${\cal H}_\infty$ Control of Nonlinear Systems: Differential Games and Viscosity Solutions

Authors:
Pierpaolo Soravia
Affiliations:
-
Venue:
SIAM Journal on Control and Optimization
Year:
1996

Citing 0
Cited 5

Robust Optimal Service Analysis of Single-Server Re-Entrant Queues

Computational Optimization and Applications
A differential game formulation of a controlled network

Queueing Systems: Theory and Applications
Convergence Rate for a Curse-of-Dimensionality-Free Method for a Class of HJB PDEs

SIAM Journal on Control and Optimization
Brief Paper: Robust Stabilization of Nonlinear Systems via Normalized Coprime Factor Representations

Automatica (Journal of IFAC)
H∞ control, stabilization, and input-output stability of nonlinear systems with homogeneous properties

Automatica (Journal of IFAC)

Quantified Score

Hi-index	0.01

Visualization

Abstract

Dealing with disturbances is one of the most important questions for controlled systems. ${\cal H}_\infty$ optimal control theory is a deterministic way to tackle the problem in the presence of unfavorable disturbances. The theory of differential games and the study of the associated Hamilton--Jacobi--Isaacs equation appear to be basic tools of the theory. We consider a general, nonlinear system and prove that the existence of a continuous, local viscosity supersolution of the Isaacs equation corresponding to the ${\cal H}_\infty$ control problem is sufficient for its solvability. We also show that the existence of a lower semicontinuous viscosity supersolution is necessary.