Max-plus representation for the fundamental solution of the time-varying differential Riccati equation

This paper also shows that under a fixed duality kernel, the semiconvex dual of a DRE solution satisfies another dual DRE, whose coefficients satisfy the matrix compatibility conditions involving Hamiltonian and certain symplectic matrices. For the time-invariant DRE, this allows us to make dual DRE linear and thereby solve the primal DRE analytically. This paper also derives various kernel/duality relationships between the primal and time shifted dual DREs, which lead to an array of DRE solution methods. Time-invariant analogue of one of these methods was first proposed in McEneaney (2008).