An SOS-Based Control Lyapunov Function Design for Polynomial Fuzzy Control of Nonlinear Systems

被引:39
|
作者
Furqon, Radian [1 ]
Chen, Ying-Jen [2 ]
Tanaka, Motoyasu [1 ]
Tanaka, Kazuo [1 ]
Wang, Hua O. [3 ]
机构
[1] Univ Electrocommun, Dept Mech Engn & Intelligent Syst, Tokyo 1828585, Japan
[2] Natl Taipei Univ, Dept Elect Engn, New Taipei 23741, Taiwan
[3] Boston Univ, Dept Mech Engn, Boston, MA 02215 USA
关键词
Control Lyapunov function (CLF); global stabilization; operation domain; polynomial fuzzy system; semiglobal stabilization; sum of squares (SOS); TAKAGI-SUGENO SYSTEMS; H-INFINITY CONTROL; STABILITY ANALYSIS; NONQUADRATIC STABILIZATION; PERFORMANCE; CRITERION; MODELS;
D O I
10.1109/TFUZZ.2016.2578339
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
This paper deals with a sum-of-squares (SOS)-based control Lyapunov function (CLF) design for polynomial fuzzy control of nonlinear systems. The design starts with exactly replacing (smooth) nonlinear systems dynamics with polynomial fuzzy models, which are known as universal approximators. Next, global stabilization conditions represented in terms of SOS are provided in the framework of the CLF design, i.e., a stabilizing controller with nonparallel distributed compensation form is explicitly designed by applying Sontag's control law, once a CLF for a given nonlinear system is constructed. Furthermore, semiglobal stabilization conditions on operation domains are derived in the same fashion as in the global stabilization conditions. Both global and semiglobal stabilization problems are formulated as SOS optimization problems, which reduce to numerical feasibility problems. Five design examples are given to show the effectiveness of our proposed approach over the existing linear matrix inequality and SOS approaches.
引用
收藏
页码:775 / 787
页数:13
相关论文
共 50 条
  • [41] An Improved Stabilizing Condition for Polynomial Systems with Bounded Actuators: An SOS-based Approach
    Jennawasin, Tanagorn
    Kawanishi, Michihiro
    Narikiyo, Tatsuo
    Lin, Chun-Liang
    [J]. 2012 IEEE MULTI-CONFERENCE ON SYSTEMS AND CONTROL (2012 IEEE MSC), 2012, : 258 - 263
  • [42] SOS Based Robust H∞ Fuzzy Dynamic Output Feedback Control of Nonlinear Networked Control Systems
    Chae, Seunghwan
    Nguang, Sing Kiong
    [J]. IEEE TRANSACTIONS ON CYBERNETICS, 2014, 44 (07) : 1204 - 1213
  • [43] Nonlinear predictive control based on robust control Lyapunov function
    Yang, Guo-Shi
    He, De-Feng
    Xue, Mei-Sheng
    [J]. Kongzhi yu Juece/Control and Decision, 2010, 25 (11): : 1752 - 1756
  • [44] A Novel Sliding Mode Control for a Class of Stochastic Polynomial Fuzzy Systems Based on SOS Method
    Zhang, Huaguang
    Wang, Yingying
    Wang, Yingchun
    Zhang, Jianyu
    [J]. IEEE TRANSACTIONS ON CYBERNETICS, 2020, 50 (03) : 1037 - 1046
  • [45] Lyapunov function based design of robust fuzzy controllers for uncertain nonlinear systems: Distinct Lyapunov functions
    Leung, FHF
    Lam, HK
    Tam, PKS
    [J]. 1998 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS AT THE IEEE WORLD CONGRESS ON COMPUTATIONAL INTELLIGENCE - PROCEEDINGS, VOL 1-2, 1998, : 577 - 582
  • [46] Design of Lyapunov Based Nonlinear Position Control of Electrohydraulic Servo Systems
    Deticek, Edvard
    Kastrevc, Mitja
    [J]. STROJNISKI VESTNIK-JOURNAL OF MECHANICAL ENGINEERING, 2016, 62 (03): : 163 - 170
  • [47] Fuzzy control design for nonlinear systems
    Chen, Song-Shyong
    Wu, Jenq-Lang
    Chang, Yuan-Chang
    Su, Shun-Feng
    [J]. 2007 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, VOLS 1-4, 2007, : 1320 - 1325
  • [48] A Survey on the Control Lyapunov Function and Control Barrier Function for Nonlinear-Affine Control Systems
    Li, Boqian
    Wen, Shiping
    Yan, Zheng
    Wen, Guanghui
    Huang, Tingwen
    [J]. IEEE-CAA JOURNAL OF AUTOMATICA SINICA, 2023, 10 (03) : 584 - 602
  • [49] The Feasible Control Lyapunov Function of Nonlinear Affine-Control Systems
    Chen XiaoDan
    Chen ShaoBai
    [J]. 2010 THIRD INTERNATIONAL SYMPOSIUM ON INTELLIGENT INFORMATION TECHNOLOGY AND SECURITY INFORMATICS (IITSI 2010), 2010, : 442 - 445
  • [50] A control Lyapunov function approach to stabilization of nonlinear systems with H∞ control
    Sugie, T
    Urashima, T
    Fujimoto, K
    [J]. PROCEEDINGS OF THE 2000 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2000, : 2139 - 2143