AN EXTENDED PENALTY-FUNCTION APPROACH TO THE NUMERICAL-SOLUTION OF CONSTRAINED OPTIMAL-CONTROL PROBLEMS

This paper presents the extended penalty function method for solving c onstrained optimal control problems. Here, equality and inequality con straints on the state and control variables are considered. Using the extended penalty function method, the original constrained optimal con trol problem is transformed into a sequence of optimal control problem s without inequality constraints. This is accomplished by adding to th e cost functional a penalty term that takes on large values when the i nequality constraints are violated and small values when the constrain ts are satisfied. Also presented is a continuation method for solving the sequence of differential-algebraic boundary value problems arising from the transformed optimal control problems. The effectiveness of t he approach is demonstrated via examples.