OPTIMAL CONTROL OF UNDERACTUATED MECHANICAL SYSTEMS: A GEOMETRIC APPROACH

Abstract. In this paper, we consider a geometric formalism for optimal control of under-actuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order constraints. We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics of the optimal control problem. These developments will allow us to develop a new class of geometric integrators based on discrete variational calculus. 1