\(H_{\infty }\) Adaptive Intermittent Noncollocated Boundary Observer Design for Nonlinear Parabolic DPSs

This paper investigates the intermittent adaptive observer design for nonlinear parabolic distributed parameter systems (DPSs) under noncollocated boundary measurements (BMs). To overcome the challenge of unavailable full states and spatially separated sensing, a Takagi–Sugeno (T-S) fuzzy observer is constructed to estimate system dynamics under intermittent BMs. Then, an adaptive boundary control scheme is introduced, in which the feedback gain is dynamically regulated to enhance robustness. Furthermore, Lyapunov-based analysis with a switching time-dependent functional ensures exponential stability of the closed-loop DPSs while satisfying an \(H_\infty \) performance. Finally, a numerical example is provided to illustrate the effectiveness and practicality of the proposed design method.