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

Abstract

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.

A variational approach to determination of maximum throw-able workspace of robotic manipulators in optimal ball pitching motion

“…This property makes this approach attractive in various fields such as torque control of Permanent Magnet Synchronous Motors (PMSMs) (Wang et al, 2019), motion control of spacecraft (Feng et al, 2019; Ge et al, 2018), speed optimization (Abbas et al, 2019) and energy management of electrical vehicles (Kim et al, 2019; Nguyen et al, 2019; Sohn et al, 2019), hybrid bus (Xie et al, 2019). It has also been used in hydrocarbon emission control of automotive engine (Azad, 2015), optimal boundary control of the manufacturing systems (Sun and Wu, 2019), and non-linear parabolic system consisting of a heat equation (Sun and Wu, 2017). Recently, this approach has received a lot of attention in the field of robotics.…”