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Numerical solution of nonlinear optimal control problems using nonlinear programming. (English) Zbl 1118.65067
Authors’ summary: For solving nonlinear control problems and especially nonlinear optimal control problems (NOCP), classical methods are not usually efficient. This paper introduces a new approach for solving this class of problems by using nonlinear programming problem (NLPP). First, the authors transfer the original problem into a new problem in form of calculus of variations. Then the new problem is discretized and solved by using NLPP packages. The solution of the NLPP is used for obtaining the optimal control and states, which are the exact solution of the original problem (NOCP). Furthermore, an NLPP is transferred to a linear programming problem (LPP) allowing to use powerful LP softwares. The degree of desirability is described for suboptimal approximate solutions. Also the nonlinear approximate solution and the optimal control are shown as a combination of polynomial functions or periodic functions. Finally, some numerical examples are treated.

MSC:
65K10 Numerical optimization and variational techniques
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