We consider the H{sub}∞ problem for a nonlinear system. The corresponding dynamic programming equation (DPE) is a fully nonlinear, first-order, steady-state partial differential equation (PDE), possessing a term which is quadratic in the gradient (for background, see [2], [4], [13], [25] among many notable others). The solutions are typically nonsmooth, and further, there are multiple viscosity solutions that is, one does not even have uniqueness among the class of viscosity solutions (cf. [17]).
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