Volterra - Hamilton

With the introduction of Pontryagin's Maximum Principle, the Hamiltonian formalism, previously only important in mechanics and physics, has jecome a useful and common tool in optimal control. Beginning about thirty years ago, a functional expansion, known as a Volterra series was introduced and used in various engineering applications. There is a large body of literature on the determination of Volterra Kernels when the input - output behavior is desoribed by a system of ordinary differential equations. Generalizing a finding the author published elsewhere (1984) on the relations between the firstorder kernel and sympletic geometry, the author shows that the Taylcr expansion of the Volterra kernels of any order can be naturally expressed in terms of the fractional derivatives of the Hamiltonian associated with the system. It is noted that a version in French of this communication has been published elsewhere.