access icon free Design of distributed sampled-data fuzzy controller for a class of non-linear hyperbolic PDE systems: input delay approach

This study addresses the problem of distributed sampled-data fuzzy controller design for a class of non-linear distributed parameter systems which are described by first-order hyperbolic partial differential equations (PDEs). To achieve this goal, first, the non-linear system is modelled by a continuous-time Takagi–Sugeno first-order hyperbolic PDE fuzzy model. Subsequently, the authors design a new distributed sampled-data fuzzy controller that generates a zero-order hold sampled-data control signal appropriate for the PDE systems. Then, a new Lyapunov–Krasovskii functional is suggested to provide the stability analysis conditions of the closed-loop control system. Moreover, the stabilisation conditions are obtained and converted to linear matrix inequalities using some new null terms. The proposed technique has removed the structural constraints on the convection and Lyapunov matrices. Finally, the proposed approach is applied on a biological system and a non-isothermal plug flow reactor .

Inspec keywords: delays; partial differential equations; hyperbolic equations; fuzzy control; distributed control; distributed parameter systems; closed loop systems; control system synthesis; flow control; Lyapunov methods; sampled data systems; nonlinear control systems; biology; chemical reactors; continuous time systems; stability criteria; linear matrix inequalities

Other keywords: stabilisation conditions; convection; first-order hyperbolic partial differential equations; linear matrix inequalities; nonlinear hyperbolic PDE systems; input delay approach; structural constraints; zero-order hold sampled-data control signal; biological system; nonlinear distributed parameter systems; distributed sampled-data fuzzy controller design; stability analysis conditions; nonisothermal plug flow reactor; closed-loop control system; continuous-time Takagi-Sugeno first-order hyperbolic PDE fuzzy model; null terms; Lyapunov-Krasovskii functional; Lyapunov matrices

Subjects: Multivariable control systems; Mathematical analysis; Distributed parameter control systems; Stability in control theory; Discrete control systems; Nonlinear control systems; Biological and medical control systems; Control system analysis and synthesis methods; Algebra; Fuzzy control; Level, flow and volume control

