Distributed Saturated Control for a Class of Semilinear PDE Systems: An SOS Approach

This paper presents a systematic approach to deal with the saturated control of a class of distributed parameter systems that can be modeled by the first-order hyperbolic partial differential equations (PDE). The approach extends (also improves over) the existing fuzzy Takagi-Sugeno (TS) state feedback designs for such systems by applying the concepts of the polynomial sum-of-squares (SOS) techniques. First, a fuzzy-polynomial model via Taylor series is used to model the semilinear hyperbolic PDE system. Second, the closed-loop exponential stability of the fuzzy-PDE system is studied through the Lyapunov theory. This allows us to derive a design methodology in which a more complex fuzzy state-feedback control is designed in terms of a set of SOS constraints, able to be numerically computed via semidefinite programming. Finally, the proposed approach is tested in simulation with the standard example of a nonisothermal plug-flow reactor.