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Jiawei Dong,Won-jong Kim 제어·로봇·시스템학회 2012 International Journal of Control, Automation, and Vol.10 No.5
This paper proposes an output feedback method to stabilize and control networked control systems (NCSs). Random time delays and packet losses are treated separately when an NCS is modeled. The random time delays in the controller-to-actuator and sensor-to-controller links are modeled with two time-homogeneous Markov chains, while the packet losses are treated by the Dirac delta functions. An asymptotic mean-square stability criterion is established to compensate for the network-induced ran-dom time delays and packet losses in both the controller-to-actuator and sensor-to-controller links simultaneously. An algorithm to implement the asymptotic mean-square stability criterion is also proposed. Further, a DC-motor speed-control test bed with Ethernet using User Datagram Protocol (UDP) is constructed and employed for experimental verification. Two sets of experiments, with and without 10% packet losses in the links, are conducted on this NCS. Experimental results illustrate the effectiveness of the proposed output feedback method compared to conventional controllers. This method could compensate for the effects of the random time delays and packet losses and guarantee the system performance and stability. The integral time and absolute error (ITAE) of the experiments without packet losses is reduced by 13% with the proposed method, and the ITAE of experiments with 10% packet losses, by 30%. The NCS can track the reference command faithfully with the proposed method when random time delays and packet losses exist in the links, whereas the NCS fails to track the reference command with the conventional control algorithms.
ASYMPTOTIC STABILITY IN GENERAL DYNAMICAL SYSTEMS
Lim, Young-Il,Lee, Kyung-Bok,Park, Jong-Soh Korean Mathematical Society 2004 대한수학회보 Vol.41 No.4
In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset M of the phase space X to be asymptotic stability.
Backstepping and Partial Asymptotic Stabilization
Chaker Jammazi 대한전기학회 2008 International Journal of Control, Automation, and Vol.6 No.6
In this paper, the problem of partial asymptotic stabilization of nonlinear control cascaded systems with integrators is considered. Unfortunately, many controllable control systems present an anomaly, which is the non complete stabilization via continuous pure-state feedback. This is due to Brockett necessary condition. In order to cope with this difficulty we propose in this work the partial asymptotic stabilization. For a given motion of a dynamical system, say x(t, x?,t?) = (y(t, y?, t?), z(t, z?, t?)), the partial stabilization is the qualitative behavior of the y-component of the motion (i.e., the asymptotic stabilization of the motion with respect to y) and the z-component converges, relative to the initial vector x(t?)=x? = (y?, z?). In this work we present new results for the adding integrators for partial asymptotic stabilization. Two applications are given to illustrate our theoretical result. The first problem treated is the partial attitude control of the rigid spacecraft with two controls. The second problem treated is the partial orientation of the underactuated ship.
Global Asymptotic Stability of FAST TCP Network with Heterogeneous Feedback Delays
CHOI, Joon-Young,KOO, Kyungmo,LEE, Jin Soo The Institute of Electronics, Information and Comm 2010 IEICE TRANSACTIONS ON COMMUNICATIONS - Vol.93 No.3
<P>We consider a single-link multi-source network with FAST TCP sources. We adopt a continuous-time dynamic model for FAST TCP sources, and propose a static model to adequately describe the queuing delay dynamics at the link. The proposed model turns out to have a structure that reveals the time-varying network feedback delay, which allows us to analyze FAST TCP with due consideration of the time-varying network feedback delay. Based on the proposed model, we establish sufficient conditions for the boundedness of congestion window of each source and for the global asymptotic stability. The asymptotic stability condition shows that the stability property of each source is affected by all other sources sharing the link. Simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.</P>
Global Asymptotic Stability of FAST TCP in the Presence of Link Dynamics
최준영,구경모,김종욱,이진수 제어·로봇·시스템학회 2009 International Journal of Control, Automation, and Vol.7 No.5
We propose a continuous-time model to describe a single-link single-source network with the FAST TCP source. The proposed model explicitly includes both the queuing delay dynamics for the link dynamics and the time-varying network feedback delay. Based on the proposed model, we establish a sufficient condition for the global asymptotic stability of the FAST TCP network. We prove the sufficient condition by constructing two sequences that represent the variations of the lower and upper bound of the source’s congestion window with respect to time, and by showing that the two sequences converge to the equilibrium point of the congestion window. The simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.
Neural-networks-based Adaptive Control for an Uncertain Nonlinear System with Asymptotic Stability
신종호,김승균,Antonios Tsourdos 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.4
This paper proposes a neural-networks(NN)-based adaptive controller for an uncertain nonlinear system with asymptotic stability. While the satisfactory performance of the NN-based adaptive controller is validated well in various uncertain nonlinear systems, the stability is commonly restricted to the uniformly ultimate boundedness( UUB). To improve the UUB of the NN-based adaptive control to the asymptotically stability(AS) with continuous control, the existing NN-based adaptive controller is augmented with a robust-integral-signum-error (RISE) feedback term, and overall closed-loop stability is rigorously analyzed by modifying the typical stability analysis for the RISE feedback control. To demonstrate the effectiveness of the proposed controller, numerical simulations for a fault tolerant flight control with a nonlinear F-16 aircraft model are performed.
Qian-qian Mu,Fei Long,Qi-xiang Wang,Lang Zhang,Li-po Mo 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.1
In this paper, the almost surely globally asymptotical stability and the almost surely exponential stability for dual switching continuous-time nonlinear system are investigated by using the probability analysis method and stochastic Multi-Lyapunov function, respectively. Different from the previous research results, it is the first time that dual switching continuous-time nonlinear system is used as a study object to investigate its switching stability. Then, the probability analysis method is used to overcome the deficiency that the ergodicity no longer holds due to the variable transition rate of Markov process. Some sufficient conditions for the globally asymptomatic stability almost surely and the almost surely exponential stability of dual switching continuous-time nonlinear system are given under the pre-designed deterministic switching strategy. Finally, two numerical examples are provided to verify the effectiveness of the proposed approach.
UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS
Sang Il Choi,구윤회 한국수학교육학회 2016 純粹 및 應用數學 Vol.23 No.1
This paper shows that the solutions to the perturbed differential system y'=f(t,y)+\int_{t_0}^tg(s,y(s),Ty(s))ds+h(t,y(t)) have asymptotic property and uniform Lipschitz stability. To show these properties, we impose conditions on the perturbed part \int_{t_0}^tg(s,y(s),Ty(s))ds, h(t,y(t)), and on the fundamental matrix of the unperturbed system y'=f(t,y).
일종의 일차 비선형 시간 지연 시스템을 위한 안정성 분석 방법
최준영(Joon-Young Choi) 제어로봇시스템학회 2008 제어·로봇·시스템학회 논문지 Vol.14 No.6
We analyze the stability property of a class of nonlinear time-delay systems with time-varying delays. We present a time-delay independent sufficient condition for the global asymptotic stability. In order to prove the sufficient condition, we exploit the inherent property of the considered systems instead of applying the Krasovskii or Razumikhin stability theory that may cause the mathematical difficulty of analysis. We prove the sufficient condition by constructing two sequences that represent the lower and upper bound variations of system state in time, and showing the two sequences converge to an identical point, which is the equilibrium point of the system. The simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.
ASYMPTOTIC EQUIVALENCE FOR LINEAR DIFFERENTIAL SYSTEMS
Choi, Sung-Kyu,Koo, Nam-Jip,Lee, Keon-Hee Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.1
We investigate the asymptotic equivalence for linear differential systems by means of the notions of $t_{\infty}$-similarity and strong stability.