Globally feedback linearizable time-invariant systems: Optimal solution for Mayer's problem

This paper discusses the optimal solution of Mayer's problem for globally f eedback linearizable systems subject to general nonlinear path and actuator constraints. This class of problems includes the minimum time problem, imp ortant for engineering applications. Globally feedback linearizable nonline ar systems are diffeomorphic to linear systems that consist of blocks of in tegrators. Using this alternate form, it is proved that the optimal solutio n always lies on a constrain arc. As a results of this optimal structure of the solution, efficient numerical procedures can be developed. For a singl e input system, this result allows to characterize and build the optimal so lution. The associated multi-point boundary value problem is then solved us ing direct solution techniques.