Fault‐Tolerant Fuzzy Boundary Control for Nonlinear Distributed Parameter Systems Under Limited Measurements and Markovian Failures

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ABSTRACT This paper proposes a boundary control method for nonlinear distributed parameter systems (DPSs) with limited boundary measurements (BMs), as typically encountered in networked cyber‐physical processes with spatially distributed dynamics such as thermal and biomedical diffusion systems. The method aims to address cyber‐physical threats and hybrid attacks whilst improving state estimation accuracy and system performance. First, a partial differential equation (PDE)‐based state observer is established, with an embedded adaptive event‐triggered mechanism (AMET) that optimises communication through dynamic sampling adjustment. Second, a Takagi–Sugeno (T–S) fuzzy noncollocated boundary sampled‐data controller (NBSDC) is designed. It adopts a spatially separated architecture to mitigate observation‐actuation mismatch under partial observability. Furthermore, the controller is designed to handle hybrid attacks with inconsistent modes, including denial‐of‐service (DoS) interruptions and deceptive signal alterations. Their impacts are bounded by energy constraints to ensure practical feasibility. In addition, a Markov jump process is employed to characterise stochastic controller failures, capturing abrupt mode transitions and enhancing fault tolerance under adverse conditions. Third, stability analysis based on Lyapunov–Krasovskii functionals (LKFs) provides theoretical guarantees for system stability and estimation error convergence. Finally, the effectiveness and applicability of the proposed method are validated through simulations on a tumour cell diffusion model.

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