RESEARCH ARTICLE
Passivity-based parameterized adaptive disturbance attenuation controller design for switched polynomial nonlinear systems
Huawei Zhu,
Xiaorong Hou,
Huawei Zhu
School of Energy Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China
Dazhou Industrial Technology Institute of Intelligent Manufacturing, Sichuan University of Arts and Science, Dazhou, China
Search for more papers by this authorCorresponding Author
Xiaorong Hou
School of Energy Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China
Correspondence
Xiaorong Hou, School of Energy Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China.
Email: [email protected]
Search for more papers by this authorHuawei Zhu,
Xiaorong Hou,
Huawei Zhu
School of Energy Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China
Dazhou Industrial Technology Institute of Intelligent Manufacturing, Sichuan University of Arts and Science, Dazhou, China
Search for more papers by this authorCorresponding Author
Xiaorong Hou
School of Energy Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China
Correspondence
Xiaorong Hou, School of Energy Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China.
Email: [email protected]
Search for more papers by this authorSummary
This paper is concerned with the adaptive disturbance attenuation control problem for a class of switched polynomial nonlinear systems. At first, a parameterized controller is designed to transform the switched polynomial nonlinear systems into switched Hamiltonian systems with polynomial structure. Then, combining with the solve-parameter algorithm described in this paper, a mixed adaptive passivity and H2/H∞ control method is devoted. Comparing with the existing results, the obtained adaptive disturbance attenuation controller has better performance. Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.
REFERENCES
- 1Li Z, Qiao Y, Qi H, Cheng D. Stability of switched polynomial systems. J Syst Sci Complex. 2008; 21(3): 362-377.
- 2Xu J, Xie L, Wang Y. Simultaneous stabilization and robust control of polynomial nonlinear systems using SOS techniques. IEEE Trans Autom Control. 2009; 54(8): 1892-1897.
- 3Yu G, Huang Y, Cheng C. Robust H∞ controller design for polynomial fuzzy control systems by sum-of-squares approach. IET Control Theory Appl. 2016; 10(14): 1684-1695.
- 4Wang M, Zhao J. Quadratic stabilization of a class of switched nonlinear systems via single Lyapunov function. Nonlinear Anal Hybrid Syst. 2010; 4(1): 44-53.
- 5Li Y, Tong S, Liu L, Feng G. Adaptive output-feedback control design with prescribed performance for switched nonlinear systems. Automatica. 2017; 80: 225-231.
- 6Branicky MS. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans Autom Control. 1998; 43(4): 475-482.
- 7Wang H, Zhao J. Passivity and H∞ control of switched discrete-time nonlinear systems using linearization. Int J Syst Sci. 2017; 49(1): 68-83.
- 8Deaecto GS, Geromel JC, Daafouz J. Dynamic output feedback H∞ control of switched linear systems. Automatica. 2011; 47(8): 1713-1720.
- 9Zhao X, Yin Y, Yang H, Li R. Adaptive control for a class of switched linear systems using state-dependent switching. Circuits Syst Signal Process. 2015; 34(11): 3681-3695.
- 10Zhang L, Shi P, Boukas EK and Wang C. H∞ control of switched linear discrete-time systems with polytopic uncertainties. Optim Control Appl Methods 2006; 27(5): 273-291.
- 11Eugene L, Kevin W, Howe D. Robust and Adaptive Control with Aerospace Applications. London, UK: Springer; 2012.
- 12Li Y, Tong S. Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems. IEEE Trans Cybern. 2017; 47(4): 1007-1016.
- 13Long L, Wang Z, Zhao J. Switched adaptive control of switched nonlinearly parameterized systems with unstable subsystems. Automatica. 2015; 54: 217-228.
- 14Li Y, Sui S, Tong S. Adaptive fuzzy control design for stochastic nonlinear switched systems with arbitrary switchings and unmodeled dynamics. IEEE Trans Cybern. 2017; 47(2): 403-414.
- 15Sui S, Tong S, Li Y. Observer-based adaptive fuzzy decentralized control for stochastic large-scale nonlinear systems with unknown dead-zones. Inform Sci. 2014; 259: 71-86.
- 16Willems JC. Dissipative dynamical systems part I: general theory. Arch Ration Mech Anal. 1972; 45(5): 321-351.
- 17Hill D, Moylan P. The stability of nonlinear dissipative systems. IEEE Trans Autom Control. 1976; 21(5): 708-711.
- 18Astolfi A, Ortega R, Sepulchre R. Stabilization and disturbance attenuation of nonlinear systems using dissipativity theory. Eur J Control. 2002; 8(5): 408-431.
- 19Byrnes CI, Isidori A, Willems JC. Passivity, feedback equivalence and the global stabilization of minimum phase nonlinear systems. IEEE Trans Autom Control. 2002; 36(11): 1228-1240.
- 20Son YI, Yang JW, Jo NH, Shim H, Seo JH. Feedback passivity approach to output feedback disturbance attenuation for uncertain nonlinear systems. Int J Syst Sci. 2004; 35(8): 467-477.
