In this paper we extend to completely general nonlinear systems the result stating that the H∞ 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. © 1999 Springer-Verlag New York Inc.
Equivalence between nonlinear H-infinity control problems and existence of viscosity solutions of Hamilton-Jacobi-Isaacs equations
SORAVIA, PIERPAOLO
1999
Abstract
In this paper we extend to completely general nonlinear systems the result stating that the H∞ 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. © 1999 Springer-Verlag New York Inc.
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