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Wang Y, Ma Y. Membership function dependent stabilization of discrete time interval type-2 fuzzy systems with mixed actuator faults. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.12.055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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Xie WB, Zhang J, Li YF, Palhares RM. A novel polynomial membership functions based control method for T-S fuzzy systems. ISA TRANSACTIONS 2022; 129:192-203. [PMID: 35221091 DOI: 10.1016/j.isatra.2022.02.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2020] [Revised: 12/07/2021] [Accepted: 02/08/2022] [Indexed: 06/14/2023]
Abstract
To solve the state feedback stabilization problem for a class of T-S fuzzy systems, a new stability synthesis method is raised to further relax the conservatism existing in the analysis process. First, a series of nonlinear polynomials are used to approximate the system membership functions. And satisfied approximation results can be obtained. Then a polynomials transformation method is raised to change the polynomial membership functions into linear form. This method can facilitate the synthesis process and achieve better approximation precision. Therefore, by a membership function involving stability analysis approach, linear matrix inequality form stability conditions are given. Finally, by presenting and analyzing a numerical and a practical examples, the conservatism reduction effects of the proposed methods are verified.
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Affiliation(s)
- Wen-Bo Xie
- School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, 200444, China; College of Automation, Harbin University of Science and Technology, Harbin, 150080, PR China
| | - Jian Zhang
- College of Power and Energy Engineering, Harbin Engineering University, Harbin, 150001, PR China.
| | - Yi-Fan Li
- College of Automation, Harbin University of Science and Technology, Harbin, 150080, PR China
| | - Reinaldo M Palhares
- Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos, 6627, 31270-010, Belo Horizonte, MG, Brazil
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Li H, Xie WB, Lam HK, Zhang J. Membership Function Derivatives Transformation Approach for Stability Analysis and Stabilization Control of T-S Fuzzy Systems. IEEE TRANSACTIONS ON CYBERNETICS 2022; 52:7906-7912. [PMID: 33417579 DOI: 10.1109/tcyb.2020.3041513] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
In this text, a membership function derivatives (MFDs) extrema-based method is proposed to relax the conservatism both in stability analysis and synthesis problems of Takagi-Sugeno fuzzy systems. By the designed algorithm, the nonpositiveness of the MFDs extrema is conquered. For an open-loop system, based on certain information of the MFs and derivatives, a series of convex stability conditions is derived. Then, an extremum-based construction method is adopted to involve the MF information. For the shape of MFDs, a coordinate transformation algorithm is proposed to involve it in the stability conditions to achieve local stable effects. For a state-feedback control system, conditions guaranteeing the stability and robustness are listed. Finally, simulation examples and comparisons are carried out to clarify the conservatism reduction results of the raised method.
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Sensor and actuator fault-tolerant control based on fuzzy unknown input observer: A polynomial fuzzy approach. Appl Soft Comput 2021. [DOI: 10.1016/j.asoc.2021.107747] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Zhang J, Wu WJ, Xie WB, Peng C. Dimensional-varying integral sliding mode controller design for uncertain Takagi–Sugeno fuzzy systems. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2021.02.062] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Membership-function-dependent stability analysis and local controller design for T–S fuzzy systems: A space-enveloping approach. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2020.09.043] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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A Data-Driven Approach of Takagi-Sugeno Fuzzy Control of Unknown Nonlinear Systems. APPLIED SCIENCES-BASEL 2020. [DOI: 10.3390/app11010062] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
A novel approach to build a Takagi-Sugeno (T-S) fuzzy model of an unknown nonlinear system from experimental data is presented in the paper. The neuro-fuzzy models or, more specifically, fuzzy basis function networks (FBFNs) are trained from input–output data to approximate the nonlinear systems for which analytical mathematical models are not available. Then, the T-S fuzzy models are derived from the direct linearization of the neuro-fuzzy models. The operating points for linearization are chosen using the evolutionary strategy to minimize the global approximation error so that the T-S fuzzy models can closely approximate the original unknown nonlinear system with a reduced number of linearizations. Based on T-S fuzzy models, optimal controllers are designed and implemented for a nonlinear two-link flexible joint robot, which demonstrates the possibility of implementing the well-established model-based optimal control method onto unknown nonlinear dynamic systems.
