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September  2020, 10(3): 381-389. doi: 10.3934/naco.2020009

Passive control for a class of Nonlinear systems by using the technique of Adding a power integrator

1. 

School of Mathematics, Liaoning University, Shenyang, 110036, China

2. 

College of Science, Liaoning Shihua University, Fushun, 113001, China

* Corresponding author: Li Yang

Received  May 2019 Revised  October 2019 Published  February 2020

Fund Project: This work is supported by the scientific research fund LQN201712 of Liaoning Provincial Education Department

This paper studies the problem of passive control for a class of uncertain nonlinear lower-triangle systems. We extend the feedback designing tool named adding a power integrator. By using it repeatedly, the passive controller is given. Under this designing method, we don't need the system to be feedback linearizable. Moreover, comparing with the backstepping technique, the coordinate in the controller designing process of this method does not need to be transformed.

Citation: Jinglai Qiao, Li Yang, Jiawei Yao. Passive control for a class of Nonlinear systems by using the technique of Adding a power integrator. Numerical Algebra, Control and Optimization, 2020, 10 (3) : 381-389. doi: 10.3934/naco.2020009
References:
[1]

W. Chen and M. Saif, Passivity and passivity based controller design of a class of switched control systems, in Proc. 16th IFAC World Congress, (2005), 143–147.

[2]

T. DengH. YaoJ. Du and J. Jiang, Neural network dynamic control for high-order nonlinear time-delay systems, Systems Engineering and Electronics, 36 (2014), 1152-1161. 

[3]

P. DoerfferO. Szulc and R. Bohing, Shock wave smearing by passive control, Journal of Thermal Science, 15 (2006), 43-47. 

[4]

A. T. EL-Sayed, Suppression of nonlinear vibration system described by nonlinear differential equations using passive controller, Nonlinear Dynamics, 78 (2014), 1683-1694.  doi: 10.1007/s11071-014-1550-7.

[5]

U. K. Kocamaz and Y. Uyaroglu, Controlling Rucklidge chaotic system with a single controller using linear feedback and passive control methods, Nonlinear Dynamics, 75 (2014), 63-72.  doi: 10.1007/s11071-013-1049-7.

[6]

Y. Li, Y. Fu and G. Duan, Robust passive control for T-S fuzzy systems, in ICIC: Computational Intelligence, (2006), 146–151.

[7]

L. Liu and L. Sun, Coordinated passivity controller design for SVC and generator excitation with state constraint, Control Engineering of China, 15 (2018), 63-72. 

[8]

Y. Liu and J. Zhao, Stabilization of switched nonlinear systems with passive and non-passive subsystems, Nonlinear Dynamics, 67 (2012), 1709-1716.  doi: 10.1007/s11071-011-0098-z.

[9]

W. Lin and C. Qian, Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems, Systems & Control Letters, 39 (2000), 339-351.  doi: 10.1016/S0167-6911(99)00115-2.

[10]

W. Lin and C. Qian, Adaptive regulation of high-order lower-triangular systems: an adding a power integrator technique, Systems & Control Letters, 39 (2000), 353-364.  doi: 10.1016/S0167-6911(99)00114-0.

[11]

T. Reis and J. C. Willems, A balancing approach to the realization of systems with internal passivity and reciprocity, Systems and Control Letters, 60 (2011), 69-74.  doi: 10.1016/j.sysconle.2010.10.009.

[12]

C. SunH. Sun and X. Diao, Continuous feedback control for a class of nonhomogeneous high-order nonlinear systems, Acta Automatica Sinca, 40 (2014), 149-155. 

[13]

J. Tian and X. Xie, Adaptive state-feedback stabilization for more general high-order stochastic nonlinear systems, Acta Autonatica Sinca, 34 (2008), 1188-1191.  doi: 10.3724/SP.J.1004.2008.01188.

[14]

Z. WuG. SuP. Shi and J. Chu, Reliable control for SSs with time-varying delays, Lecture Notes in Control and Information Sciences, 443 (2013), 37-52. 

[15]

Z. Q. WuM. H. Song and L. Y. Fu, Passivity-based backstepping control for multimachine power system, Advanced Technology of Electrical Engineering and Energy, 32 (2013), 28-31. 

[16]

H. Xiao and L. Zhao, Robust passive control of uncertain switched time-delay systems: a sliding mode control design, Journal of Control Theory and Applications, 11 (2013), 96-102.  doi: 10.1007/s11768-013-1033-2.

