Non-fragile control of fuzzy affine dynamic systems via piecewise Lyapunov functions

Abstract

This paper addresses the robust ℋ_∞ static output feedback (SOF) controller design problem for a class of uncertain fuzzy affine systems that are robust against both the plant parameter perturbations and controller gain variations. More specifically, the purpose is to synthesize a non-fragile piecewise affine SOF controller guaranteeing the stability of the resulting closed-loop fuzzy affine dynamic system with certainℋ_∞ performance index. Based on piecewise quadratic Lyapunov functions and applying some convexification procedures, two different approaches are proposed to solve the robust and non-fragile piecewise affine SOF controller synthesis problem. It is shown that the piecewise affine controller gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation examples are given to illustrate the effectiveness of the proposed methods.

Keywords

fuzzy affine systems / non-fragile / robust output feedback control

References

[1] SalaA, GuerraT M, BabŭskaR . Perspectives of fuzzy systems and control. Fuzzy Sets and Systems, 2005, 156(3): 432–444

[2] FengG. A survey on analysis and design of model-based fuzzy control systems. IEEE Transactions on Fuzzy Systems, 2006, 14(5): 676–697

[3] TakagiT, SugenoM. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man and Cybernetics, 1985, SMC-15(1): 116–132

[4] TanakaK, WangH O. Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley, 2001

[5] TeixeiraM C M, Żak S H. Stabilizing controller design for uncertain nonlinear systems using fuzzy models. IEEE Transactions on Fuzzy Systems, 1999, 7(2): 133–142

[6] GaoH, ChenT. Stabilization of nonlinear systems under variable sampling: a fuzzy control approach. IEEE Transactions on Fuzzy Systems, 2007, 15(5): 972–983

[7] ZhangC, FengG, GaoH, Qiu J. ℋ_∞ filtering for nonlinear discretetime systems subject to quantization and packet dropouts. IEEE Transactions on Fuzzy Systems, 2011, 19(2): 353–365

[8] LiuM, CaoX, ShiP. Fuzzy-model-based fault-tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults. IEEE Transactions on Fuzzy Systems, 2013, 21(5): 789–799

[9] QiuJ, GaoH, DingS X. Recent advances on fuzzy-model-based nonlinear networked control systems: a survey. IEEE Transactions on Industrial Electronics, 2016, 63(2): 1207–1217

[10] LiL, DingS X, QiuJ, Yang Y. Real-time fault detection approach for nonlinear systems and its asynchronous T-S fuzzy observer-based implementation. IEEE Transactions on Cybernetics, doi: 10.1109/TCYB.2015.2513438

[11] JohanssonM, Rantzer A, ÅrzénK E. Piecewise quadratic stability of fuzzy systems. IEEE Transaction on Fuzzy Systems, 1999, 7(6): 713–722

[12] FengG, ChenC L, SunD, Zhu Y. ℋ_∞ controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities. IEEE Transactions on Fuzzy Systems, 2005, 13(1): 94–103

[13] QiuJ, FengG, GaoH. Observer-based piecewise affine output feedback controller synthesis of continuous-time T-S fuzzy affine dynamic systems using quantized measurements. IEEE Transactions on Fuzzy Systems, 2012, 20(6): 1046–1062

[14] FuS, WangM, QiuJ, He Y. T-S fuzzy affine model based nonsynchronized state estimation for nonlinear Itô stochastic systems. Neurocomputing, 2015, 167: 424–433

[15] LiL, DingS X, QiuJ, Yang Y, ZhangY . Weighted fuzzy observerbased fault detection approach for discrete-time nonlinear systems via piecewise-fuzzy Lyapunov functions. IEEE Transactions on Fuzzy Systems, doi: 10.1109/TFUZZ.2016.2514371

[16] ZhouK, DoyleJ C, GloverK. Robust Optimal Control, Englewood Cliffs, NJ: Prentice Hall, 2001

[17] ZhangC, FengG, QiuJ, Shen Y. Control synthesis for a class of linear network-based systems with communication constraints. IEEE Transactions on Industrial Electronics, 2013, 60(8): 3339–3348

