Global impulsive optimal control computation

In this paper, we develop a global computational approach to a classof optimal control problems governed by impulsive dynamical systemsand subject to continuous state inequality constraint. We show thatthis problem is equivalent to an optimal control problem governed byordinary differential equations with periodic boundary conditionsand subject to a set of the continuous state inequality constraints.For this equivalent optimal control problem, a constrainttranscription method is used in conjunction with a penalty functionto construct an appended new cost functional. This leads to asequence of approximate optimal control problems only subject toperiodic boundary conditions. Each of these approximate problems canbe solved as an optimization problem using gradient-basedoptimization techniques. However, these techniques are designed onlyto find local optimal solutions. Thus, a filled function method isintroduced to supplement the gradient-based optimization method.This leads to a combined method for finding a global optimalsolution. A numerical example is solved using the proposed approach.