Fuzzy hyperbolic guaranteed cost control design for a class of nonlinear continuous-time dynamics systems

Abstract

This paper studies fuzzy hyperbolic guaranteed cost control for nonlinear continuous-time systems with parameter uncertainties. The same as Takagi-Sugeno (T-S) fuzzy model, fuzzy hyperbolic model (FHM) is a universal approximator, and can be used to establish the model for unknown complex systems. Furthermore, the main advantage of using FHM over T-S fuzzy model is that no premise structure identification is needed and no completeness design of premise variables space is needed. Also a FHM is a kind of valid global description and nonlinear model in nature. First, the fuzzy hyperbolic model (FHM) is proposed to represent the state-space model for nonlinear continuous-time systems. Next, a nonlinear quadratic cost function is considered as a performance measurement of the closed-loop fuzzy system. Some sufficient conditions are provided for the construction of a fuzzy hyperbolic guaranteed cost controller via state feedback. These conditions are given in terms of the feasibility of linear matrix inequalities (LMIs). Thus the problem of fuzzy hyperbolic guaranteed cost controller design is converted into linear matrix inequalities problem, which can be efficiently solved using convex optimization techniques, such as the interior point algorithm. Simulation examples are provided to illustrate the design procedure of the proposed method.