Faults Estimation with Proportional-Integral Observer for T-S Fuzzy Multi-Agent Systems under Unmeasured Premise Variables

Networked robotic systems and smart manufacturing platforms increasingly rely on fleets of cooperative agents—collaborative manipulators, autonomous mobile robots, and distributed actuation modules—whose operational integrity depends on the reliable detection and reconstruction of failures within the network. Ensuring accurate failure estimation in such systems is particularly complex when agents are subject to simultaneous actuator and sensor failures, exogenous disturbances, and nonlinear dynamics. This paper addresses this problem for continuous-time Takagi–Sugeno (T-S) fuzzy multi-agent systems (MAS) operating with unmeasured premise variables (UPVs). This combination has not yet been addressed in a unified distributed estimation framework in the existing literature. The proposed approach introduces a distributed fuzzy proportional-integral observer (PIO) that jointly reconstructs system states, actuator faults, and sensor faults from local measurements and information from neighboring agents. To compensate for the discrepancy between ideal and implementable membership functions induced by UPVs, a Lipschitz bounding technique is developed that reformulates the membership function error as a norm-bounded uncertainty, thereby making it amenable to convex analysis. A consensus-based fault estimation architecture is also proposed, in which graph-coupled disagreement terms are injected into the fault reconstruction channel to exploit network redundancy—a mechanism particularly well-suited to multi-robot and production line supervisory scenarios. Stability, [Formula: see text] disturbance attenuation, and robustness against membership-function deviations are established through a poly-quadratic Lyapunov analysis formulated in terms of linear matrix inequalities (LMIs), from which the observer gains are directly synthesized. Numerical simulations on a network of five homogeneous single-link robotic manipulators with heterogeneous actuator/sensor faults and transient disturbances illustrate the proposed framework, demonstrating accurate fault reconstruction, fast convergence of estimation errors, and preserved coordination under UPVs. The obtained results support the relevance of the approach within the considered homogeneous networked robotic benchmark.