Pontryagin's maximum principle for optimal boundary control of a generalised Korteweg–de Vries equation

2010 ◽  
Vol 41 (6) ◽  
pp. 699-708
Author(s):  
Bing Sun
Keyword(s):  
Maximum Principle ◽  
Boundary Control ◽  
Vries Equation ◽  
Pontryagin’S Maximum Principle ◽  
Pontryagin's Maximum Principle ◽  
Optimal Boundary ◽  
Optimal Boundary Control ◽  
De Vries

Optimal boundary control of a coupled system consisting of Kuramoto–Sivashinsky–Korteweg–de Vries and heat equations

2016 ◽  
Vol 39 (12) ◽  
pp. 1829-1840
Author(s):  
Bing Sun ◽  
Mi-Xia Wu
Keyword(s):  
Optimal Control ◽  
Boundary Control ◽  
Necessary Optimality Conditions ◽  
Coupled System ◽  
Heat Equations ◽  
Controlled System ◽  
Optimal Boundary ◽  
Optimal Boundary Control ◽  
De Vries ◽  
Horizon Case

This paper is concerned with the optimal boundary control of a non-dimensional non-linear parabolic system consisting of the Kuramoto–Sivashinsky–Korteweg–de Vries equation and a heat equation. By the Dubovitskii and Milyutin functional analytical approach, first in the fixed final horizon case we prove the Pontryagin maximum principle of the optimal control problem of this coupled system. Then under weaker additional conditions, we study the controlled system in the free final horizon case and present further investigational results of current interests. The necessary optimality conditions are established for optimal control problems in these two cases. Finally, a remark on how to utilize the obtained results is also made for illustration.

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