Maximum principle for optimal distributed control of the viscous Dullin–Gottwald–Holm equation

Sun, Bing

doi:10.1016/j.nonrwa.2011.07.037

Cited by 25 publications

(12 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Naturally, an optimization problem needs to be considered in this shallow water wave equation. It [78]. In [79] [80], recently, our research team studied optimal distributed control of the Fornberg-Whitham equation and the θ-equation which involve complex nonlinear items respectively.…”

Section: 1mentioning

confidence: 99%

Optimal Distributed Control Problem for the <i>b</i>-Equation

Shen¹

2017

JAMP

View full text Add to dashboard Cite

This paper is concerned with the optimal distributed control problem governed by b-equation. We firstly investigate the existence and uniqueness of weak solution for the controlled system with appropriate initial value and boundary condition. By contrasting with our previous result, the proof without considering viscous coefficient is a big improvement. Secondly, based on the well-posedness result, we find a unique optimal control for the controlled system with the quadratic cost functional. Moreover, by means of the optimal control theory, we obtain the sufficient and necessary optimality condition of an optimal control, which is another major novelty of this paper. Finally, we also present the optimality conditions corresponding to two physical meaningful distributive observation cases.

show abstract

Section: 1mentioning

confidence: 99%

Optimal Distributed Control Problem for the <i>b</i>-Equation

Shen¹

2017

JAMP

View full text Add to dashboard Cite

show abstract

“…In this situation, the Dubovitskii and Milyutin functional analytical approach has been turned out to be very powerful to solve such kind of extremum problems (see, e.g., [3,4,16,17]). The general Dubovitskii and Milyutin theorem for problem (5) can be stated as the following theorem.…”

Section: Optimal Distributed Control Problemmentioning

confidence: 99%

Necessary optimality conditions for optimal distributed and (Neumann) boundary control of Burgers equation

Sun

2015

NAMC

Self Cite

View full text Add to dashboard Cite

Abstract. In this paper, we investigate the optimal control of the Burgers equation. For both optimal distributed and (Neumann) boundary control problems, the Dubovitskii and Milyutin functional analytical approach is adopted in investigation of the Pontryagin maximum principles of the systems. The necessary optimality conditions are, respectively, presented for two kinds of optimal control problems in both fixed and free final horizon cases, four extremum problems in all. Moreover, in free final horizon case, the assumptions of admissible control set on convexity and non-empty interior are removed so that it can be any set including an interesting case contains only finite many points. Finally, a remark on how to utilize the obtained results is also made for the illustration.

show abstract

“…On the other hand, many researchers use the techniques in [20] to the study of the optimal control problems for fluids models [21][22][23][24][25][26][27][28][29][30]. The optimal control problems for the DullinGottwald-Holm equation were studied in [31][32][33], which is similar in structure to the Camassa-Holm equation and the Degasperis-Procesi equation. Hwang [33] obtained the necessity optimal condition of optimal control to the control problem.…”

Section: Introductionmentioning

confidence: 99%

The optimal control problem with necessity condition for a viscous shallow water equation

Ming

Lai

2018

Bound Value Probl

View full text Add to dashboard Cite

The optimal control problem for a shallow water equation with a viscous term is analyzed. The existence of optimal control to the control problem is investigated. The necessity condition of optimal control is derived by using the first order Gâteaux derivative of cost functional and adjoint equation. The local uniqueness of the optimal control is established by means of the second order Gâteaux derivative of cost functional. The novelty of this paper is that the necessity condition and local uniqueness of optimal control to the problem are obtained with viscous coefficient ε > 0.

show abstract

Maximum principle for optimal distributed control of the viscous Dullin–Gottwald–Holm equation

Cited by 25 publications

References 19 publications

Optimal Distributed Control Problem for the <i>b</i>-Equation

Optimal Distributed Control Problem for the <i>b</i>-Equation

Necessary optimality conditions for optimal distributed and (Neumann) boundary control of Burgers equation

The optimal control problem with necessity condition for a viscous shallow water equation

Contact Info

Product

Resources

About

Maximum principle for optimal distributed control of the viscous Dullin–Gottwald–Holm equation

Cited by 25 publications

References 19 publications

Optimal Distributed Control Problem for the &lt;i&gt;b&lt;/i&gt;-Equation

Optimal Distributed Control Problem for the &lt;i&gt;b&lt;/i&gt;-Equation

Necessary optimality conditions for optimal distributed and (Neumann) boundary control of Burgers equation

The optimal control problem with necessity condition for a viscous shallow water equation

Contact Info

Product

Resources

About

Optimal Distributed Control Problem for the <i>b</i>-Equation

Optimal Distributed Control Problem for the <i>b</i>-Equation