References

    1. 1)
      • 21. Wu, Z., Peng, L., Xie, L., et al: ‘Asymptotic bounded consensus tracking of double-integrator multi-agent systems with a bounded-jerk target via sampled-data control’, IET Control Theory Appl., 2015, 9, (12), pp. 19091915.
    2. 2)
      • 17. Lam, H.K.: ‘Sampled-data output-feedback fuzzy controller for nonlinear systems based on polynomial fuzzy model-based control approach’, in ‘Polynomial fuzzy model-based control systems’ (Springer, Berlin, Germany, 2016), pp. 197220.
    3. 3)
      • 4. Wu, H.N., Wang, J.W., Li, H.X.: ‘Exponential stabilization for a class of nonlinear parabolic pde systems via fuzzy control approach’, IEEE Trans. Fuzzy Syst., 2012, 20, (2), pp. 318329.
    4. 4)
      • 23. Demetriou, M.A., Kazantzis, N.: ‘A new integrated output feedback controller synthesis and collocated actuator/sensor scheduling framework for distributed parameter processes’, Comput. Chem. Eng., 2005, 29, (4), pp. 867876.
    5. 5)
      • 36. Pitarch, J.L., Rakhshan, M., Mardani, M.M., et al: ‘Distributed saturated control for a class of semilinear pde systems: a SOS approach’, IEEE Trans. Fuzzy Syst., 2017, doi: 10.1109/TFUZZ.2017.2688379.
    6. 6)
      • 30. Wu, H.N., Wang, J.W., Li, H.X.: ‘Design of distributed hinf fuzzy controllers with constraint for nonlinear hyperbolic pde systems’, Automatica, 2012, 48, pp. 25352543.
    7. 7)
      • 3. Ray, W.H.: ‘Advanced process control’ (McGraw-Hill, New York, 1981).
    8. 8)
      • 32. Chen, M., Li, J., Zhang, W.: ‘Non-fragile guaranteed cost fuzzy control for nonlinear first-order hyperbolic partial differential equation systems’, Int. J. Comput. Math., 2015, 92, (1), pp. 77100.
    9. 9)
      • 20. Wu, Y.Q., Su, H., Wu, Z.G.: ‘Synchronisation control of dynamical networks subject to variable sampling and actuators saturation’, IET Control Theory Appl., 2015, 9, (3), pp. 381391.
    10. 10)
      • 28. Wang, J.W., Li, H.X., Wu, H.N.: ‘Fuzzy guaranteed cost sampled-data control of nonlinear systems coupled with a scalar reaction–diffusion process’, Fuzzy Sets Syst., 2015, 302, pp. 121142.
    11. 11)
      • 11. Al.Gherwi Kumar, D., W., Budman, H.: ‘Robust-distributed mpc tolerant to communication loss’, Comput. Chem. Eng., 2016, 88, pp. 3038.
    12. 12)
      • 19. Lam, H.K., Leung, F.H.F.: ‘Stability analysis of fuzzy-model-based control systems’, 264 (Springer, Berlin, Germany, 2011).
    13. 13)
      • 13. Xie, X., Yue, D., Ma, T., et al: ‘Further studies on control synthesis of discrete-time ts fuzzy systems via augmented multi-indexed matrix approach’, IEEE Trans. Cybern., 2014, 44, (12), pp. 27842791.
    14. 14)
      • 33. Tanaka, K., Wang, H.O.: ‘Fuzzy control systems design and analysis: a linear matrix inequality approach’ (John Wiley & Sons, New York, NY, USA, 2004).
    15. 15)
      • 29. Wang, Z.P., Wu, H.N.: ‘Finite dimensional guaranteed cost sampled-data fuzzy control for a class of nonlinear distributed parameter systems’, Inf. Sci., 2016, 327, pp. 2139.
    16. 16)
      • 1. Wang, J.W., Wu, H.N., Li, H.X.: ‘Distributed fuzzy control design of nonlinear hyperbolic pde systems with application to nonisothermal plug-flow reactor’, IEEE Trans. Fuzzy Syst., 2011, 19, (3), pp. 514526.
    17. 17)
      • 25. Yang, C.D., Qiu, J., Wang, J.W.: ‘Robust control for a class of nonlinear distributed parameter systems via proportional-spatial derivative control approach’, in ‘Abstract and applied analysis’, 2014, 2014, (2014), pp. 18.
    18. 18)
      • 34. Wang, J.W., Wu, H.N.: ‘Fuzzy output tracking control of semi-linear first-order hyperbolic pde systems with matched perturbations’, Fuzzy Sets Syst., 2014, 254, pp. 4766.
    19. 19)
      • 38. Aksikas, I., Winkin, J.J., Dochain, D.: ‘Optimal lq-feedback regulation of a nonisothermal plug flow reactor model by spectral factorization’, IEEE Trans. Autom. Control, 2007, 52, (7), pp. 11791193.
    20. 20)
      • 10. Tabarisaadi, P., Mardani, M.M., Shasadeghi, M., et al: ‘A sum-of-squares approach to consensus of nonlinear leader-follower multi-agent systems based on novel polynomial and fuzzy polynomial models’, J. Franklin Inst., 2017, 354, (18), pp. 83988420.
