Similar articles

Abstract: A robust polynomial observer is designed based on passive synchronization of a given class of fractional-order Colpitts (FOC) systems with mismatched uncertainties and disturbances. The primary objective of the proposed observer is to minimize the effects of unknown bounded disturbances on the estimation of errors. A more practicable output-feedback passive controller is proposed using an adaptive polynomial state observer. The distributed approach of a continuous frequency of the FOC is considered to analyze the stability of the observer. Then we derive some stringent conditions for the robust passive synchronization using Finsler’s lemma based on the fractional Lyapunov stability theory. It is shown that the proposed method not only guarantees the asymptotic stability of the controller but also allows the derived adaptation law to remove the uncertainties within the nonlinear plant’s dynamics. The entire system using passivity is implemented with details in PSpice to demonstrate the feasibility of the proposed control scheme. The results of this research are illustrated using computer simulations for the control problem of the fractional-order chaotic Colpitts system. The proposed approach depicts an efficient and systematic control procedure for a large class of nonlinear systems with the fractional derivative.

基于多项式鲁棒观测器实现结构扰动下非线性分数阶系统被动式同步

[1]Aghababa MP, 2012a. Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique. Nonl Dynam, 69(1):247-261.

[2]Aghababa MP, 2012b. Robust finite-time stabilization of fractional-order chaotic systems based on fractional Lyapunov stability theory. J Comput Nonl Dynam, 7(2): 021010.

[3]Aghababa MP, 2014. Control of fractional-order systems using chatter-free sliding mode approach. J Comput Dynam, 9(3):031003.

[4]Aghababa MP, 2015a. A fractional sliding mode for finite- time control scheme with application to stabilization of electrostatic and electromechanical transducers. Appl Math Model, 39(20):6103-6113.

[5]Aghababa MP, 2015b. Synchronization and stabilization of fractional second-order nonlinear complex systems. Nonl Dynam, 80(4):1731-1744.

[6]Ammar HH, Azar AT, Shalaby R, et al., 2019. Metaheuristic optimization of fractional order incremental conductance (FO-INC) maximum power point tracking (MPPT). Complexity, 2019:7687891.

[7]Azar AT, Vaidyanathan S, Ouannas A, 2017a. Fractional Order Control and Synchronization of Chaotic Systems. Springer, Cham, Germany.

[8]Azar AT, Volos C, Gerodimos NA, et al., 2017b. A novel chaotic system without equilibrium: dynamics, synchronization, and circuit realization. Complexity, 2017:7871467.

[9]Azar AT, Radwan AG, Vaidyanathan S, 2018a. Fractional Order Systems: Optimization, Control, Circuit Realizations and Applications. Elsevier, Amsterdam, the Netherlands.

[10]Azar AT, Radwan AG, Vaidyanathan S, 2018b. Mathematical Techniques of Fractional Order Systems. Elsevier, Amsterdam, the Netherlands.

[11]Byrnes CI, Isidori A, Willems JC, 1991. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Trans Autom Contr, 36(11):1228-1240.

[12]Chen LP, Chai Y, Wu RC, et al., 2012. Cluster synchronization in fractional-order complex dynamical networks. Phys Lett A, 376(35):2381-2388.

[13]Chen LP, Li TT, Chen YQ, et al., 2019. Robust passivity and feedback passification of a class of uncertain fractional- order linear systems. Int J Syst Sci, 50(6):1149-1162.

[14]Cho YM, Rajamani R, 1997. A systematic approach to adaptive observer synthesis for nonlinear systems. IEEE Trans Autom Contr, 42(4):534-537.

[15]Dadras S, Momeni HR, 2013. Passivity-based fractional-order integral sliding-mode control design for uncertain fractional-order nonlinear systems. Mechatronics, 23(7): 880-887.

[16]Dasgupta T, Paral P, Bhattacharya S, 2015. Fractional order sliding mode control based chaos synchronization and secure communication. Proc Int Conf on Computer Communication and Informatics, p.8-10.

[17]de Oliveira MC, Skelton RE, 2000. Stability tests for constrained linear systems. In: Moheimani SOR (Ed.), Perspectives in Robust Control. Springer, London, UK. p.241-257.

[18]Diethelm K, Ford NJ, Freed AD, 2002. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonl Dynam, 29(1-4):3-22.

[19]Djeddi A, Dib D, Azar AT, et al., 2019. Fractional order unknown inputs fuzzy observer for Takagi-Sugeno systems with unmeasurable premise variables. Mathematics, 7(10):984.

[20]Feki M, 2003. Observer-based exact synchronization of ideal and mismatched chaotic systems. Phys Lett A, 309(1-2):53-60.

[21]Fotsin HB, Daafouz J, 2005. Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification. Phys Lett A, 339(3-5):304-315.