[18] WeiY, QiuJ, KarimiH R, Wang M. ℋ_∞ model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information. International Journal of Systems Science, 2014, 45(7): 1496–1507

[19] QiuJ, WeiY, KarimiH R. New approach to delay-dependent ℋ_∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions. Journal of The Franklin Institute, 2015, 352(1): 189–215

[20] WangT, GaoH, QiuJ. A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control. IEEE Transactions on Neural Networks and Learning Sys tems, 2016, 27(2): 416–425

[21] KeelL H, Bhattacharyya S P. Robust, fragile, or optimal? IEEE Transactions on Automatic Control, 1997, 42(8): 1098–1105

[22] DuH, LamJ, SzeK Y. Design of non-fragile ℋ_∞ controller for active vehicle suspensions. Journal of Vibration and Control, 2005, 11(2): 225–243

[23] ZhangB, ZhouS, LiT. A new approach to robust and non-fragile ℋ_∞ control for uncertain fuzzy systems. Information Sciences, 2007, 177(22): 5118–5133

[24] ChenJ D, YangC D, LienC H, Horng J H. New delay-dependent nonfragile ℋ_∞ observer-based control for continuous time-delay systems. Information Sciences, 2008, 178(24): 4699–4706

[25] FanY, LiuL, FengG, Wang Y. Self-triggered consensus for multiagent systems with Zeno-free triggers. IEEE Transactions on Automatic Control, 2015, 60(10): 2779–2784

[26] MahmoudM S, Almutairi N B. Resilient decentralized stabilization of interconnected time-delay systems with polytopic uncertainties. International Journal of Robust and Nonlinear Control, 2011, 21(4): 355–372

[27] DadkhahN, Rodrigues L. Non-fragile state-feedback control of uncertain piecewise-affine slab systems with input constraints: a convex optimisation approach. IET Control Theory & Application, 2014, 8(8): 626–632

[28] El GhaouiL, OustryF, AitRamiM. A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control, 1997, 42(8): 1171–1176

[29] QiuJ, FengG, GaoH. Static-output-feedback control of continuoustime T-S fuzzy affine systems via piecewise Lyapunov functions. IEEE Transactions on Fuzzy Systems, 2013, 21(2): 245–261

[30] KchaouM, El Hajjaji A, ToumiA . Non-fragile ℋ_∞ output feedback control design for continuous-time fuzzy systems. ISA Transactions, 2015, 54: 3–14

[31] SyrmosV L, Abdallah C T, DoratoP , GrigoriadisK. Static output feedback-a survey. Automatica, 1997, 33(2): 125–137

[32] QiuJ, FengG, GaoH. Asynchronous output feedback control of networked nonlinear systems with multiple packet dropouts: T-S fuzzy affine model based approach. IEEE Transactions on Fuzzy Systems, 2011, 19(6): 1014–1030

[33] WeiY, QiuJ, KarimiH R, Wang M. New results on ℋ_∞ dynamic output feedback control for Markovian jump systems with time-varying delay and deficient mode information. Optimal Control Applications and Methods, 2014, 35(6): 656–675

[34] ChenL, HuangX, FuS. Observer-based sensor fault-tolerant control for semi-Markovian jump systems. Nonlinear Analysis: Hybrid Systems, 2016, 22: 161–177

[35] XieL. Output feedback ℋ_∞ control of systems with parameter uncertainty. International Journal of Control, 1996, 63(4): 741–750

[36] BoydS, El Ghaoui L, FeronE , BalakrishnanV. Linear Matrix Inequality in Systems and Control Theory. Philadelphia: Society for Industrial and Applied Mathematics, 1994

[37] QiuJ, DingS X, GaoH, Yin S. Fuzzy-model-based reliable static output feedback ℋ_∞ control of nonlinear hyperbolic PDE systems. IEEE Transaction on Fuzzy Systems, 2016, 24(2): 388–400

[38] WeiY, QiuJ, LamH K, Wu L. Approaches to T-S fuzzy affine model based reliable output feedback control for nonlinear Itô stochastic systems. IEEE Transaction on Fuzzy Systems, doi: 10.1109/TFUZZ.2016.2566810

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