A Review on the Direct and Indirect Methods for Solving Optimal Control Problems with Differential-Algebraic Constraints

In the article the main features of direct and indirect approaches for solving optimal control problems were presented. The mentioned methods can be effectively applied in the Model Predictive Control of the complex technological systems in electrical, chemical and aerospace engineering, often described by nonlinear differential-algebraic equations. Among the direct and indirect methods for solving optimal control problems one can mention Euler-Lagrange equations, direct optimization methods and indirect gradients methods.