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.
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Accepted 14 February 1997
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Soravia, P. 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. . Appl Math Optim 39, 17–32 (1999). https://doi.org/10.1007/s002459900096
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DOI: https://doi.org/10.1007/s002459900096