A Fuzzy Approach for Robust Reference-Tracking-Control Design of Nonlinear Distributed Parameter Time-Delayed Systems and Its Application

This paper addresses the robust reference-tracking-control problem for nonlinear distributed parameter systems (NDPSs) with time delays, external disturbances, and measurement noises. The NDPS is measured at several sensor locations for output-feedback tracking control. A fuzzy-spatial state-space model derived via finite-difference approach is introduced to represent the nonlinear distributed parameter time-delayed system. Thus, we use a fuzzy interpolation method with several local linear systems to approximate the nonlinear system and employ the finite-difference method to approximate the partial differential operators in fuzzy-spatial state-space model. Based on this model, a robust fuzzy-observer-based reference-tracking controller is proposed to control the NDPS to track a desired reference trajectory. First, a 2-D tracking performance in a spatiotemporal domain is proposed for robust tracking design of nonlinear distributed parameter time-delayed systems. Then, an equivalent 1-D reference-tracking design is developed to simplify the design procedure, and the linear-matrix-inequality (LMI) technique is applied to solve the control gains and observer gains for the robust tracking-design problem via a systematic control-design procedure. Finally, a tracking-control-design example for the nervous system is given to confirm the proposed reference-tracking-control scheme of nonlinear distributed parameter time-delayed systems.