On the Algorithmic Stability of Optimal Control with Derivative Operators
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On the Algorithmic Stability of Optimal Control with Derivative Operators Tim Chen1 · J. C.‑Y. Cheng2,3 Received: 2 January 2019 / Revised: 1 May 2020 / Accepted: 5 May 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The aim of this paper is to develop a productive numerical technique to deal with a class of time partial ideal AI control issues. The classical fuzzy inference methods cannot work to their full potential in such circumstances, because the given knowledge does not cover the entire problem domain. In addition, the requirements of fuzzy systems may change over time. The use of a static rule base may affect the effectiveness of fuzzy rule interpolation due to the absence of the most concurrent (dynamic) rules. The experimental result indicates that evolved bat algorithm with our proposed fitness function presents a 93.77% success rate in average for finding the feasible solutions. The contribution of this study is that near outcomes likewise confirm that the partial administrator for a Mittag–Leffler circuit in the Caputo sense improves the execution of the AI controlled framework as far as the transient reaction, in contrast with the other fragmentary and whole number subordinate administrators. Keywords Fractional derivative · Optimal AI control · Necessary condition · Nonsingular kernel · Iterative method
1 Introduction Fractional calculus and fuzzy control, a branch of mathematical analysis, has been used to investigate the extension of this methodology to other kinds of applications [27]. Nowadays, new applications are growing fast and can be found in different * J. C.‑Y. Cheng [email protected] Tim Chen [email protected] 1
AI LAB, Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam
2
Covenant University, 10 Idiroko Road, Canaan Land, Ota, Ogun State, Nigeria
3
NAAM Research Group, King Abdulaziz University, Jeddah 21589, Saudi Arabia
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Circuits, Systems, and Signal Processing
areas such as for chaos synchronization [25], PD control [20] and economics [21]. Additionally, the utility of optimal control problems (OCPs) has attracted the attention of many researchers. Biswas and Sen [12] converted a fractional optimal control problem (FOCP) into a system of algebraic equations. Almeida and Torres [5] approximated the OCP finite difference method for system analysis. Sweilam and Al-Mekhlafi [35] investigated OCPs with a generalized Euler method. Mashayekhi and Razzaghi [29] suggested an approximation scheme for dealing with OCPs by hybrid functions. In a recent study, Sahu and Ray [32] made a comparison between orthonormal wavelets to solve the OCP. More recently, a new iterative algorithm was developed by Jajarmi et al. [26] for nonlinear OCPs with external persistent disturbances. The control theory can be considered advantageous for a given complex dynamic, because we can choose an adequate fractional operator with or without singularity [6–10]. However, there is still a need to introduce new met
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