A perturbation method for control systems with multiple switch points

We consider a system arising from an application of the Maximum Principle to a free endpoint trajectory optimization problem arising in control. The system involves a small parameter, and has the property that the optimal control associated with the reduced problem ( ) moves on and off the boundary of the control region a finite number of times. We show how a technique involving a nonlinear chgnge of independent variables can be used to obtain uniformly valid parameter expansions for the solution of the full problem for ε small, and we establish conditions on the Hamiltonian under which this procedure may be carried out.