Previous Articles Next Articles
CHEN Juan^{1}, ZHUANG Bo^{2}
[1] Podlubny I, Fractional Differential Equations, Academic Press, San Diego, 1999. [2] Chen J, Zhuang B, Chen Y Q, et al., Backsteppingbased boundary feedback control for a fractional reaction diffusion system with mixed or Robin boundary conditions, IET Control Theory & Applications, 2017, 11(17):29642976. [3] Laskin K, Fractional schrödinger equation, Physical Review E, 2002, 66(5):056108. [4] Pagnini G, Nonlinear timefractional differential equations in combustion science, Fractional Calculus and Applied Analysis, 2011, 14(1):8093. [5] Murio D A, Stable numerical solution of a fractionaldiffusion inverse heat conduction problem, Computers & Mathematics with Applications, 2007, 53(10):14921501. [6] Sun H G, Chen W, Li C P, et al., Fractional differential models for anomalous diffusion, Physica A:Statistical Mechanics and Its Applications, 2010, 389(14):27192724. [7] Laskin N, Fractional quantum mechanics, Physical Review E, 2000, 62(3):3135. [8] Krstic M and Smyshlyaev A, Boundary Control of PDEs:A Course on Backstepping Designs, Siam, Philadelphia, 2008. [9] Matignon D, Stability results for fractional differential equations with applications to control processing, Computational Engineering in Systems Applications, 1996, 2:963968. [10] Ge F D, Chen Y Q, and Kou C H, Boundary feedback stabilisation for the time fractionalorder anomalous diffusion system, IET Control Theory & Applications, 2016, 10(11):12501257. [11] Zhou H C and Guo B Z, Boundary feedback stabilization for an unstable time fractional reaction diffusion equation, SIAM Journal on Control and Optimization, 2018, 56(1):75101. [12] Mai V T and Dinh C H, Robust finitetime stability and stabilization of a class of fractionalorder switched nonlinear systems, Journal of Systems Science and Complexity, 2019, 32(6):14791497. [13] Dinh C H and Mai V T, New Results on stability and stabilization of delayed Caputo fractional order systems with convex polytopic uncertainties, Journal of Systems Science and Complexity, 2020, 33(3):563583. [14] Gafiychuk V, Datsko B, Meleshko V, et al., Analysis of the solutions of coupled nonlinear fractional reactiondiffusion equations, Chaos, Solitons & Fractals, 2009, 41(3):10951104. [15] Li Y, Chen Y Q, and Podlubny I, Stability of fractionalorder nonlinear dynamic systems:Lyapunov direct method and generalized MittagLeffler stability, Computers & Mathematics with Applications, 2010, 59(5):18101821. [16] Li H L, Jiang Y L, Wang Z L, et al., Global mittagleffler stability of coupled system of fractionalorder differential equations on network, Applied Mathematics and Computation, 2015, 270:269277. [17] Ge F D, Meurer T, and Chen Y Q, Mittagleffler convergent backstepping observers for coupled semilinear subdiffusion systems with spatially varying parameters, Systems & Control Letters, 2018, 122:8692. [18] Chen J, Tepljakov A, Petlenkov E, et al., Boundary state and output feedbacks for underactuated systems of coupled timefractional pdes with different spacedependent diffusivity, International Journal of Systems Science, 2020, 51(15):29222942. [19] Deutscher J and Kerschbaum S, Backstepping control of coupled linear parabolic PIDEs with spatiallyvarying coefficients, IEEE Transactions on Automatic Control, 2018, 63(12):42184233. [20] Orlov Y, Pisano A, Pilloni A, et al., Output feedback stabilization of coupled reactiondiffusion processes with constant parameters, SIAM Journal on Control and Optimization, 2017, 55:41124155. [21] Xu Q W and Xu Y F, Extremely low order timefractional differential equation and application in combustion process, Communications in Nonlinear Science and Numerical Simulation, 2018, 64:135148. [22] Li J and Liu Y G, Stabilization of coupled PDEODE systems with spatially varying coefficient, Journal of Systems Science and Complexity, 2013, 26(2):151174. [23] Henry B I and Wearne S L, Fractional reactiondiffusion, Physica A:Statistical Mechanics and Its Applications, 2000, 276(34):448455. [24] Uchaikin V V and Sibatov R T, Fractional theory for transport in disordered semiconductors, Communications in Nonlinear Science and Numerical Simulation, 2008, 13(4):715727. [25] Chen J, Cui B T, and Chen Y Q, Backsteppingbased boundary control design for a fractional reaction diffusion system with a spacedependent diffusion coefficient, ISA Transactions, 2018, 80:203211. [26] Zhou Y J, Chen J, and Cui B T, Observer design for boundary coupled fractional order distributed parameter systems, International Conference on Control, Mechatronics and Automation (ICCMA 2019), Delft, 2019:384388. [27] Kilbas A A A, Srivastava H M, and Trujillo J J, Theory and Applications of Fractional Differential Equations, Elsevier