Nonsmooth H-infinity control

Yury Orlov, CICESE, Ensenada, Mexico

Abstract:  The state-space approach to the nonlinear H-infinity  optimization is
developed in the nonsmooth setting. Since the Hamilton-Jacobi partial
differential equation, associated with the nonlinear L2-gain analysis,
may not admit a continuously differentiable solution the present L2-gain
analysis follows the line of reasoning where the corresponding 
Hamilton-Jacobi equation is viewed in the sense of Clarke proximal 
superdifferentials and it is required to be negative definite, i.e., to 
be in an inequality (rather than equation) form.  The resulting 
controller is associated with specific proximal solutions of the 
Hamilton-Jacobi-Isaacs partial differential inequalities and it
is straightforwardly designed while solving the problem locally. The
proposed approach is illustrated by applications to (orbital) 
stabilization of (possibly, underactuated) mechanical systems with 
nonsmooth phenomena such as dry friction and actuator deadzone.