• Title/Summary/Keyword: Lyapunov Function

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On Convergence and Parameter Selection of an Improved Particle Swarm Optimization

  • Chen, Xin;Li, Yangmin
    • International Journal of Control, Automation, and Systems
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    • v.6 no.4
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    • pp.559-570
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    • 2008
  • This paper proposes an improved particle swarm optimization named PSO with Controllable Random Exploration Velocity (PSO-CREV) behaving an additional exploration behavior. Different from other improvements on PSO, the updating principle of PSO-CREV is constructed in terms of stochastic approximation diagram. Hence a stochastic velocity independent on cognitive and social components of PSO can be added to the updating principle, so that particles have strong exploration ability than those of conventional PSO. The conditions and main behaviors of PSO-CREV are described. Two properties in terms of "divergence before convergence" and "controllable exploration behavior" are presented, which promote the performance of PSO-CREV. An experimental method based on a complex test function is proposed by which the proper parameters of PSO-CREV used in practice are figured out, which guarantees the high exploration ability, as well as the convergence rate is concerned. The benchmarks and applications on FCRNN training verify the improvements brought by PSO-CREV.

Observer-based H Fuzzy Controller Design of Interval Type-2 Takagi-Sugeno Fuzzy Systems Under Imperfect Premise Matching (불완전한 전반부 정합 하에서의 관측기 기반 구간 2형 T-S 퍼지 시스템의 H 퍼지 제어기 설계)

  • Hwang, Sounghwan;Park, Jin Bae;Joo, Young Hoon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.66 no.11
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    • pp.1620-1627
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    • 2017
  • In this paper, we design an observer-based $H_{\infty}$ fuzzy controller for interval type-2 Takagi-Sugeno (T-S) fuzzy systems under imperfect premise matching. The designed observer-based controller can effectively estimate the state of the system and make fuzzy system satisfy the $H_{\infty}$ disturbance attenuation performance. Using the slack matrix, the derived stabilization condition is expressed in terms of a linear matrix inequality. Finally, the effectiveness of the proposed method is verified through a simulation example.

Tip Position Control of a Flexible-Link Manipulator with Neural Networks

  • Tang Yuan-Gang;Sun Fu-Chun;Sun Zeng-Qi;Hu Ting-Liang
    • International Journal of Control, Automation, and Systems
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    • v.4 no.3
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    • pp.308-317
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    • 2006
  • To control the tip position of a flexible-link manipulator, a neural network (NN) controller is proposed in this paper. The dynamics error used to construct NN controller is derived based on output redefinition approach. Without the filtered tracking error, the proposed NN controller can still guarantee the closed-loop system uniformly asymptotically stable as well as NN weights bounded. Furthermore, the tracking error of desired trajectory can converge to zero with the proposed controller. For comparison an NN controller with filtered tracking error is also designed for the flexible-link manipulator. Finally, simulation studies are carried out to verify the theoretic results.

Parameter-dependent Robust Stability of Uncertain Singular Systems with Time-varying Delays (시변 시간지연을 가지는 불확실 특이시스템의 변수 종속 강인 안정성)

  • Kim, Jong-Hae
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.47 no.4
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    • pp.1-6
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    • 2010
  • In this paper, we present a new delay-dependent and parameter-dependent robust stability condition for uncertain singular systems with polytopic parameter uncertainties and time-varying delay. The robust stability criterions based on parameter-dependent Lyapunov function are expressed as LMI (linear matrix inequality). Moreover, the proposed robust stability condition is a general algorithm for both singular systems and non-singular systems. Finally, numerical examples are presented to illustrate the feasibility and less conservativeness of the proposed method.

Static Output Feedback Robust $H\infty$ Fuzzy Control of Discrete-Time Nonlinear Systems with Time-Varying Delay (시변 지연 이산 시간 비선형 시스템에 대한 정적 출력 궤환 $H\infty$ 퍼지 강인 제어기 설계)

  • Kim Taek Ryong;Park Jin Bae;Joo Young Hoon
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2005.04a
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    • pp.149-152
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    • 2005
  • In this paper, a robust $H\infty$ stabilization problem to a uncertain discrete-time fuzzy systems with time-varying delay via static output feedback is investigated. The Takagi -Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear systems with time-varying delayed state. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H\infty$ controllers are given in terms of linear matrix inequalities.

