On Two-Point Boundary Conditions in Optimal Control Problems

M. Ahmadinia and M. Radjabalipour
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M. Ahmadinia: Ghom University
M. Radjabalipour: University of Kerman

Journal of Optimization Theory and Applications, 2004, vol. 122, issue 2, No 10, 425-432

Abstract: Abstract Let x=g(t,x(t),u(t)) be the governing equation of an optimal control problem with two-point boundary conditions h 0(x(a))+h 1(x(b)) = 0, where x: [a,b] → ℝ n is continuous, u: [a,b] → ℝ k-n is piecewise continuous and left continuous, h0,h1: ℝ n → ℝ q are continuously differentiable, and g:[a,b]× ℝ k → ℝ n is continuous. The paper finds functions ξ i ∈ C1([a,b]× ℝ n ) such that (x(t),u(t)) is a solution of the governing equation if and only if $$\int {_a^b [(\partial \xi _i /\partial x)g + \partial \xi _i /\partial t]} dt = 0, i = 1,2,3,....$$

Keywords: Riesz representation theorem; optimal control problems; two-point boundary conditions; linear programming; mixed 0–1 integer linear programming (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTA.0000042529.80440.04

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