi—Isaacs Equations rid="*" id="*" This work was written while the author was visiting the University of California at Santa Barbara. He was partially supported by Consiglio Nazionale delle Ricerche of Italy.

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 work was written while the author was visiting the University of California at Santa Barbara. He was partially supported by Consiglio Nazionale delle Ricerche of Italy.

, Volume 39 (1) – Jun 1, 2007
16 pages

/lp/springer_journal/equivalence-between-nonlinear-h-control-problems-and-existence-of-tt8z5oUpSy
Publisher
Springer-Verlag
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
D.O.I.
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 OptimizationSpringer Journals

Published: Jun 1, 2007

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