• Title, Summary, Keyword: Nonlinear systems

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A Nash Solution to Predictive Control Problem for a Class of Nonlinear Systems

  • Ahn, Choon-Ki;Kwon, Wook-Hyun
    • 제어로봇시스템학회:학술대회논문집
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    • pp.76.5-76
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    • 2002
  • In this paper, we provide a Nash solution to predictive control problem for nonminimum phase singular nonlinear systems. Until now, there is no result on predictive control problem for this class of nonlinear systems. Chen's recent work considered predictive control problem for a class of nonlinear systems with ill-defined relative degree. Since his work is not a result considered in the feedback linearization framework, there is no a result on singular probem in his paper. In contrast to the existing predictive control result, our work considers two main obstacles (singularity and nonminimum phase) in the feedback linearization framework. For a generally formu...

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Control of Dynamical Systems: An Intelligent Approach

  • Ammar, Soukkou;Khellaf, Abdelhafid;Leulmi, Salah;Grimes, Mourad
    • International Journal of Control, Automation, and Systems
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    • v.6 no.4
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    • pp.583-595
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    • 2008
  • In this paper, we introduce a fuzzy nonlinear feedback approach to the control of a class of chaotic dynamical systems. The fuzzy Parallel Distributed Compensation with Reduced Rule Base approach (PDC_RRB) is proposed. The design procedure is conceptually simple and considered to a nonlinear optimal and robust control problem due to the nonlinear nature of the Takagi-Sugeno (TS) fuzzy system. Simulation results are provided to show the effictiveness of the proposed methodology.

MULTIPLE VALUED ITERATIVE DYNAMICS MODELS OF NONLINEAR DISCRETE-TIME CONTROL DYNAMICAL SYSTEMS WITH DISTURBANCE

  • Kahng, Byungik
    • Journal of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.17-39
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    • 2013
  • The study of nonlinear discrete-time control dynamical systems with disturbance is an important topic in control theory. In this paper, we concentrate our efforts to multiple valued iterative dynamical systems, which model the nonlinear discrete-time control dynamical systems with disturbance. After establishing the validity of such modeling, we study the invariant set theory of the multiple valued iterative dynamical systems, including the controllability/reachablity problems of the maximal invariant sets.

Stabilization of nonlinear two-generator five-bus power systems using fuzzy control (퍼지제어를 이용한 비선형 2기 5모선 전력계통의 안정화)

  • Moon, Un-Chul
    • Journal of Institute of Control, Robotics and Systems
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    • v.6 no.1
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    • pp.42-49
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    • 2000
  • This paper presents the application of a FARMA controller to stabilization of nonlinear Two-Generator Five-Bus power Systems. The control rules and the membership functions of the FARMA controller are generated automatically without using any plant model high complexity and severe nonlinearity of power systems are introduced and two-Machine Five -Bus Power system stabilization problem is formulated. The simulation results demonstrate the effectiveness and application possibility of the FARMA controller to the control problem of high order and nonlinear plants.

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Locating and identifying model-free structural nonlinearities and systems using incomplete measured structural responses

  • Liu, Lijun;Lei, Ying;He, Mingyu
    • Smart Structures and Systems
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    • v.15 no.2
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    • pp.409-424
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    • 2015
  • Structural nonlinearity is a common phenomenon encountered in engineering structures under severe dynamic loading. It is necessary to localize and identify structural nonlinearities using structural dynamic measurements for damage detection and performance evaluation of structures. However, identification of nonlinear structural systems is a difficult task, especially when proper mathematical models for structural nonlinear behaviors are not available. In prior studies on nonparametric identification of nonlinear structures, the locations of structural nonlinearities are usually assumed known and all structural responses are measured. In this paper, an identification algorithm is proposed for locating and identifying model-free structural nonlinearities and systems using incomplete measurements of structural responses. First, equivalent linear structural systems are established and identified by the extended Kalman filter (EKF). The locations of structural nonlinearities are identified. Then, the model-free structural nonlinear restoring forces are approximated by power series polynomial models. The unscented Kalman filter (UKF) is utilized to identify structural nonlinear restoring forces and structural systems. Both numerical simulation examples and experimental test of a multi-story shear building with a MR damper are used to validate the proposed algorithm.

