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Keywords:

  • guaranteed cost control;
  • distributed parameter systems;
  • Takagi–Sugeno fuzzy model;
  • exponential stability;
  • linear matrix inequalities

The guaranteed cost distributed fuzzy (GCDF) observer-based control design is proposed for a class of nonlinear spatially distributed processes described by first-order hyperbolic partial differential equations (PDEs). Initially, a T–S fuzzy hyperbolic PDE model is proposed to accurately represent the nonlinear PDE system. Then, based on the fuzzy PDE model, the GCDF observer-based control design is developed in terms of a set of space-dependent linear matrix inequalities. In the proposed control scheme, a distributed fuzzy observer is used to estimate the state of the PDE system. The designed fuzzy controller can not only ensure the exponential stability of the closed-loop PDE system but also provide an upper bound of quadratic cost function. Moreover, a suboptimal fuzzy control design is addressed in the sense of minimizing an upper bound of the cost function. The finite difference method in space and the existing linear matrix inequality optimization techniques are used to approximately solve the suboptimal control design problem. Finally, the proposed design method is applied to the control of a nonisothermal plug-flow reactor. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2366–2378, 2013