Dynamic Fuzzy Boundary Output Feedback Control for Nonlinear Delayed Parabolic Partial Differential Equation Systems Under Noncollocated Boundary Measurement

Abstract

For nonlinear space-varying parabolic partial differential equation systems (PPDESs) with random time-varying delay, this paper introduces a dynamic fuzzy boundary output feedback (DFBOF) control under non-collocated boundary measurement (NCBM). Initially, the nonlinear delayed PPDESs are represented by Takagi-Sugeno (T–S) fuzzy models and random time-varying delay is considered by taking the influence of uncertain factors, which belongs to two intervals in a probabilistic way. Since the system state is not fully available and NCBM makes the boundary control design very difficult, a fuzzy observer under NCBM is presented to surmount the design difficulty. Subsequently, an observer-based fuzzy boundary controller is proposed and spatial linear matrix inequality (SLMI) based sufficient conditions to ensure mean square exponential stability are obtained for closed-loop delayed PPDESs by utilizing the Lyapunov direct method and Wirtinger inequality. Then, to solve the SLMIs, the feasibility conditions of DFBOF controller design for nonlinear delayed PPDES are expressed in LMIs. Lastly, two examples are offered to demonstrate the validity of the presented dynamic fuzzy boundary control approach.