×

Nonlinear \(H^\infty\) controller design via viscosity supersolutions of the Isaacs equation. (English) Zbl 0918.93013

McEneaney, William M. (ed.) et al., Stochastic analysis, control, optimization and applications. A volume in honor of Wendell H. Fleming, on the occasion of his 70th birthday. Boston: Birkhäuser. 151-170 (1999).
This paper deals with the solvability of Hamilton-Jacobi-Isaacs equations that arise in finite and infinite horizon nonlinear \(H^\infty\) control problems, where the system is affine in the control and the disturbance, while the cost function is not necessarily continuous. The authors proved the existence of viscosity supersolutions when the value function is finite, and established a connection between supersolutions and feedback controller design. They also obtained a result on global asymptotic stability of the system.
For the entire collection see [Zbl 0905.00042].
Reviewer: M.Nisio (Osaka)

MSC:

93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
93B51 Design techniques (robust design, computer-aided design, etc.)
93D15 Stabilization of systems by feedback
PDFBibTeX XMLCite