Numerical solution of nonlinear optimal control problems using nonlinear programming

摘要

To solving nonlinear control problems and especially nonlinear optimal control problems (NOCP), classical methods are not usually efficient. In this paper we introduce a new approach for solving this class of problems by using Nonlinear Programming Problem (NLPP). First, we transfer the original problem to a new problem in form of calculus of variations. Then we discretize the new problem and solve it by using NLPP packages. The solution of the NLPP is used to obtain the optimal control and states, which are the exact solution of the original problem (NOCP). What is more, a NLPP is transferred to a Linear Programming Problem (LPP) which empower us 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, efficiency of our approach is confirmed by some numerical examples.