Computation of max-plus eigenvector representations for nonlinear H ∞ value functions

We consider the H_∞ problem for a nonlinear system. The corresponding dynamic programming equation takes the form of a nonlinear, first-order PDE possessing a term which is quadratic in the gradient. However, the associated semi-group is linear over the max-plus algebra, and the correct solution of the PDE (the available storage) is a fixed point of this semi-group. Also, the solution lies in the space of semi-convex functions, and one has a max-plus basis for this space. Combining this max-plus basis with the max-plus linearity of the semi-group leads to a reduction of the problem to that of finding a max-plus eigenvector corresponding to eigenvalue 0, that is, the nonlinear problem reduces to a max-plus linear problem