[22]Gai MJ, Cui SW, Liang S, et al., 2016. Frequency distributed model of Caputo derivatives and robust stability of a class of multi-variable fractional-order neural networks with uncertainties. Neurocomputing, 202:91-97.

[23]Gauthier JP, Hammouri H, Othman S, 1992. A simple observer for nonlinear systems applications to bioreactors. IEEE Trans Autom Contr, 37(6):875-880.

[24]Ghoudelbourk S, Dib D, Omeiri A, et al., 2016. MPPT control in wind energy conversion systems and the application of fractional control (PI^α) in pitch wind turbine. Int J Model Ident Contr, 26(2):140-151.

[25]Hammouch Z, Mekkaoui T, 2018. Circuit design and simulation for the fractional-order chaotic behavior in a new dynamical system. Compl Intell Syst, 4(4):251-260.

[26]Issakhov A, Baitureyeva AR, 2018. Numerical modelling of a passive scalar transport from thermal power plants to air environment. Adv Mech Eng, 10(10):1-14.

[27]Kammogne ST, Fotsin HB, 2014. Adaptive control for modified projective synchronization-based approach for estimating all parameters of a class of uncertain systems: case of modified Colpitts oscillators. J Chaos, 2014:659647.

[28]Kammogne ST, Fotsin HB, Kountchou NM, et al., 2013. A robust observer design for passivity-based synchronization of uncertain modified Colpitts oscillators and circuit simulation. Asian J Sci Technol, 5(1):29-41.

[29]Kammogne AST, Azar AT, Bertrand FH, et al., 2019. Robust observer-based synchronisation of chaotic oscillators with structural perturbations and input nonlinearity. Int J Autom Contr, 13(4):387-412.

[30]Kammogne AST, Azar AT, Kengne R, et al., 2020. Stability analysis and robust synchronisation of fractional-order modified Colpitts oscillators. Int J Autom Contr, 14(1):52-79.

[31]Kengne R, Tchitnga R, Mabekou S, et al., 2018. On the relay coupling of three fractional-order oscillators with time-delay consideration: global and cluster synchronizations. Chaos Sol Fract, 111:6-17.

[32]Khalil HK, 2007. Nonlinear Systems (3^rd Ed.). Prentice Hall, Upper Saddle River, New Jersey, USA.

[33]Khan A, Singh S, Azar AT, 2020a. Combination-combination anti-synchronization of four fractional order identical hyperchaotic systems. Int Conf on Advanced Machine Learning Technologies and Applications, p.406-414.

[34]Khan A, Singh S, Azar AT, et al., 2020b. Synchronization between a novel integer-order hyperchaotic system and a fractional-order hyperchaotic system using tracking control. Proc 10^th Int Conf on Modelling, Identification and Control, p.382-391.

[35]Kuntanapreeda S, 2016. Adaptive control of fractional-order unified chaotic systems using a passivity-based control approach. Nonl Dynam, 84(4):2505-2515.

[36]Li C, Xiong J, Li W, et al., 2013. Robust synchronization for a class of fractional-order dynamical system via linear state variable. Ind J Phys, 87(7):673-678.

[37]Li CP, Deng WH, 2007. Remarks on fractional derivatives. Appl Math Comput, 187(2):777-784.

[38]Li LL, Yao QG, 2014. Robust synchronization of chaotic systems using sliding mode and feedback control. J Zhejiang Univ-Sci C (Comput & Electron), 15(3):211-222.

[39]Li TZ, Wang Y, Zhao C, 2017. Synchronization of fractional chaotic systems based on a simple Lyapunov function. Adv Differ Equat, 2017(1):304.

[40]Liu CX, 2011. Fractional-Order Chaotic Circuit Theory and Applications. Xi’an Jiaotong University Press, Xi’an, China (in Chinese).

[41]Ngouonkadi EBM, Fotsin HB, Fotso PL, 2014. Implementing a memristive Van der Pol oscillator coupled to a linear oscillator: synchronization and application to secure communication. Phys Scr, 89(3):035201.

[42]Nijmeijer H, Mareels IMY, 1997. An observer looks at synchronization. IEEE Trans Circ Syst I, 44(10):882-890.

[43]Noube MK, Louodop P, Bowong S, et al., 2013. Optimization of the synchronization of the modified Duffing system. J Adv Res Dynam Contr Syst, 6(2):1-24.

[44]Noun S, Botmart T, 2018. New results on passivity criteria for a class of neural networks with interval and distributed time-varying delays. Proc Int Multiconf of Engineers and Computer Scientists.

[45]Pecora LM, Carroll TL, 1990. Synchronization in chaotic systems. Phys Rev Lett, 64(8):821-824.

[46]Pelap FB, Tanekou GB, Fogang CF, et al., 2018. Fractional- order stability analysis of earthquake dynamics. J Geo- phys Eng, 15(4):1673-1687.

