Brief paper: Optimal control of nonlinear power systems by an imbedding method
Automatica (Journal of IFAC)
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A manifold imbedding algorithm is described for the solution of two-point boundary value problems arising in optimization problems. A one-parameter imbedding of the initial and terminal manifolds is introduced so that a member of the resulting imbedded class of problems has an immediate solution. This problem is the first of a finite sequence of problems including the original one as last element. By a continuation procedure, these problems are successively solved. In contrast to a previous imbedding technique for solving two-point boundary value problems, the system equations are left unchanged. Intermediate problems therefore keep their physical meaning and the choice of a proper imbedding is easier. Moreover, a reduction of computation time is achieved. The manifold imbedding method may be regarded as a variation of the Newton-Raphson iterative procedure characterized by an extended region of convergence. The resulting reduction of guesswork and the unified approach to a wide range of optimization problems are amongst the favorable features. The minimization of the transfer time of a low-thrust ion rocket between the orbits of Earth and Mars illustrates the application of the method.