Convergence and error analysis for a max-plus algorithm

We consider max-plus based algorithms for the solution of nonlinear H-infinity problems. This class of algorithms has been described for several problem types such as nonlinear H(infinity)filtering, nonlinear H-infinity control and nonlinear H-infinity control under partial information. Previous treatments have been oriented towards the general introduction of the algorithms. It has been noted that the corresponding convergence analysis was lacking in those papers. Here we demonstrate, in the case of nonlinear H-infinity control, that the errors introduced by the truncation to a finite number of max-plus basis functions go to zero as the number of basis functions increases. Some error bounds are also obtained.