Novel optimal guaranteed cost control of non-linear systems with mixed multiple time-varying delays

Thuan, Viet; Nguyen, Thanh Huyen Thi

doi:10.1093/imamci/dnr020

Cited by 4 publications

(4 citation statements)

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“…Generally speaking, the goal of GCC is to design a proper controller such that the states (tracking errors) of the closed-loop system are bounded or asymptotically stable, and, most importantly, the corresponding cost function, which is often defined to make the system satisfying extra performance requirements except stability, is bounded by a known function (In this paper, for readability, the function is termed the upper bound of cost function (UBCF)) (Chang and Peng, 1972; Chen et al, 2004; Li et al, 2019; Senger and Trofino, 2016). At present, many relevant works have been reported (Boukas et al, 2003; Chen et al, 2003; Guo, 2002; Mai and Thanht, 2011; Niamsup and Phat, 2015; Park, 2004; Ren and Zhang, 2012; Xie and Tang, 2006; Zhang and Fang, 2008; Zhang et al, 2009). For linear systems, the GCC problems have been solved for descriptor systems (Ren and Zhang, 2012), discrete systems (Guo, 2002; Park, 2004), and Markovian jump systems (Boukas et al, 2003; Chen et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

“…For linear systems, the GCC problems have been solved for descriptor systems (Ren and Zhang, 2012), discrete systems (Guo, 2002; Park, 2004), and Markovian jump systems (Boukas et al, 2003; Chen et al, 2003). For nonlinear ones, the GCCs of time-delay systems, large-scale systems, and stochastic systems has been investigated, respectively, in Xie and Tang (2006), Niamsup and Phat (2015), Mai and Thanht (2011), Zhang et al (2009), and Zhang and Fang (2008). More recently, Tian et al (2021), Sun et al (2021), and Zhang and Peng (2020) have solved, respectively, the GCC problems of the high-speed train system, the T-S fuzzy system, and the networked control system.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive guaranteed cost tracking control for high-order nonlinear systems based on fully actuated system approaches

Hu,

Duan

2023

Transactions of the Institute of Measurement and Control

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This paper considers the adaptive guaranteed cost tracking (AGCT) control problems for two classes of high-order nonlinear systems with unknown parameters. A new local smooth nonlinear function (LSNF) is introduced first, which provides an important mathematical tool for our controller design. Then, based on the LSNF and the high-order fully actuated (HOFA) system approaches, the AGCT controller is designed for HOFA system with unknown parameter, which guarantees that all of the states of the closed-loop HOFA system are globally bounded, and the tracking error is asymptotically convergent. Moreover, the upper bound of cost function (UBCF) characterizing the tracking performance can be arbitrarily preseted, and is completely independent of the system initial value and the unknown parameter, which significantly improves the tracking performance, and is difficult to achieve by using existing guaranteed cost control (GCC). Furthermore, an extra result, the AGCT controller for a class of strict-feedback systems with high-order form and unknown parameters, is obtained in this paper, which also guarantees that the system tracking error is globally asymptotically convergent with the arbitrarily preseted UBCF characterizing the tracking performance. Three simulation examples, including an inverted pendulum, are presented to show the effect and the superiority of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive guaranteed cost tracking control for high-order nonlinear systems based on fully actuated system approaches

Hu,

Duan

2023

Transactions of the Institute of Measurement and Control

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“…This approach provides an upper bound on a given system performance index, and thus, the system performance degradation incurred by the uncertainties is guaranteed to be less than this bound. The Lyapunov direct method together with the LMI‐based design approach has been among the popular and effective tool to study the problem of guaranteed cost control for dynamical systems and some important results have been reported in the literature . In particular, by using the Lyapunov method and LMI technique, Park and Choi studied the guaranteed cost control problem of uncertain nonlinear neutral systems with time delays.…”

Section: Introductionmentioning

confidence: 99%

Robust guaranteed cost control for time‐delay fractional‐order neural networks systems

Thuận

Huong

2019

Optim Control Appl Methods

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In this paper, we investigate the problem of guaranteed cost control of uncertain fractional-order neural networks systems with time delays. By employing the Lyapunov-Razumikhin theorem, a sufficient condition for designing a state-feedback controller which makes the closed-loop system asymptotically stable and guarantees an adequate cost level of performance is derived in terms of bilinear matrix inequalities. Two numerical examples are given to show the effectiveness of the obtained results. KEYWORDS asymptotically stable, bilinear matrix inequalities, fractional-order neural networks, guaranteed cost control Optim Control Appl Meth. 2019;40:613-625.wileyonlinelibrary.com/journal/oca

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“…Owing to the rise of fractional-order derivatives, the theory and applied research on this subject has become an important issue worldwide. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] More and more researchers are studying fractional systems and have gained results related to the fractional-order system. [32][33][34][35][36][37][38][39][40] In particular, in, [23] new results on the stabilization of fractional-order nonlinear systems, which lays a foundation for the research of fractional-order systems in the future is proposed.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of a novel time‐lag four‐dimensional fractional‐order financial system

Zhang

Cheng

et al. 2019

Asian Journal of Control

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In this paper, a novel four‐dimensional fractional‐order financial system (FFS) with time delay is presented. Unlike traditional bifurcation analysis of financial systems, the selection rules of two bifurcation points within the system are discussed. In addition, the motion state of the system in the vicinity of two bifurcation points are analyzed separately, such that the dynamic analysis of this novel nonlinear fourth‐dimensional FFS is more comprehensive. The detailed dynamical behaviors of this financial system, such as oscillation, stability, and bifurcation points, are deduced via rigorous mathematical analysis. Finally, some simulations are performed to verify the dynamic characteristics of the FFS around the two bifurcation points which satisfy the selection conditions of the bifurcation point.

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Novel optimal guaranteed cost control of non-linear systems with mixed multiple time-varying delays

Cited by 4 publications

References 0 publications

Adaptive guaranteed cost tracking control for high-order nonlinear systems based on fully actuated system approaches

Adaptive guaranteed cost tracking control for high-order nonlinear systems based on fully actuated system approaches

Robust guaranteed cost control for time‐delay fractional‐order neural networks systems

Dynamic analysis of a novel time‐lag four‐dimensional fractional‐order financial system

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