- 21Travieso-Torres JC, Duarte-Mermoud MA, Sepúleveda DI. Passivity-based control for stabilization, regulation and tracking purposes of a class of nonlinear systems. Int J Adapt Control Signal Process. 2007; 21(7): 582-602.
- 22Jayawardhana B, Weiss G. Tracking and disturbance rejection for fully actuated mechanical systems. Automatica. 2008; 44: 2863-2868.
- 23Ha CS, Zuo ZY, Choi FB, Lee D. Passivity-based adaptive backstepping control of quadrotor-type UAVs. Robotics Auton Syst. 2014; 62(9): 1305-1315.
- 24Jiang ZP, Hill DJ, Fradkov AL. A passification approach to adaptive nonlinear stabilization. Syst Control Lett. 1996; 28(2): 73-84.
- 25Van Der Schaft AJ. L2-Gain and Passivity Techniques in Nonlinear Control. Second ed. London, UK: Springer; 1999.
- 26Pang HB, Zhao J. Robust passivity, feedback passification and global robust stabilization for switched non-linear systems with structural uncertainty. IET Control Theory Appl. 2015; 9(11): 1723-1730.
- 27Pang HB, Zhao J. Adaptive feedback passivity-based disturbance attenuation for switched nonlinearly parameterized systems. Trans Inst Meas Control. 2016; 39(12): 1811-1820.
- 28Xiang W, Xiao J. H∞ control synthesis of switched descrete-time fuzzy systems via hybrid approach. Optim Control Appl Methods. 2013; 34(6): 635-655.
- 29Zhao J, Hill DJ. On stability, L2-gain and H∞ control for switched systems. Automatica. 2008; 44(5): 1220-1232.
- 30Li C, Zhao J. Passivity-based H∞ control for a class of switched nonlinear systems. Optim Control Appl Methods. 2017; 38(4): 559-574.
- 31Ku CC. Robust mixed H2/passivity performance controller design for uncertain drum-boiler system. J Mar Sci Technol. 2016; 24(5): 1003-1010.
- 32Orihuela L, Millán P, Vivas C, Rubio FR. H2/H∞ control for discrete TDS with application to networked control systems: periodic and asynchronous communication. Optim Control Appl Methods. 2015; 36: 60-76.
- 33Chen C, Dong W, Djapic V. Distributed H2/H∞ filtering over infinite horizon. Int J Adapt Control Signal Process. 2018; 32: 330-343.
- 34Tseng C. Mixed H2/H∞ adaptive tracking control design for uncertain constrained robots. Asian J Control. 2005; 7(3): 296-309.
- 35Baghbani F, Akbarzadeh TM, Akbarzadeh A, Ghaemi M. Robust adaptive mixed H2/H∞ interval type-2 fuzzy control of nonlinear uncertain systems with minimal control effort. Eng Appl Artif Intel. 2016; 49: 88-102.
- 36EI-Sousy FFM. Intelligent mixed H2/H∞ adaptive tracking control system design using self-organizing recurrent fuzzy-wavelet-neural-network for uncertain two-axis motion control system. Appl Soft Comput. 2016; 41: 22-50.
- 37Wang Y, Lu J, Zhang S, Chu Y. Mixed H2/H∞ control for a class of nonlinear discrete-time networked control systems with random delays and stochastic packet dropouts. Optim Control Appl Methods. 2015; 36: 825-843.
- 38Gao M, Sheng L, Zhang W. Stochastic H2/H∞ control of nonlinear systems with time-delay and state-dependent noise. Appl Math Comput. 2015; 266: 429-440.
- 39Lee Y, Shin D, Kin W, Chung C. Nonlinear H2control for a nonlinear system with bounded varying parameters: application to PM stepper motors. IEEE/ASME Trans Mechatron. 2017; 22(3): 1349-1359.
- 40Jeong C, Yaz E, Yaz Y. Design of mixed H2 - dissipative observers with stochastic resilience for discrete-time nonlinear systems. J Franklin Inst. 2011; 348: 790-809.
- 41Sadeghzadeh A, Karimi A. Fixed-structure H2 controller design for polytopic systems via LMIs. Optim Control Appl Methods. 2016; 36(6): 794-809.
- 42Langson W, Allcync A. Infinite horizon optimal control of a class of nonlinear systems. In: Proceedings of the 1997 American Control Conference; 1997; Albuquerque, NM.
- 43Armon DS, Collins GE, McCallum S. Cylindrical algebraic decomposition I: the basic algorithm. SIAM J Comput. 1982; 13(4): 878-889.
- 44Chakraborty A, Seiler P, Balas GJ. Nonlinear region of attraction analysis for flight control verification and validation. Control Eng Pract. 2011; 19: 335-345.
- 45Wu M, Yang Z, Lin W. Domain-of-attraction estimation for uncertain non-polynomial systems. Commun Nonlinear Sci Numer Simulat. 2014; 19: 3044-3052.
