A max-plus primal space fundamental solution for a class of differential Riccati equations

Abstract

A class of differential Riccati equations (DREs) is considered for which the evolution of any solution can be identified with the propagation of a value function of a corresponding optimal control problem arising in L2-gain analysis. By exploiting the semigroup properties inherited from the attendant dynamic programming principle, a max-plus primal space fundamental solution semigroup of max-plus linear max-plus integral operators is developed that encapsulates all such value function propagations. Using this semigroup, a one-parameter fundamental solution semigroup of matrices is constructed for the aforementioned class of DREs. It is demonstrated that this semigroup can be used to compute ..