On Converting Optimal Control Problems into Nonlinear Programming Problems

Abstract

Direct solutions of the optimal control problem are considered. Two discretization schemes are proposed which are based on the parameterization of the control functions and on the parameterization of the control and the state functions, leading to direct shooting and direct collocation algorithms, respectively. The former is advantageous for problems with unspecified final state, the latter for prescribed final state and especially for stiff problems. The sparsity of the Jacobian matrix of the constraints and the Hessian matrix of the Lagrangian must be exploited in the direct collocation method in order to be efficient. The great advantage of the collocation approach lies in the availability of analytical gradients.