Numerical Solution of Optimal Control Problems

The solution of an optimal control problem requires the satisfaction of differential equations subject to initial as well as final conditions. Except when the equations are linear and the objective functional is simple enough, an analytical solution is impossible. This is the reality of most of the problems for which optimal controls can only be determined using numerical methods. 

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Numerical Solution of Optimal Control Problems U2 (K) is the reactor temperature as a function of time. 

Numerical Solution of Optimal Control Problems 6. Given a positive real number 3 close to zero, if the error... 

For the numerical solution of optimal control problems, there are basically two well-established approaches, the indirect approach, e. g., via the solution of multipoint boxmdary-value problems based on the necessary conditions of optimal control theory, and the direct approach via the solution of constrained nonlinear programming problems based on discretizations of the control and/or the state variables. The application of an indirect method is not advisable if the equations are too complicated or a moderate accuracy of the numerical solution is commensurate with the model accuracy. Therefore, the easier-to-handle direct approach has been chosen here. Direct collocation methods, see, e. g., Stryk [6], as well as direct multiple shooting methods, see, e. g., Bock and Plitt [1], belong to this approach. In view of forthcoming large scale problems, we will focus here on the direct multiple shooting method, since only the control variables have to be discretized for this method. This leads to lower dimensional nonlinear programming problems. 

Oberle, H.J. and Grimm, W. (2001) BNDSCO A Program for the Numerical Solution of Optimal Control Problems. Inst, fiir Angewandte Mathematik, Hamburg, Germany. 

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