Numerical solution of constrained optimal control problems with parameters

This article presents a numerical solution technique for constrained optimal control problems that contain parameters. Here, the state, control, and parameter inequality constraints are accommodated via an extended penalty function. This penalty function takes on large values a-hen the constraints are violated and small values when the constraints are satisfied. Using the calculus of variation it is shown that the first-order necessary conditions for optimality are in the form of a two-point boundary-value problem involving differential and algebraic equations (BVP-DAE). A multiple shooting/continuation method is developed for solving this BVP-DAE. Two examples are presented to demonstrate the effectiveness of the solution approach developed in the paper.