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Zhang D, Zhou Z, Jia X. Networked fuzzy output feedback control for discrete-time Takagi–Sugeno fuzzy systems with sensor saturation and measurement noise. Inf Sci (N Y) 2018. [DOI: 10.1016/j.ins.2018.02.026] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Hou R, Wang L, Gao Q, Hou Y, Wang C. Indirect adaptive fuzzy wavelet neural network with self- recurrent consequent part for AC servo system. ISA TRANSACTIONS 2017; 70:298-307. [PMID: 28583350 DOI: 10.1016/j.isatra.2017.04.010] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2016] [Revised: 01/03/2017] [Accepted: 04/10/2017] [Indexed: 06/07/2023]
Abstract
This paper proposes a novel indirect adaptive fuzzy wavelet neural network (IAFWNN) to control the nonlinearity, wide variations in loads, time-variation and uncertain disturbance of the ac servo system. In the proposed approach, the self-recurrent wavelet neural network (SRWNN) is employed to construct an adaptive self-recurrent consequent part for each fuzzy rule of TSK fuzzy model. For the IAFWNN controller, the online learning algorithm is based on back propagation (BP) algorithm. Moreover, an improved particle swarm optimization (IPSO) is used to adapt the learning rate. The aid of an adaptive SRWNN identifier offers the real-time gradient information to the adaptive fuzzy wavelet neural controller to overcome the impact of parameter variations, load disturbances and other uncertainties effectively, and has a good dynamic. The asymptotical stability of the system is guaranteed by using the Lyapunov method. The result of the simulation and the prototype test prove that the proposed are effective and suitable.
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Affiliation(s)
- Runmin Hou
- Department of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China.
| | - Li Wang
- Department of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
| | - Qiang Gao
- Department of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
| | - Yuanglong Hou
- Department of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
| | - Chao Wang
- Department of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
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Tsai ZR, Chang YZ, Zhang HW, Lin CT. Relax the chaos-model-based human behavior by electrical stimulation therapy design. COMPUTERS IN HUMAN BEHAVIOR 2017. [DOI: 10.1016/j.chb.2016.10.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Liu C, Lam H, Ban X, Zhao X. Design of polynomial fuzzy observer–controller with membership functions using unmeasurable premise variables for nonlinear systems. Inf Sci (N Y) 2016. [DOI: 10.1016/j.ins.2016.03.038] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Zhao T, Wei Z, Dian S, Xiao J. Observer-based H∞ controller design for interval type-2 T–S fuzzy systems. Neurocomputing 2016. [DOI: 10.1016/j.neucom.2015.10.074] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Grey Wolf Optimizer-Based Approach to the Tuning of Pi-Fuzzy Controllers with a Reduced Process Parametric Sensitivity. ACTA ACUST UNITED AC 2016. [DOI: 10.1016/j.ifacol.2016.07.089] [Citation(s) in RCA: 74] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Wang LK, Peng JL, Liu XD, Zhang HG. An approach to observer design of continuous-time Takagi–Sugeno fuzzy model with bounded disturbances. Inf Sci (N Y) 2015. [DOI: 10.1016/j.ins.2015.06.034] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Ganjefar S, Tofighi M. Single-hidden-layer fuzzy recurrent wavelet neural network: Applications to function approximation and system identification. Inf Sci (N Y) 2015. [DOI: 10.1016/j.ins.2014.09.054] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Han H, Lam HK. Discrete Sliding-Mode Control for a Class of T-S Fuzzy Models with Modeling Error. JOURNAL OF ADVANCED COMPUTATIONAL INTELLIGENCE AND INTELLIGENT INFORMATICS 2014. [DOI: 10.20965/jaciii.2014.p0908] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
This paper proposes a discrete sliding-mode controller for a class of nonlinear systems described by a T-S fuzzy model subject to modeling error, which may influence the system performance and the overall system stability. While most of existing literature treats the modeling error under the so-called parallel distributed compensation framework by using some norm-bounded matrices, the proposed control scheme in this paper integrates a feedback component, which mainly consists of fuzzy approximators to deal with the modeling error and an auxiliary component of the variable structure control with a sector to guarantee the global stability of the closed-loop system when the system state travels outside the sector. With the consideration of system stability, adaptive laws adjusting the parameters in the system are developed based on the Lyapunov synthesis approach. Finally, simulation results will confirm the effectiveness of the approach proposed in this paper.
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Lee DH, Joo YH, Tak MH. Local stability analysis of continuous-time Takagi–Sugeno fuzzy systems: A fuzzy Lyapunov function approach. Inf Sci (N Y) 2014. [DOI: 10.1016/j.ins.2013.08.036] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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