Numerical Algorithm for Solving Optimal Control Problems with Mixed Constraints

Abstract

: In this research, the numerical solutions of optimal control problems constrained by ordinary differential equation and integral equation are examined. We obtained the numerical solution by applying the “first discretize then optimize” technique. The discretization of the objective function, differential and integral constraints was done using trapezoidal rule, Simpson’s rule and fourth-order Adams-Moulton respectively. Thereafter, the formulated constrained optimization problem was converted into unconstrained problem by applying augmented lagrangian functional. We finally applied the Quasi-Newton algorithm of the Broydon-Fletcher-Goldfrab-Shannon (BFGS) type to obtain our optimal solution. Two examples of optimal control problems constrained by ordinary differential equation and an integral equation are considered. We obtained promising results with linear convergence.