Mixed Fuzzy Control plus Mobile Actuator/Sensor Guidance for Semilinear Parabolic Distributed Parameter Systems

This article addresses the issue of fuzzy control design subject to a mixed H 2/H\infty performance constraint and guidance law design for semilinear parabolic distributed parameter systems (DPSs) with mobile collocated actuator/sensor pairs. Initially, via the local sector nonlinearity method, a Takagi-Sugeno (T-S) fuzzy model is constructed to accurately describe the spatiotemporal dynamics of the DPSs. Then, based on the obtained T-S fuzzy model and Lyapunov technique, a membership-function-dependent mixed H2/H\infty fuzzy control design is developed and the mobile actuator/sensor guidance laws are also determined simultaneously, such that the resulting closed-loop system is exponentially stable while providing an H2 performance bound under the given H\infty performance of disturbance attenuation, and the transient response of closed-loop state is improved. Moreover, a suboptimal mixed H2/H\infty fuzzy control design is derived in the sense of minimizing the upper bound of the given H2 performance function by applying the existing linear matrix inequality optimization techniques. At last, some simulation results for a numerical example are presented to verify the proposed method.