Applications of the penalty function method in constrained optimal control problems

Abstract

This paper uses the penalty function method to solve constrained optimal control problems. Under suitable assumptions, we can solve a constrained optimal control problem by solving a sequence of unconstrained optimal control problems. In turn, the constrained solution to the main problem can be obtained as the limit of the solutions of the sequence. In using the penalty function method to solve constrained optimal control problems, it is usually assumed that each of the modified unconstrained optimal control problems has at least one solution. Here we establish an existence theorem for those problems. Two numerical examples are presented to demonstrate the findings.

The non‐parameter penalty function method in constrained optimal control problems

“…Theorem 5-If there exists a subsequence of {u] which converges to some u"= u"(t), then u" is a solution to the original constrained optimal control problem (1) (4 In particular, limP (u wi) = O.…”

“…In recent years, these method have been widely used to solve infinite dimensional optimization problems. Applications of interior and exterior penalty function methods can be found in [3] and [4]. The combination of these two methods forms the so-called mixed penalty function method which has been used by Chen [2] to solve constrained optimal control problems.…”

Dynamically Dimensioned Search Grey Wolf Optimizer Based on Positional Interaction Information

“…Complexity problems [55]. DGWO and GWO parameters for these three real-world engineering optimization applications were provided as follows: the population size was 30, the maximum number of iterations was 1000, and each problem was run independently 30 times.…”