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Applied Mathematics and Optimization

, Volume 39, Issue 1, pp 17–32 | Cite as

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.

  • P. Soravia

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.

Key words. Nonlinear H∞ control, Differential games, Viscosity solutions, Isaacs equations, Nonlinear systems. AMS Classification. 93B36, 49L25, 90D25. 

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Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

  • P. Soravia
    • 1
  1. 1.Dipartimento di Matematica Pura e Applicata, Università Degli Studi di Padova, via Belzoni 7, 35131 Padova, Italy soravia@math.unipd.it IT

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