Second Order Conditions for Optimality and Local Controllability of Discrete-Time Systems

摘要

We study local controllability and optimal control problems for invertiblediscrete-time control systems. We present second order necessary conditions foroptimality and sufficient conditions for local controllability. The conditionsare stated in geometric terms, using vector fields naturally associated to thesystem. The Hessian of the optimal problem is computed in terms of Lie bracketsof vector fields of the system.