Solution of boundary-value DAE in optimal control

This paper 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 when 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).