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.
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This work was partially supported by the National Natural Science Foundation of China under Grant 11771344.
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Communicated by Michael Hinze.
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Duan, Y., Wang, L. Minimal Norm Control Problem Governed by Semilinear Heat Equation with Impulse Control. J Optim Theory Appl 184, 400–418 (2020). https://doi.org/10.1007/s10957-019-01594-9
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DOI: https://doi.org/10.1007/s10957-019-01594-9