Skip to main content
SpringerLink
Log in

Improved Robust Adaptive Control Law for a Class of Uncertain Nonlinear Systems and Its Application to Chaotic Systems

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions of Electrical Engineering Aims and scope Submit manuscript

Abstract

An adaptive robust control scheme is proposed for a class of unknown nonlinear systems. For achieving this purpose, a class of uncertain nonlinear systems is firstly considered. Then, the regulation and tracking problems are solved with the well-known Lyapunov stability theory. It is shown that although the system dynamic may not be fully or partially known, some adaptive control laws can be mathematically derived by using the proposed control method. Hence, by the proposed control method, the closed-loop system would be globally stabilized in the sense of the Lyapunov stability theory. Finally, the proposed robust adaptive control law is numerically applied into the Lorenz and Van der Pol chaotic systems. The efficiency of the suggested approach is shown by numerical simulation via comparison with an existing method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Arefi MM (2016) Adaptive robust stabilization of Rossler system with time-varying mismatched parameters via scalar input. J Comput Nonlinear Dyn 11:041024

    Article  Google Scholar 

  • Asemani MH, Vatankhah R (2017) NON-PDC observer-based T–S fuzzy tracking controller design and its application in CHAOS control. Asian J Control 19:969–982

    Article  MathSciNet  Google Scholar 

  • Åström KJ, Wittenmark B (2013) Adaptive control. Courier Corporation, Mineola

    MATH  Google Scholar 

  • Azar AT, Vaidyanathan S (2015) Chaos modeling and control systems design. Springer, Berlin

    Book  Google Scholar 

  • Berezowski M (2001) Effect of delay time on the generation of chaos in continuous systems. One-dimensional model. Two-dimensional model–tubular chemical reactor with recycle. Chaos, Solitons Fractals 12:83–89

    Article  Google Scholar 

  • Che Y, Liu B, Li H, Lu M, Wang J, Wei X (2017) Robust stabilization control of bifurcations in Hodgkin-Huxley model with aid of unscented Kalman filter. Chaos, Solitons Fractals 101:92–99

    Article  MathSciNet  Google Scholar 

  • Faramin M, Ataei M (2016) Chaotic attitude analysis of a satellite via Lyapunov exponents and its robust nonlinear control subject to disturbances and uncertainties. Nonlinear Dyn 83:361–374

    Article  MathSciNet  Google Scholar 

  • Geiyer D, Kauffman JL (2015) Chaotic control of a piezomagnetoelastic beam for improved energy harvesting. Act Passiv Smart Struct Integr Syst 2015:943100

    Google Scholar 

  • Ghaffari V, Karimaghaee P (2012) Design of adaptive discrete time controller for a class of nonlinear systems. Nonlinear Stud 19:149–159

    MathSciNet  MATH  Google Scholar 

  • Hua C, Guan X (2004) Adaptive control for chaotic systems. Chaos Solitons Fractals 22:55–60

    Article  MathSciNet  Google Scholar 

  • Ioannou PA, Sun J (1996) Robust adaptive control. Prentice-Hall, Upper Saddle River

    MATH  Google Scholar 

  • Khalil HK (2003) Nonlinear systems. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Khan W, Lin Y, Khan SU, Ullah N (2018) Quantized adaptive decentralized control for interconnected nonlinear systems with actuator faults. Appl Math Comput 320:175–189

    MathSciNet  MATH  Google Scholar 

  • Krstic M, Kanellakopoulos I, Kokotovic PV (1995) Nonlinear and adaptive control design. Wiley, Hoboken

    MATH  Google Scholar 

  • Li J, Yue H (2015) Adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time-varying delays. Appl Math Comput 256:514–528

    MathSciNet  MATH  Google Scholar 

  • Liu C, Sun Z, Ye D, Shi K (2018) Robust adaptive variable structure tracking control for spacecraft chaotic attitude motion. IEEE Access 6:3851–3857

    Article  Google Scholar 

  • Louodop P, Fotsin H, Bowong S (2012) A strategy for adaptive synchronization of an electrical chaotic circuit based on nonlinear control. Phys Scr 85:025002

    Article  Google Scholar 

  • Luo R (2015) The robust adaptive control of chaotic systems with unknown parameters and external disturbance via a scalar input. Int J Adapt Control Signal Process 29:1296–1307

    Article  MathSciNet  Google Scholar 

  • Mascolo S (1997) Backstepping design for controlling Lorenz chaos. In: Proceedings of the 36th IEEE conference on decision and control, pp 1500–1501

