Zonotopic Fault Detection for Space Tethered Satellite Fuzzy System Based on Polynomial Chaos Expansion

This paper develops an observer-based fault detection scheme for Space Tethered Satellite (STS) systems, integrating Polynomial Chaos Expansion (PCE) with a zono topic approach. To manage system complexity, the STS is first modeled using a Takagi-Sugeno (T-S) fuzzy framework with local Lipschitz function. A robust observer is then designed using H_∞ optimization techniques, employing a generalized method to handle Lipschitz nonlinearity with fewer restrictions than traditional approaches. By combining PCE with zono topes, the scheme simultaneously accounts for time-invariant probabilistic uncertainties and set-based bounded uncertainties. This hybrid quantification reduces the inherent conservatism of purely bound-based methods, yielding more accurate estimation results. Finally, fault detection is achieved by monitoring the residual-containing zonotopic sets. Numerical simulations on an STS system demonstrate the effectiveness and accuracy of the proposed methodology.