Necessary Conditions for the Impulsive-Optimal Control of Mechanical Systems with Blockable Degrees of Freedom
In this work, the necessary conditions for the impulsive optimal control of rigid-body mechanical systems is studied, where the dynamics is represented in the first-order form. By the application of subdifferential calculus techniques to extended-valued lower semi-continuous functionals, Pontryagin's Maximum Principle (PMP) kind conditions are obtained. This representation enables to relate
the necessary conditions to the classical nonimpulsive Pontryagin's principle. The necessary conditions are derived by making use of the concepts of internal boundary variations and discontinuous transversality conditions. These concepts are developed by the author and are presented in first-order
and second-order representations, respectively. In this work, it is assumed that the instant of discontinuity is reduced to an instant with Lebesgue measure zero, instead of taking an interval opening approach, which is the approach considered in literature so far.that is evaluated on multiple intervals. Contrary to the approach taken in literature so far, instead of taking an interval opening approach, the instant of
discontinuity is reduced to an instant with Lebesgue measure zero. The approach requires different system modes and their order to be specified in advance. The necessary conditions obtained, enable the determination the optimal transition time and location.