Fuzzy controllers as gain scheduling approximators

Abstract Nonlinear systems can be linearized according to Lyapunov's linearization method and then approximated by Takagi/Sugeno (TS) fuzzy models. The paper shows that the corresponding control strategy with TS controllers is closely related to traditional gain scheduling. Generally speaking, gain scheduling deals with the connection of different linear controllers acting as a global nonlinear control law. TS control defines a linear controller for each linearized region, as well as smooth control transitions between those regions. In this connection slowly varying operating conditions are assumed. For the design of the linear controllers the LQR design method has been used which guarantees optimal control of a linearized system with respect to an integral criterion. However, since TS control is an approximation method, solutions are bound to be suboptimal, and stability is hence a concern. The method is compared with a continuous change of control parameters, based on the continuous (on-line) LQR design for each point in state space. Additional control rule weights have been introduced to promote optimization. The above method is illustrated by a simple one-link manipulator arm.