  • Mierczyński J (2015) Lower estimates of top Lyapunov exponent for cooperative random systems of linear ODEs. Proc Am Math Soc 143:1127–1135

    Article  MathSciNet  Google Scholar 

  • Mobayen S, Ma J (2018) Robust finite-time composite nonlinear feedback control for synchronization of uncertain chaotic systems with nonlinearity and time-delay. Chaos, Solitons Fractals 114:46–54

    Article  MathSciNet  Google Scholar 

  • Mousavi SH, Khayatian A (2013) Adaptive control for a class of hysteretic systems. J Comput Nonlinear Dyn 8:011003

    Article  Google Scholar 

  • Nepomuceno EG, Martins SA, Lacerda MJ, Mendes EM (2018) On the use of interval extensions to estimate the largest Lyapunov exponent from chaotic data. Math Probl Eng 2018:6909151

    Article  MathSciNet  Google Scholar 

  • Ni J, Liu L, Liu C, Hu X, Li S (2017) Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans Circuits Syst II Express Briefs 64:151–155

    Article  Google Scholar 

  • Noroozi N, Roopaei M, Karimaghaee P (2009) Adaptive control and synchronization in a class of partially unknown chaotic systems. Chaos Interdiscipl J Nonlinear Sci 19:023121

    Article  MathSciNet  Google Scholar 

  • Noroozi N, Roopaei M, Karimaghaee P, Safavi AA (2010) Simple adaptive variable structure control for unknown chaotic systems. Commun Nonlinear Sci Numer Simul 15:707–727

    Article  MathSciNet  Google Scholar 

  • Pan L, Zhou W, Fang JA, Li D (2010) Analysis of linear and adaptive feedback synchronization in a new unified chaotic system. Int J Adapt Control Signal Process 24:708–716

    MathSciNet  MATH  Google Scholar 

  • Pang Z, Jin D (2016) Experimental verification of chaotic control of an underactuated tethered satellite system. Acta Astronaut 120:287–294

    Article  Google Scholar 

  • Roopaei M, Zolghadri Jahromi M (2008) Synchronization of two different chaotic systems using novel adaptive fuzzy sliding mode control. Chaos Interdiscip J Nonlinear Sci 18:033133

    Article  MathSciNet  Google Scholar 

  • Shen Z, Li J (2017) Chaos control for a unified chaotic system using output feedback controllers. Math Comput Simul 132:208–219

    Article  MathSciNet  Google Scholar 

  • Tong S, Zhang L, Li Y (2016) Observed-based adaptive fuzzy decentralized tracking control for switched uncertain nonlinear large-scale systems with dead zones. IEEE Trans Syst Man Cybern Syst 46:37–47

    Article  Google Scholar 

  • Tran X-T, Kang H-J (2015) Robust adaptive chatter-free finite-time control method for chaos control and (anti-) synchronization of uncertain (hyper) chaotic systems. Nonlinear Dyn 80:637–651

    Article  MathSciNet  Google Scholar 

  • Wang Z, Tian Q, Hu H, Flores P (2016) Nonlinear dynamics and chaotic control of a flexible multibody system with uncertain joint clearance. Nonlinear Dyn 86:1571–1597

    Article  Google Scholar 

  • Wang P, Jin W, Su H (2018) Synchronization of coupled stochastic complex-valued dynamical networks with time-varying delays via aperiodically intermittent adaptive control. Chaos Interdiscip J Nonlinear Sci 28:043114

    Article  MathSciNet  Google Scholar 

  • Xi X, Mobayen S, Ren H, Jafari S (2018) Robust finite-time synchronization of a class of chaotic systems via adaptive global sliding mode control. J Vib Control 24:3842–3854

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, School of Engineering, Persian Gulf University, Bushehr, Iran

    Valiollah Ghaffari & Abolhassan Razminia

  2. Hydro-Aeronautical Research Center, Shiraz University, Shiraz, Iran

    Mojtaba Mirzaei

Authors
  1. Valiollah Ghaffari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abolhassan Razminia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mojtaba Mirzaei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valiollah Ghaffari.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghaffari, V., Razminia, A. & Mirzaei, M. Improved Robust Adaptive Control Law for a Class of Uncertain Nonlinear Systems and Its Application to Chaotic Systems. Iran J Sci Technol Trans Electr Eng 43, 741–756 (2019). https://doi.org/10.1007/s40998-019-00194-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40998-019-00194-7

Keywords

Search

Navigation