A design of discrete time nonlinear control system with disturbances using model following method

  • Zhang, Yuan-Sheng;Okubo, Shigenori
    • 제어로봇시스템학회:학술대회논문집
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    • pp.239-242
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    • 1996
  • A model following control system(MFCS) can give general output signals following desired ones. In previous studies, a method of nonlinear MFCS was proposed by S.Okubo[1]. In this paper, the method of nonlinear MFCS will be extended to discrete time nonlinear systems. It is easy to extend the method to discrete time systems. But in the case .gamma.=1 discrete time systems, the proof becomes difficult, because the transfer function from f(v(k)) to v(k) can't be a positive real function. In this case, to ensure that internal states are stable, a new criterion is proposed.

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Design of nonlinear system controller based on radial basis function network (Radial Basis 함수 회로망을 이용한 비선형 시스템 제어기의 설계에 관한 연구)

  • 박경훈;이양우;차득근
    • 제어로봇시스템학회:학술대회논문집
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    • pp.1165-1168
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    • 1996
  • The neural network approach has been shown to be a general scheme for nonlinear dynamical system identification. Unfortunately the error surface of a Multilayer Neural Network(MNN) that widely used is often highly complex. This is a disadvantage and potential traps may exist in the identification procedure. The objective of this paper is to identify a nonlinear dynamical systems based on Radial Basis Function Networks(RBFN). The learning with RBFN is fast and precise. This paper discusses RBFN as identification procedure is based on a nonlinear dynamical systems. and A design method of model follow control system based on RBFN controller is developed. As a result of applying this method to inverted pendulum, the simulation has shown that RBFN can be used as identification and control of nonlinear dynamical systems effectively.

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A Nonlinear Filtered-X LMS Algorithm for the Nonlinear Compensation of the Secondary Path in Active Noise Control (능동 소음 제어 시스템의 2차 경로 비선형 특성을 보상하기 위한 적응 비선형 Filtered-X Least Mean Square (FX-LMS) 알고리듬)

  • Jeong, I.S.;Kim, D.H.;Nam, S.W.
    • Proceedings of the KIEE Conference
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    • pp.565-567
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    • 2004
  • In active noise control (ANC) systems, the convergence behavior of the conventional Filtered-X Least Mean Square (FXLMS) algorithm may be affected by nonlinear distortions in the secondary path (e.g., in the power amplifiers, loudspeakers, transducers, etc.), which may lead to degradation of the error-reduction performance of the ANC systems. In this paper, a stable FXLMS algorithm with fast convergence is proposed to compensate for undesirable nonlinear distortions in the secondary-path of ANC systems by employing the Volterra filtering approach. In particular, the proposed approach is based on the utilization of the conventional P-th order inverse approach to nonlinearity compensation in the secondary path of ANC systems. Finally, the simulation results showed that the proposed approach yields a better convergence behavior In the nonlinear ANC systems than the conventional FXLMS.

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Advances in Nonlinear Predictive Control: A Survey on Stability and Optimality

  • Kwon, Wook-Hyun;Han, Soo-Hee;Ahn, Choon-Ki
    • International Journal of Control, Automation, and Systems
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    • v.2 no.1
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    • pp.15-22
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    • 2004
  • Some recent advances in stability and optimality for the nonlinear receding horizon control (NRHC) or the nonlinear model predictive control (NMPC) are assessed. The NRHCs with terminal conditions are surveyed in terms of a terminal state equality constraint, a terminal cost, and a terminal constraint set. Other NRHCs without terminal conditions are surveyed in terms of a control Lyapunov function (CLF) and cost monotonicity. Additional approaches such as output feedback, fuzzy, and neural network are introduced. This paper excludes the results for linear receding horizon controls and concentrates only on the analytical results of NRHCs, not including applications of NRHCs. Stability and optimality are focused on rather than robustness.

Time-Discretization of Nonlinear Systems with Delayed Multi-Input Using Taylor Series

  • Park, Ji-Hyang;Chong, Kil-To;Nikolaos Kazantzis;Alexander G. Parlos
    • Journal of Mechanical Science and Technology
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    • v.18 no.7
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    • pp.1107-1120
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    • 2004
  • This study proposes a new scheme for the sampled-data representation of nonlinear systems with time-delayed multi-input. The proposed scheme is based on the Taylor-series expansion and zero-order hold assumption. The mathematical structure of a new discretization scheme is explored. On the basis of this structure, the sampled-data representation of nonlinear systems including time-delay is derived. The new scheme is applied to nonlinear systems with two inputs and then the delayed multi-input general equation is derived. The resulting time-discretization provides a finite-dimensional representation of nonlinear control systems with time-delay enabling existing controller design techniques to be applied to them. In order to evaluate the tracking performance of the proposed scheme, an algorithm is tested for some of the examples including maneuvering of an automobile and a 2-DOF mechanical system.