Optimal boundary control of a continuum model for a highly re-entrant manufacturing system

Abstract

In this paper, we are concerned with the optimal boundary control of a continuum model for a highly re-entrant manufacturing system. Using the Dubovitskii–Milyutin functional analytical approach, we establish the Pontryagin maximum principles for the optimal boundary control problems in both fixed and free final time horizon cases. A remark is then made about the application of the obtained results.

Optimal control of transverse vibration of a moving string with time-varying lengths

“…Therefore, we can rewrite the optimal control problem (5) into the extremum problem (7) on the inequality constraint Ω 1 and the equality constraint Ω 2 . To utilize the pretty well-established Dubovitskii and Milyutin functional analytical approach ( [3,9,21]), in the following Theorem 3.1, we present the general Dubovitskii and Milyutin theorem for the extremum problem (7). )).…”

“…However, in view of the complexity caused by both the investigational system and the necessary optimality condition, we, by the Pontryagin maximum principle along with an iterative algorithm, only give the profile for numerically solving the optimal control problem for the transverse vibration of a moving string with time-varying lengths in fixed final horizon case, i.e., the problem (5). For further discussion on the numerical solutions of optimal control problems via the Pontryagin maximum principle, we can refer to [20,21] and so on. We can also find the feedback control formulation in [13,19], to mention but a few.…”

“…(II) In view of z 0 (s, t), w 0 (s, t) and the Pontryagin maximum principle (21), to determine v 1 (t).…”

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.…”