• Title/Summary/Keyword: Lyapunov functions

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Direct Adaptive Fuzzy Sliding Mode Control for Under-actuated Uncertain Systems

  • Su, Shun-Feng;Hsueh, Yao-Chu;Tseng, Cio-Ping;Chen, Song-Shyong;Lin, Yu-San
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.15 no.4
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    • pp.240-250
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    • 2015
  • The development of the control algorithms for under-actuated systems is important. Decoupled sliding mode control has been successfully employed to control under-actuated systems in a decoupling manner with the use of sliding mode control. However, in such a control scheme, the system functions must be known. If there are uncertainties in those functions, the control performance may not be satisfactory.In this paper, the direct adaptive fuzzy sliding mode control is employed to control a class of under-actuated uncertain systems which can be regarded as a combination of several subsystems with one same control input. By using the hierarchical sliding control approach, a sliding control law is derived so as to make every subsystem stabilized at the same time. But, since the system considered is assumed to be uncertain, the sliding control law cannot be readily facilitated. Therefore, in the study, based on Lyapunov stable theory a fuzzy compensator is proposed to approximate the uncertain part of the sliding control law. From those simulations, it can be concluded that the proposed compensator can indeed cope with system uncertainties. Besides, it can be found that the proposed compensator also provide good robustness properties.

Design of the Adaptive Fuzzy Control Scheme and its Application on the Steering Control of the UCT (무인 컨테이너 운송 조향 제어의 적응 퍼지 제어와 응용)

  • 이규준;이영진;윤영진;이원구;김종식;이만형
    • Journal of Korean Port Research
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    • v.15 no.1
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    • pp.37-46
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    • 2001
  • Fuzzy logic control(FLC) is composed of three parts : fuzzy rule-bases, membership functions, and scaling factors. Well-defined fuzzy rule-base should contain proper physical intuition on the plant, so are needed lots of experiences of the skillful expert. When membership functions are considered, some parameters on the memberships function such as function shape, support, allocation density should be selected well. The rule of scaling factors is 'scaling'(amplifying or reducing) for both input and output signals of the FLC to fit in the membership function support and to operate the plant intentionally. To get a better performance of the FLC, it is necessary to adjust the parameters of the FLC. In general, the adaptation of the scaling factors is the most effective adjustment scheme, compared with that of the fuzzy rule-base or membership function parameters. This study proposes the adaptation scheme of the scaling factors. When the adaptation is performed on-line, the stability of the adaptive FLC should be guaranteed. The stable FLC system can be designed with stability analysis in the sense of Lyapunov stability. To adapt the scaling factors for the error signals, the concept of the conventional MRAC would be introduced into slightly modified form. A tracking accuracy of the control system would be enhanced by the modified shape and support of the membership function. The simulation is achieved on the pilot plant with the hydraulic steering control of a UCT(Unmanned Container Transporter) of which modeling dynamics have lots of severe uncertainties and modeling errors.

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Optimization of Dynamic Neural Networks for Nonlinear System control (비선형 시스템 제어를 위한 동적 신경망의 최적화)

  • Ryoo, Dong-Wan;Lee, Jin-Ha;Lee, Young-Seog;Seo, Bo-Hyeok
    • Proceedings of the KIEE Conference
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    • 1998.07b
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    • pp.740-743
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    • 1998
  • This paper presents an optimization algorithm for a stable Dynamic Neural Network (DNN) using genetic algorithm. Optimized DNN is applied to a problem of controlling nonlinear dynamical systems. DNN is dynamic mapping and is better suited for dynamical systems than static forward neural network. The real time implementation is very important, and thus the neuro controller also needs to be designed such that it converges with a relatively small number of training cycles. SDNN has considerably fewer weights than DNN. The object of proposed algorithm is to the number of self dynamic neuron node and the gradient of activation functions are simultaneously optimized by genetic algorithms. To guarantee convergence, an analytic method based on the Lyapunov function is used to find a stable learning for the SDNN. The ability and effectiveness of identifying and controlling, a nonlinear dynamic system using the proposed optimized SDNN considering stability' is demonstrated by case studies.

