Solution of Two-Point Boundary-Value Problems Using Lagrange Implicit Function Theorem
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An implicit derivative Newton's shooting method to solve a class of two-point boundary-value problems (TPBVPs), most often encountered in the solution of optimal control problems has been reported. TPBVP forms an important ingredient in the solution of several multiphysics modeling and control analyses, including but not limited to guidance, navigation, and control problems of aerospace engineering. The Lagrange implicit function theorem is an important result in analysis facilitating several theoretical and practical applications in applied mathematics and engineering. The Lagrange implicit function theorem is applied to develop a numerical iteration (of Newton type) procedure for the solution of two-point boundary-value problems in optimal control. The procedure thus set up is applied to an orbit transfer problem. The modification to Newton iterates derived from the implicit function theorem therefore provides us optimism about the utility of the theory of implicit functions and its generalizations in similar problems of dynamic optimization.
