Necessary Conditions for the Impulsive Time-Optimal Control of Finite-Dimensional Lagrangian Systems

摘要

In this work, necessary conditions for the impulsive time-optimal control of finite-dimensional Lagrangian systems are stated. The conditions are obtained by the application sub-differential calculus techniques to extended-valued lower semi-continuous functionals. The considered functional is a generalized Bolza functional that is evaluated on multiple intervals. Contrary to the approach in literature so far, the instant of possibly impulsive transition is considered as an instant of Lebesgue measure zero. This approach is in comparison to other impulsive necessary conditions consistent with different hybrid system modeling methods in which transitions happen instantaneously. The necessary conditions provide necessary criteria for the determination of optimal transition times and locations.