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Cluster Robots Line formatted Navigation Based on Virtual Hill and Virtual Sink (Virtual Hill 및 Sink 개념 기반의 군집 로봇의 직선 대형 주행 기법)

  • Kang, Yo-Hwan;Lee, Min-Cheol;Kim, Chi-Yen;Yoon, Sung-Min;Noh, Chi-Bum
    • The Journal of Korea Robotics Society
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    • v.6 no.3
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    • pp.237-246
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    • 2011
  • Robots have been used in many fields due to its performance improvement and variety of its functionality, to the extent which robots can replace human tasks. Individual feature and better performance of robots are expected and required to be created. As their performances and functions have increased, systems have gotten more complicated. Multi mobile robots can perform complex tasks with simple robot system and algorithm. But multi mobile robots face much more complex driving problem than singular driving. To solve the problem, in this study, driving algorithm based on the energy method is applied to the individual robot in a group. This makes a cluster be in a formation automatically and suggests a cluster the automatic driving method so that they stably arrive at the target. The energy method mentioned above is applying attractive force and repulsive force to a special target, other robots or obstacles. This creates the potential energy, and the robot is controlled to drive in the direction of decreasing energy, which basically satisfies lyapunov function. Through this method, a cluster robot is able to create a formation and stably arrives at its target.

Approximation-Based Decentralized Adaptive Output-Feedback Control for Nonlinear Interconnected Time-Delay Systems (비선형 상호 연결된 시간 지연 시스템을 위한 함수 예측 기법에 기반한 분산 적응 출력 궤환 제어)

  • Yoo, Sung-Jin
    • Journal of the Korean Institute of Intelligent Systems
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    • v.22 no.2
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    • pp.174-180
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    • 2012
  • This paper proposes a decentralized adaptive output-feedback controller design for nonlinear interconnected systems with unknown time delays. The interaction terms with unknown delays are related to all states of subsystems. The time-delayed functions are compensated by using appropriate Lyapunov-Krasovskii functionals and function approximation technique. The observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem. In addition, we prove that all signals in the closed-loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin.

Robust H Disturbance Attenuation Control of Continuous-time Polynomial Fuzzy Systems (연속시간 다항식 퍼지 시스템을 위한 강인한 H 외란 감쇠 제어)

  • Jang, Yong Hoon;Kim, Han Sol;Joo, Young Hoon;Park, Jin Bae
    • Journal of Institute of Control, Robotics and Systems
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    • v.22 no.6
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    • pp.429-434
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    • 2016
  • This paper introduces a stabilization condition for polynomial fuzzy systems that guarantees $H_{\infty}$ performance under the imperfect premise matching. An $H_{\infty}$ control of polynomial fuzzy systems attenuates the effect of external disturbance. Under the imperfect premise matching, a polynomial fuzzy model and controller do not share the same membership functions. Therefore, a polynomial fuzzy controller has an enhanced design flexibility and inherent robustness to handle parameter uncertainties. In this paper, the stabilization conditions are derived from the polynomial Lyapunov function and numerically solved by the sum-of-squares (SOS) method. A simulation example and comparison of the performance are provided to verify the stability analysis results and demonstrate the effectiveness of the proposed stabilization conditions.

Robust Adaptive Fuzzy Backstepping Control for Trajectory Tracking of an Electrically Driven Nonholonomic Mobile Robot with Uncertainties (불확실성을 가지는 전기 구동 논홀로노믹 이동 로봇의 궤적 추종을 위한 강인 적응 퍼지 백스테핑 제어)

  • Shin, Jin-Ho
    • Journal of Institute of Control, Robotics and Systems
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    • v.18 no.10
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    • pp.902-911
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    • 2012
  • This paper proposes a robust adaptive fuzzy backstepping control scheme for trajectory tracking of an electrically driven nonholonomic mobile robot with uncertainties and actuator dynamics. A complete model of an electrically driven nonholonomic mobile robot described in this work includes all models of the uncertain robot kinematics with a nonholonomic constraint, the uncertain robot body dynamics with uncertain frictions and unmodeled disturbances, and the uncertain actuator dynamics with disturbances. The proposed control scheme uses the backstepping control approach through a kinematic controller and a robust adaptive fuzzy velocity tracking controller. The presented control scheme has a voltage control input with an auxiliary current control input rather than a torque control input. It has two FBFNs(Fuzzy Basis Function Networks) to approximate two unknown nonlinear robot dynamic functions and a robust adaptive control input with the proposed adaptive laws to overcome the uncertainties such as parameter uncertainties and external disturbances. The proposed control scheme does not a priori require the accurate knowledge of all parameters in the robot kinematics, robot dynamics and actuator dynamics. It can also alleviate the chattering of the control input. Using the Lyapunov stability theory, the stability of the closed-loop robot control system is guaranteed. Simulation results show the validity and robustness of the proposed control scheme.

