In this paper, we develop a global computational approach to a class
of optimal control problems governed by impulsive dynamical systems
and subject to continuous state inequality constraint. We show that
this problem is equivalent to an optimal control problem governed by
ordinary differential equations with periodic boundary conditions
and subject to a set of the continuous state inequality constraints.
For this equivalent optimal control problem, a constraint
transcription method is used in conjunction with a penalty function
to construct an appended new cost functional. This leads to a
sequence of approximate optimal control problems only subject to
periodic boundary conditions. Each of these approximate problems can
be solved as an optimization problem using gradient-based
optimization techniques. However, these techniques are designed only
to find local optimal solutions. Thus, a filled function method is
introduced to supplement the gradient-based optimization method.
This leads to a combined method for finding a global optimal
solution. A numerical example is solved using the proposed approach.