    21. 21)
      • 8. Zanil, M., Hussain, M.: ‘Multivariable adaptive Lyapunov fuzzy controller for ph neutralisation process’, 2015, 37, pp. 16431648.
    22. 22)
      • 31. Qiu, J., Ding, S., Gao, H., et al: ‘Fuzzy-model-based reliable static output feedback h-infinity control of nonlinear hyperbolic pde systems’, IEEE Trans. Fuzzy Syst., 2015, 24, (2), pp. 388400.
    23. 23)
      • 16. Koo, G.B., Park, J.B., Joo, Y.H.: ‘Intelligent digital redesign of fuzzy controller for non-linear systems with packet losses’, IET Control Theory Appl., 2016, 10, (3), pp. 292299.
    24. 24)
      • 5. Wu, H.N., Li, H.X.: ‘A multiobjective optimization based fuzzy control for nonlinear spatially distributed processes with application to a catalytic rod’, IEEE Trans. Ind. Inf., 2012, 8, (4), pp. 860868.
    25. 25)
      • 12. Xie, X.P., Liu, Z.W., Zhu, X.L.: ‘An efficient approach for reducing the conservatism of lmi-based stability conditions for continuous-time t–s fuzzy systems’, Fuzzy Sets Syst., 2015, 263, pp. 7181.
    26. 26)
      • 35. Pitarch, J., Rakhshan, M., Mardani, M.M., et al: ‘Distributed nonlinear control of a plug-flow reactor under saturation’, IFAC-PapersOnLine, 2016, 49, (24), pp. 8792.
    27. 27)
      • 24. Wu, H.N., Li, H.X.: ‘H fuzzy observer-based control for a class of nonlinear distributed parameter systems with control constraints’, IEEE Trans. Fuzzy Syst., 2008, 16, (2), pp. 502516.
    28. 28)
      • 9. Vafamand, N., Mardani, M.M., Khayatian, A., et al: ‘Non-iterative SOS-based approach for guaranteed cost control design of polynomial systems with input saturation’, IET Control Theory Appl., 2017, 11, (16), pp. 27242730.
    29. 29)
      • 7. Tanaka, K., Tanaka, M., Chen, Y.J., et al: ‘A new sum-of-squares design framework for robust control of polynomial fuzzy systems with uncertainties’, IEEE Trans. Fuzzy Syst., 2016, 24, pp. 94110.
    30. 30)
      • 14. Xie, X., Yue, D., Zhu, X.: ‘Further studies on control synthesis of discrete-time t–s fuzzy systems via useful matrix equalities’, IEEE Trans. Fuzzy Syst., 2014, 22, (4), pp. 10261031.
    31. 31)
      • 27. Wang, J.W., Li, H.X., Wu, H.N.: ‘A membership-function-dependent approach to design fuzzy pointwise state feedback controller for nonlinear parabolic distributed parameter systems with spatially discrete actuators’, IEEE Trans. Syst. Man Cybern. Syst., 2017, 47, (7), pp. 14861499.
    32. 32)
      • 15. Sadeghi, M.S., Vafamand, N., Babaei, M.S.: ‘Non-quadratic exponential stabilisation of non-linear hyperbolic partial differential equation systems’, IET Sci. Meas. Technol., 2014, 8, (6), pp. 537545.
    33. 33)
      • 6. Mozelli, L., Palhares, R.M., Mendes, E.: ‘Equivalent techniques, extra comparisons and less conservative control design for Takagi Sugeno (ts) fuzzy systems’, IET Control Theory Appl., 2010, 4, (12), pp. 28132822.
    34. 34)
      • 37. Lofberg, J.: ‘Yalmip: a toolbox for modeling and optimization in matlab’. 2004 IEEE Int. Symp. Computer Aided Control Systems Design, 2004, pp. 284289.
    35. 35)
      • 2. Wang, J.W., Wu, H.N., Li, H.X.: ‘Distributed proportional–spatial derivative control of nonlinear parabolic systems via fuzzy pde modelling approach’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2012, 42, (3), pp. 927938.
    36. 36)
      • 22. Peng, C., Zhang, J.: ‘Event-triggered output-feedback h control for networked control systems with time-varying sampling’, IET Control Theory Appl., 2015, 9, (9), pp. 13841391.
    37. 37)
      • 26. Wang, J.W., Wu, H.N.: ‘Exponential pointwise stabilization of semi-linear parabolic distributed parameter systems via the Takagi-Sugeno fuzzy pde model’, IEEE Trans. Fuzzy Syst., 2016, doi. 10.1109/TFUZZ.2016.2646745.
    38. 38)
      • 18. Yoneyama, J.: ‘Robust sampled-data stabilization of uncertain fuzzy systems via input delay approach’, Inf. Sci., 2012, 198, pp. 169176.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2017.0915
Loading

Related content

content/journals/10.1049/iet-cta.2017.0915
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading