Abstract
<p style='text-indent:20px;'>In this work, we consider the two dimensional tidal dynamics equations in a bounded domain and address some optimal control problems like total energy minimization, minimization of dissipation of energy of the flow, etc. We also examine an another interesting control problem which is similar to that of the data assimilation problems in meteorology of obtaining unknown initial data, when the system under consideration is the tidal dynamics, using optimal control techniques. For these cases, different distributed optimal control problems are formulated as the minimization of suitable cost functionals subject to the controlled two dimensional tidal dynamics system. The existence of an optimal control as well as the first order necessary conditions of optimality for such systems are established and the optimal control is characterized via the adjoint variable. We also establish the uniqueness of optimal control in small time interval.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Control and Optimization,General Medicine
Reference40 articles.
1. F. Abergel, R. Temam.On some control problems in fluid mechanics, Theoretical and Computational Fluid Dynamics, 1 (1990), 303-325.
2. P. Agarwal, U. Manna, D. Mukherjee.Stochastic control of tidal dynamics equation with Lévy noise, Appl. Math. Optim., 79 (2019), 327-396.
3. V. I. Agoshkov, E. A. Botvinovsky.Numerical solution of a hyperbolic-parabolic system by splitting methods and optimal control approaches, Comput. Methods Appl. Math., 7 (2007), 193-207.
4. V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems, Mathematics in
Science and Engineering, vol. 190, Academic Press, Inc., Boston, MA, 1993.
5. N. R. C. Birkett and N. K. Nichols, Optimal control problems in tidal power generation,
Industrial Numerical Analysis, Oxford Sci. Publ., Oxford Univ. Press, New York, 1986, 53-89.
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献