[47]Podlubny I, 1999. Fractional Differential Equations. Academic Press, San Diego, CA, USA.

[48]Qi WH, Gao XW, Wang JY, 2016. Finite-time passivity and passification for stochastic time-delayed Markovian switching systems with partly known transition rates. Circ Syst Signal Process, 35(11):3913-3934.

[49]Rabah K, Ladaci S, Lashab M, 2018. Bifurcation-based fractional-order PI^λD^μ controller design approach for nonlinear chaotic systems. Front Inform Technol Electron Eng, 19(2):180-191.

[50]Rajavel S, Samidurai R, Cao JD, et al., 2017. Finite-time non-fragile passivity control for neural networks with time-varying delay. Appl Math Comput, 297:145-158.

[51]Sabatier J, Farges C, 2017. Analysis of fractional models physical consistency. J Vibr Contr, 23(6):895-908.

[52]Shen J, Lam J, 2014. H_∞ model reduction for positive fractional order systems. Asian J Contr, 16(2):441-450.

[53]Skelton RE, Iwasaki T, Grigoriadis KM, 1998. A Unified Algebraic Approach to Linear Control Design. Taylor & Francis, London, UK.

[54]Song J, He SP, 2015. Finite-time robust passive control for a class of uncertain Lipschitz nonlinear systems with time-delays. Neurocomputing, 159:275-281.

[55]Song QK, Wang ZD, 2010. New results on passivity analysis of uncertain neural networks with time-varying delays. Int J Comput Math, 87(3):668-678.

[56]Song S, Song XN, Balsera IT, 2017. Mixed H_∞ and passive projective synchronization for fractional-order memristor-based neural networks with time delays via adaptive sliding mode control. Mod Phys Lett B, 31(14):1750160.

[57]Sun D, Naghdy F, Du HP, 2017. Neural network-based passivity control of teleoperation system under time-varying delays. IEEE Trans Cybern, 47(7):1666-1680.

[58]Tavazoei MS, 2010. Notes on integral performance indices in fractional-order control systems. J Process Contr, 20(3):285-291.

[59]Tavazoei MS, Haeri M, 2007. A necessary condition for double scroll attractor existence in fractional-order systems. Phys Lett A, 367(1-2):102-113.

[60]Tavazoei MS, Haeri M, 2008. Chaotic attractors in incommensurate fractional order systems. Phys D, 237(20):2628-2637.

[61]Thuan MV, Huong DC, Hong DT, 2019. New results on robust finite-time passivity for fractional-order neural networks with uncertainties. Neur Process Lett, 50(2):1065-1078.

[62]Vaidyanathan S, Azar AT, 2015a. Anti-synchronization of identical chaotic systems using sliding mode control and an application to Vaidyanathan-Madhavan chaotic systems. In: Azar AT, Zhu QM (Eds.), Advances and Applications in Sliding Mode Control Systems. Springer, Cham, Germany, p.527-547.

[63]Vaidyanathan S, Azar AT, 2015b. Hybrid synchronization of identical chaotic systems using sliding mode control and an application to Vaidyanathan chaotic systems. In: Azar AT, Zhu QM (Eds.), Advances and Applications in Sliding Mode Control Systems. Springer, Cham, Germany, p.549-569.

[64]Vaidyanathan S, Azar AT, 2016a. Qualitative study and adaptive control of a novel 4-D hyperchaotic system with three quadratic nonlinearities. In: Azar AT, Vaidyanathan S (Eds.), Advances in Chaos Theory and Intelligent Control. Springer, Cham, Germany, p.179-202.

[65]Vaidyanathan S, Azar AT, 2016b. Generalized projective synchronization of a novel hyperchaotic four-wing system via adaptive control method. In: Azar AT, Vaidyanathan S (Eds.), Advances in Chaos Theory and Intelligent Control. Springer, Cham, Germany, p.275-296.

[66]Vaidyanathan S, Sampath S, Azar AT, 2015. Global chaos synchronisation of identical chaotic systems via novel sliding mode control method and its application to Zhu system. Int J Model Ident Contr, 23(1):92-100.

[67]Vaidyanathan S, Azar AT, Akgul A, et al., 2019. A memristor- based system with hidden hyperchaotic attractors, its circuit design, synchronisation via integral sliding mode control and an application to voice encryption. Int J Autom Contr, 13(6):644-667.

[68]Wang JW, Ma QH, Zeng L, 2013. Observer-based synchronization in fractional-order leader-follower complex networks. Nonl Dynam, 73(1-2):921-929.

[69]Zhang RX, Yang SP, 2013. Robust synchronization of two different fractional-order chaotic systems with unknown parameters using adaptive sliding mode approach. Nonl Dynam, 71(1):269-278.