Minimal Norm Control Problem Governed by Semilinear Heat Equation with Impulse Control

Yueliang Duan () and Lijuan Wang ()
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Yueliang Duan: Wuhan University
Lijuan Wang: Wuhan University

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 2, No 5, 400-418

Abstract: Abstract This paper studies a kind of minimal norm optimal control problem for a semilinear heat equation with impulse controls; it consists in finding an impulse control, which has the minimal norm among all controls steering solutions of the controlled system to a given target from an initial state in a fixed time interval. We will study the existence of optimal controls to this problem. Then, we will establish a nontrivial Pontryagin’s maximum principle of this problem.

Keywords: Minimal norm control; Impulse control; Pontryagin’s maximum principle; Semilinear heat equation; 49K20; 49J20; 93C20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-019-01594-9

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