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An On-Line Adaptive Control of Underwater Vehicles Using Neural Network

  • Kim, Myung-Hyun;Kang, Sung-Won;Lee, Jae-Myung
    • Journal of Ocean Engineering and Technology
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    • v.18 no.2
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    • pp.33-38
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    • 2004
  • All adaptive neural network controller has been developed for a model of an underwater vehicle. This controller combines a radial basis neural network and sliding mode control techniques. No prior off-line training phase is required, and this scheme exploits the advantages of both neural network control and sliding mode control. An on-line stable adaptive law is derived using Lyapunov theory. The number of neurons and the width of Gaussian function should be chosen carefully. Performance of the controller is demonstrated through computer simulation.

Design and Analysis of Dynamic Positioning System Using a Nonlinear Robust Observer

  • Kim, Myung-Hyun
    • International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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    • v.5 no.1
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    • pp.46-52
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    • 2002
  • A robust nonlinear observer, utilizing the sliding mode concept, is developed for the dynamic positioning of ships. The observer provides the estimates of linear velocities of the ship and bias from slowly varying environmental loads. It also filters out wave frequency motion to avoid wear of actuators and excessive fuel consumption. The main advantage of the proposed observer is in its robustness. Especially, the observer structure with a saturation function makes the proposed observer robust against neglected nonlinearties, disturbances and uncertainties. Since the mathematical model of DP ships is difficult to obtain and includes uncertainties and disturbances, it is very important for the observer to be robust. A nonlinear output feedback controller is derives based on the developed observer using the observer backstepping technique, and the global stability of the observer and control law is shown by Lyapunov stability theory.. A set of simulation was carried out to investigate the performance of the proposed observer for dynamic positioning of ships.

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A Vertical Line Following Guidance Law Design (수직면 직선추종유도법칙 설계)

  • Whang, Ick-Ho;Cho, Sung-Jin
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.59 no.7
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    • pp.1309-1313
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    • 2010
  • In this paper, we propose a novel guidance law for controlling an UAV(Unmanned Air-Vehicle) to follow a reference line in vertical plane. A kinematics model representing the relative motion of the UAV to the reference line is derived. And then LQR(Linear Quadratic Regulator) theory is applied to the model to derive the VLFG(Vertical Line Following Guidance) law. The resultant guidance law forms a gain-scheduling controller scheduled by a simple parameter $\sigma$ which is a function of the UAV's velocity, axial acceleration, gravity, and the slope of the reference line. Also derived is a stability condition for the $\sigma$ variation based on Lyapunov theory. Simulation results show that the proposed guidance law can be applied effectively to UAV guidance algorithm design.

A Design of Tracking Controller of Wheeled Mobile Robot using Fuzzy Logic and Genetic Algorithm (퍼지논리와 유전알고리즘을 이용한 차륜형 이동로봇의 제어기 설계)

  • Kim, Dae-Jun;Choi, Young-Kiu
    • Proceedings of the KIEE Conference
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    • 2000.07d
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    • pp.2837-2839
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    • 2000
  • We design a stable controller for a mobile robot with variable gains and reference velocity in order to apply the proper gains and reference velocity, which are generated with fuzzy logic in on-line. The stability is guranteed by the Lyapunov theory. The fuzzy logic rules is found in off-line with GA strategy which drives each object function to be the least. The proposed controller is applied smooth path tracking due to the local path planing. Simulation results show robust performances under a different initial conditions.

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NON-FRAGILE GUARANTEED COST CONTROL OF UNCERTAIN LARGE-SCALE SYSTEMS WITH TIME-VARYING DELAYS

  • Park, Ju-H.
    • Journal of applied mathematics & informatics
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    • v.9 no.1
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    • pp.61-76
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    • 2002
  • The robust non-fragile guaranteed cost control problem is studied in this paper for class of uncertain linear large-scale systems with time-varying delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-hounded arid time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound far all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost contrellers is 7iven in terms of the feasible solution to a certain LMI. Finally, in order to show the application of the proposed method, a numerical example is included.