Finite-time boundedness of fuzzy DP-CPS with input quantization and network attack via fuzzy dynamic parabolic controller approach

This paper focuses on the research of nonlinear distributed parameter cyber physical systems (DP-CPS) via finite-time interval. The nonlinearity of the DP-CPS is captured through the utilization of the Takagi–Sugeno (T–S) fuzzy model, which gives rise to a class of fuzzy parabolic partial differential equation (PDE). In order to optimize the network resources, a class of dynamic quantizer is employed to quantize the measurement output and control input signals. Then a fuzzy spatial-dependent dynamic parabolic control strategy with attack is firstly proposed to simplify the control design strategy and address the issue of degraded control performance caused by the inability of traditional control methods to effectively handle spatial variations in system parameters for systems with spatially distributed characteristics. The analysis of finite-time boundedness for the fuzzy parabolic PDE is conducted based on the Lyapunov functional. The finite-time boundedness controller design conditions and the adjustment parameters for the dynamic quantizers are presented for the fuzzy closed-loop system. Additionally, an any given matrix method is employed to decouple the coupled nonlinear terms in the control design conditions. The effectiveness of the proposed control approach has been confirmed through simulation conducted on a cascaded system comprising two cylindrical lithium batteries.