Volume 26, 2020
|Number of page(s)||43|
|Published online||10 December 2020|
Dynamic programming and feedback analysis of the two dimensional tidal dynamics system
Department of Mathematics, Indian Institute of Technology Roorkee-IIT Roorkee, Haridwar Highway,
* Corresponding author: email@example.com
Accepted: 28 April 2020
In this work, we consider the controlled two dimensional tidal dynamics equations in bounded domains. A distributed optimal control problem is formulated as the minimization of a suitable cost functional subject to the controlled 2D tidal dynamics equations. The existence of an optimal control is shown and the dynamic programming method for the optimal control of 2D tidal dynamics system is also described. We show that the feedback control can be obtained from the solution of an infinite dimensional Hamilton-Jacobi equation. The non-differentiability and lack of smoothness of the value function forced us to use the method of viscosity solutions to obtain a solution of the infinite dimensional Hamilton-Jacobi equation. The Bellman principle of optimality for the value function is also obtained. We show that a viscosity solution to the Hamilton-Jacobi equation can be used to derive the Pontryagin maximum principle, which give us the first order necessary conditions of optimality. Finally, we characterize the optimal control using the adjoint variable.
Mathematics Subject Classification: 49J20 / 35F21 / 35Q35 / 76D03
Key words: Tidal dynamics system / Pontryagin’s maximum principle / optimal control / value funtion / Hamilton-Jacobi equation / Viscosity solution
© EDP Sciences, SMAI 2020
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