Science Limited, Amsterdam, 2006. [28] Bazhlekova E, The abstract cauchy problem for the fractional evolution equation, Fractional Calculus and Applied Analysis, 1998, 1(3):255270. [29] Friedman A, Partial Differential Equations of Parabolic Type, PrenticeHall, Englewood Cliffs, 1964. [30] Curtain R F and Zwart H, An Introduction to InfiniteDimensional Linear Systems Theory, SpringerVerlag, Berlin, 1995. [31] DuarteMermoud M A, AguilaCamacho N, Gallegos J A, et al., Using general quadratic lyapunov functions to prove Lyapunov uniform stability for fractional order systems, Communications in Nonlinear Science & Numerical Simulation, 2015, 22(13):650659. [32] Miller K S and Samko S G, Completely monotonic functions, Integral Transforms & Special Functions, 2001, 12(4):389402. [33] Baccoli A, Pisano A, and Orlov Y, Boundary control of coupled reactiondiffusion processes with constant parameters, Automatica, 2015, 54:8090. [34] Li C, Wang J C, Lu J G, et al., Observerbased stabilisation of a class of fractional order nonlinear systems for 0<α<2 case, IET Control Theory & Applications, 2014, 8(13):12381246. [35] Saad K M and GómezAguilar J F, Coupled reactiondiffusion waves in a chemical system via fractional derivatives in LiouvilleCaputo sense, Revista Mexicana de Fısica, 2018, 64(5):539547. [36] Rasheed A and Anwar M S, Simulations of variable concentration aspects in a fractional nonlinear viscoelastic fluid flow, Communications in Nonlinear Science and Numerical Simulation, 2018, 65:216230. [37] Luchko Y, Mainardi F, and Povstenko Y, Propagation speed of the maximum of the fundamental solution to the fractional diffusionwave equation, Computers & Mathematics with Applications, 2013, 66(5):774784. [38] Li H F, Cao J X, and Li C P, Highorder approximation to Caputo derivatives and Caputotype advectiondiffusion equations (III), Journal of Computational & Applied Mathematics, 2016, 299(3):159175. [39] Ablowitz M J, Kruskal M D, and Ladik J, Solitary wave collisions, SIAM Journal on Applied Mathematics, 1979, 36(3):428437. [40] Wang K and Fridman E, Boundary control of delayed ODEheat cascade under actuator saturation, Automatica, 2017, 83:252261. 
[1]  HU Chuanfeng, HU Hui, LIN Hongwei, YAN Jiacong. Isogeometric AnalysisBased Topological Optimization for Heterogeneous Parametric Porous Structures [J]. Journal of Systems Science and Complexity, 2023, 36(1): 2952. 
[2]  FENG Xiaodan, ZHANG Zhifei. Boundary Control of Coupled Wave Systems with SpatiallyVarying Coefficients [J]. Journal of Systems Science and Complexity, 2022, 35(4): 13101329. 
[3]  YANG Ruohan, ZHOU Deyun. Distributed EventTriggered Tracking Control of Heterogeneous DiscreteTime MultiAgent Systems with Unknown Parameters [J]. Journal of Systems Science and Complexity, 2022, 35(4): 13301347. 
[4]  MO Lipo, YU Yongguang, REN Guojian, YUAN Xiaolin. Constrained Consensus of ContinuousTime Heterogeneous MultiAgent Networks with Nonconvex Constraints and Delays [J]. Journal of Systems Science and Complexity, 2022, 35(1): 105122. 
[5]  KUANG Xiong · WANG Qian · CHEN Xia. The Effectiveness of Structural Monetary Policy and MacroPrudential Policies — Based on the DSGE Model That Includes Bank Heterogeneous Credit [J]. Journal of Systems Science and Complexity, 2021, 34(6): 22672290. 
[6]  ZHAO Zhixue,GUO Baozhu. Boundary Control Method to Identification of Elastic Modulus of String Equation from NeumannDirichlet Map [J]. Journal of Systems Science and Complexity, 2016, 29(5): 12121225. 
[7]  WEN Ruili,CHAI Shugen. Regularity for EulerBernoulli Equations with Boundary Control and Collocated Observation [J]. Journal of Systems Science and Complexity, 2015, 28(4): 788798. 
[8]  FENG Xu , ZHANG Wei , ZHANG Yongjie , XIONG Xiong. INFORMATION IDENTIFICATION IN DIFFERENT NETWORKS WITH HETEROGENEOUS INFORMATION SOURCES [J]. Journal of Systems Science and Complexity, 2014, 27(1): 92116. 
[9]  Yifen MU , Lei GUO. TOWARDS A THEORY OF GAMEBASED NONEQUILIBRIUM CONTROL SYSTEMS [J]. Journal of Systems Science and Complexity, 2012, 25(2): 209226. 
[10]  Hongquan LI, Shouyang WANG, Wei SHANG. HETEROGENEITY, NONLINEARITY AND ENDOGENOUS MARKET VOLATILITY [J]. Journal of Systems Science and Complexity, 2011, 24(6): 11301142. 
[11]  Orazio ARENA;Walter LITTMAN. BOUNDARY CONTROL OF TWO PDE'S SEPARATED BY INTERFACE CONDITIONS [J]. Journal of Systems Science and Complexity, 2010, 23(3): 431437. 
[12]  W.L.Ohan;Guo Baozhu. APPROXIMATE OPTIMAL BIRTH CONTROL OF POTULATION SYSTEMS [J]. Journal of Systems Science and Complexity, 1990, 1(1): 46052. 
[13]  Ding Zhonghai;Feng Dexing. EXACT CONTROLLABILITY OF A CLASS OF DISTRIBUTED PARAMETER SYSTEMS [J]. Journal of Systems Science and Complexity, 1989, 2(3): 257265. 
Viewed  
Full text 


Abstract 