[17]

L. Yang, X. Liu et al., Exponentially dissipative control for singular impulsive dynamical systems, Journal of Dynamic systems, Measurement and Control, 139 (2017), 041008-1–041008-6.

[18]

L. YangX. Liu and Z. Zhang, Dissipative control for singular impulsive dynamical systems, Electronic Journal of Qualitative Theory of Differential Equations, 32 (2012), 1-11.  doi: 10.14232/ejqtde.2012.1.32.

show all references

References:
[1]

W. Chen and M. Saif, Passivity and passivity based controller design of a class of switched control systems, in Proc. 16th IFAC World Congress, (2005), 143–147.

[2]

T. DengH. YaoJ. Du and J. Jiang, Neural network dynamic control for high-order nonlinear time-delay systems, Systems Engineering and Electronics, 36 (2014), 1152-1161. 

[3]

P. DoerfferO. Szulc and R. Bohing, Shock wave smearing by passive control, Journal of Thermal Science, 15 (2006), 43-47. 

[4]

A. T. EL-Sayed, Suppression of nonlinear vibration system described by nonlinear differential equations using passive controller, Nonlinear Dynamics, 78 (2014), 1683-1694.  doi: 10.1007/s11071-014-1550-7.

[5]

U. K. Kocamaz and Y. Uyaroglu, Controlling Rucklidge chaotic system with a single controller using linear feedback and passive control methods, Nonlinear Dynamics, 75 (2014), 63-72.  doi: 10.1007/s11071-013-1049-7.

[6]

Y. Li, Y. Fu and G. Duan, Robust passive control for T-S fuzzy systems, in ICIC: Computational Intelligence, (2006), 146–151.

[7]

L. Liu and L. Sun, Coordinated passivity controller design for SVC and generator excitation with state constraint, Control Engineering of China, 15 (2018), 63-72. 

[8]

Y. Liu and J. Zhao, Stabilization of switched nonlinear systems with passive and non-passive subsystems, Nonlinear Dynamics, 67 (2012), 1709-1716.  doi: 10.1007/s11071-011-0098-z.

[9]

W. Lin and C. Qian, Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems, Systems & Control Letters, 39 (2000), 339-351.  doi: 10.1016/S0167-6911(99)00115-2.

[10]

W. Lin and C. Qian, Adaptive regulation of high-order lower-triangular systems: an adding a power integrator technique, Systems & Control Letters, 39 (2000), 353-364.  doi: 10.1016/S0167-6911(99)00114-0.

[11]

T. Reis and J. C. Willems, A balancing approach to the realization of systems with internal passivity and reciprocity, Systems and Control Letters, 60 (2011), 69-74.  doi: 10.1016/j.sysconle.2010.10.009.

[12]

C. SunH. Sun and X. Diao, Continuous feedback control for a class of nonhomogeneous high-order nonlinear systems, Acta Automatica Sinca, 40 (2014), 149-155. 

[13]

J. Tian and X. Xie, Adaptive state-feedback stabilization for more general high-order stochastic nonlinear systems, Acta Autonatica Sinca, 34 (2008), 1188-1191.  doi: 10.3724/SP.J.1004.2008.01188.

[14]

Z. WuG. SuP. Shi and J. Chu, Reliable control for SSs with time-varying delays, Lecture Notes in Control and Information Sciences, 443 (2013), 37-52. 

[15]

Z. Q. WuM. H. Song and L. Y. Fu, Passivity-based backstepping control for multimachine power system, Advanced Technology of Electrical Engineering and Energy, 32 (2013), 28-31. 

[16]

H. Xiao and L. Zhao, Robust passive control of uncertain switched time-delay systems: a sliding mode control design, Journal of Control Theory and Applications, 11 (2013), 96-102.  doi: 10.1007/s11768-013-1033-2.

[17]

L. Yang, X. Liu et al., Exponentially dissipative control for singular impulsive dynamical systems, Journal of Dynamic systems, Measurement and Control, 139 (2017), 041008-1–041008-6.

[18]

L. YangX. Liu and Z. Zhang, Dissipative control for singular impulsive dynamical systems, Electronic Journal of Qualitative Theory of Differential Equations, 32 (2012), 1-11.  doi: 10.14232/ejqtde.2012.1.32.

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