An Augmented Lagrangian for Optimal Control of DAE Systems: Algorithm and Properties

This article proposes a relax-and-discretize approach for optimal control of continuous-time differential algebraic systems. It works by relaxing the algebraic equations and penalizing the violation into the objective function using the augmented Lagrangian, which converts the original problem into a sequence of optimal control problems (OCPs) of ordinary differential equations (ODEs). The relax-and-discretize approach brings about flexibility, by allowing the OCPs of ODEs to be solved by the method of choice, such as direct or indirect methods. Conditions are developed for global, local, and suboptimal convergence in terms of the solution of the underlying OCPs. The method is applied to an illustrative example.