An Improved EEG Signal Classification Using Neural Network with the Consequence of ICA and STFT

  • Sivasankari, K.;Thanushkodi, K.
    • Journal of Electrical Engineering and Technology
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    • v.9 no.3
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    • pp.1060-1071
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    • 2014
  • Signals of the Electroencephalogram (EEG) can reflect the electrical background activity of the brain generated by the cerebral cortex nerve cells. This has been the mostly utilized signal, which helps in effective analysis of brain functions by supervised learning methods. In this paper, an approach for improving the accuracy of EEG signal classification is presented to detect epileptic seizures. Moreover, Independent Component Analysis (ICA) is incorporated as a preprocessing step and Short Time Fourier Transform (STFT) is used for denoising the signal adequately. Feature extraction of EEG signals is accomplished on the basis of three parameters namely, Standard Deviation, Correlation Dimension and Lyapunov Exponents. The Artificial Neural Network (ANN) is trained by incorporating Levenberg-Marquardt(LM) training algorithm into the backpropagation algorithm that results in high classification accuracy. Experimental results reveal that the methodology will improve the clinical service of the EEG recording and also provide better decision making in epileptic seizure detection than the existing techniques. The proposed EEG signal classification using feed forward Backpropagation Neural Network performs better than to the EEG signal classification using Adaptive Neuro Fuzzy Inference System (ANFIS) classifier in terms of accuracy, sensitivity, and specificity.

Smart composite repetitive-control design for nonlinear perturbation

  • ZY Chen;Ruei-Yuan Wang;Yahui Meng;Timothy Chen
    • Steel and Composite Structures
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    • v.51 no.5
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    • pp.473-485
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    • 2024
  • This paper proposes a composite form of fuzzy adaptive control plan based on a robust observer. The fuzzy 2D control gains are regulated by the parameters in the LMIs. Then, control and learning performance indices with weight matrices are constructed as the cost functions, which allows the regulation of the trade-off between the two performance by setting appropriate weight matrices. The design of 2D control gains is equivalent to the LMIs-constrained multi-objective optimization problem under dual performance indices. By using this proposed smart tracking design via fuzzy nonlinear criterion, the data link can be further extended. To evaluate the performance of the controller, the proposed controller was compared with other control technologies. This ensures the execution of the control program used to track position and trajectory in the presence of great model uncertainty and external disturbances. The performance of monitoring and control is verified by quantitative analysis. The goals of this paper are towards access to adequate, safe and affordable housing and basic services, promotion of inclusive and sustainable urbanization and participation, implementation of sustainable and disaster-resilient buildings, sustainable human settlement planning and manage. Therefore, the goal is believed to achieved in the near future by the ongoing development of AI and control theory.

Fuzzy sliding mode controller design for improving the learning rate (퍼지 슬라이딩 모드의 속도 향상을 위한 제어기 설계)

  • Hwang, Eun-Ju;Cho, Young-Wan;Kim, Eun-Tai;Park, Mignon
    • Journal of the Korean Institute of Intelligent Systems
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    • v.16 no.6
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    • pp.747-752
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    • 2006
  • In this paper, the adaptive fuzzy sliding mode controller with two systems is designed. The existing sliding mode controller used to $approximation{\^{u}}(t)$ with discrete sgn function and sat function for keeping the state trajectories on the sliding surface[1]. The proposed controller decrease the disturbance for uncertain control gain and This paper is concerned with an Adaptive Fuzzy Sliding Mode Control(AFSMC) that the fuzzy systems ate used to approximate the unknown functions of nonlinear system. In the adaptive fuzzy system, we adopt the adaptive law to approximate the dynamics of the nonlinear plant and to adjust the parameters of AFSMC. The stability of the suggested control system is proved via Lyapunov stability theorem, and convergence and robustness properties ate demonstrated. Futhermore, fuzzy tuning improve tracking abilities by changing some sliding conditions. In the traditional sliding mode control, ${\eta}$ is a positive constant. The increase of ${\eta}$ has led to a significant decrease in the rise time. However, this has resulted in higher overshoot. Therefore the proposed ${\eta}$ tuning AFSMC improve the performances, so that the controller can track the trajectories faster and more exactly than ordinary controller. The simulation results demonstrate that the performance is improved and the system also exhibits stability.