Abstract
In this paper, the existence of step-like contrast structure for a class of singularly perturbed optimal control problem is shown by the contrast structure theory. By means of direct scheme of boundary function method, we construct the uniformly valid asymptotic solution for the singularly perturbed optimal control problem. Finally, an example is presented to show the result. 2000 Mathematics Subject Classification. 34B15; 34E15.
Highlights
The contrast structure in a singularly perturbed problem is mainly classified as a step-like contrast structure or a spike-like contrast structure
This issue is called as internal layer solution problem in western [4]
In [12], the authors consider the existence of contrast structure for the following singularly perturbed differential equations with integral boundary conditions y(0, μ) =
Summary
The contrast structure in a singularly perturbed problem is mainly classified as a step-like contrast structure or a spike-like contrast structure (see [1]-[3]) This issue is called as internal layer solution problem in western [4]. In [12], the authors consider the existence of contrast structure for the following singularly perturbed differential equations with integral boundary conditions y(0, μ) =. 0 < t < 1, h1(y(s, μ))ds, y(1, μ) = h2(y(s, μ))ds, by using of the theory of differential equalities In this present paper, the singularly perturbed optimal control problem with integral boundary conditions is considered, we prove the existence of step-like contrast structure for the singularly perturbed optimal control problem, and construct asymptotic solution to the optimal controller and optimal trajectory
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