A Polynomial Chaos Expansion Approach to Interval Estimation for Uncertain Fuzzy Systems

In this article, we propose a polynomial chaos expansion (PCE) approach to interval estimation for uncertain Takagi–Sugeno fuzzy systems by considering time-invariant parameter uncertainties. First, we design the observer to get the point-valued estimates, where the accuracy of interval estimation is ensured by optimizing the gain matrices of the designed observer. Second, to obtain the interval estimation results of real states, the error dynamics is split into a random process with stochastic uncertainties and a bounded process with set-based uncertainties. Different from the interval estimation methods presented in the literature, which use only zonotopic analysis for interval estimation, we use the PCE approach in conjunction with zonotopic analysis for interval estimation, where the random process is analyzed using PCE in conjunction with the zonotopic method, and the bounded process is studied using the zonotopic analysis method. Moreover, a numerical simulation is proposed, and its results illustrate that the presented approach can decrease the conservatism of interval estimation and facilitate more interval estimation accuracy compared to an advanced interval observer design approach. Finally, interval estimation is performed for a vehicle lateral dynamic model to illustrate the applicability and superiority of the presented approach.