Repetitive control of Hamiltonian systems based on variational symmetry

This paper is concerned with repetitive control of Hamiltonian systems, which is based on iterative learning control utilizing the variational symmetry of those systems. Variational symmetry allows us to obtain an algorithm to solve a certain class of optimal control problems in a repetitive control framework. Therefore, the proposed method can deal with not only trajectory tracking control problems but also optimal trajectory generation problems, never before considered in a repetitive control framework. A convergence analysis of this algorithm is also discussed. Furthermore, some numerical simulations demonstrate the effectiveness of the proposed method.