Second order necessary and sufficient optimality conditions for singular solutions of partially-affine control problems
Copyright policy )Second order necessary and sufficient optimality conditions for singular solutions of partially-affine control problems
In this article we study optimal control problems for systems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the initial and final values of the state. We investigate singular optimal solutions for this class of problems, for which we obtain second order necessary and sufficient conditions for weak optimality in integral form. We also derive Goh pointwise necessary optimality conditions. We show an example to illustrate the results.
This article has been accepted for publication in Discrete Contin. Dyn. Syst. Ser. S. arXiv admin note: substantial text overlap with arXiv:1210.7425
49K15, shooting algorithm, singular control, Goh conditions, Optimality conditions for problems involving ordinary differential equations, optimal control, first order optimality condition, Existence theories for optimal control problems involving ordinary differential equations, second order optimality condition, Optimization and Control (math.OC), FOS: Mathematics, Legendre-Clebsch condition, Mathematics - Optimization and Control, Control/observation systems governed by ordinary differential equations, Lagrage multipliers
49K15, shooting algorithm, singular control, Goh conditions, Optimality conditions for problems involving ordinary differential equations, optimal control, first order optimality condition, Existence theories for optimal control problems involving ordinary differential equations, second order optimality condition, Optimization and Control (math.OC), FOS: Mathematics, Legendre-Clebsch condition, Mathematics - Optimization and Control, Control/observation systems governed by ordinary differential equations, Lagrage multipliers
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