Robust Minimum Variance Lower Bound Estimation by Uncertainty Modeling Using Interval Type‐2 Fuzzy set

Abstract

The Minimum Variance Lower Bound (MVLB) represents the best achievable controller capability in a variance sense. Estimation of the MVLB for nonlinear systems confronts some difficulties. If one simply ignores these nonlinearities, there is the danger of over-estimating the performance of the control loop in rejecting uncertainties. Assuming that almost all models have uncertainties, in this paper, the MVLB has been estimated considering three types of uncertainties: structural, parametric, and algorithmic. To achieve accurate estimation of the MVLB an interval type-2 fuzzy set has been utilized. This paper utilizes a strategy for modeling of symmetric interval type-2 fuzzy sets using their uncertainty degrees. Then, based on this uncertainty measure, one method to construct interval type-2 fuzzy set models using the uncertain interval data is introduced. Finally, simulation studies demonstrate the effectiveness of the proposed control scheme.

MV bound and MV controller for convex‐non‐linear systems with input constraints

“…The true value for the MVLB (without constraint) for the tested quadruple‐tank process is 0.01 and MVLB for the linear controller is 0.0351 [31]. The weighting coefficients have been selected as and the sampling time is 0.1 s. The MVLB for a constrained quadruple‐tank system based on Theorem 1 is calculated and is shown in Fig.…”

Minimum variance lower bound estimation with Gaussian Process models

“…The algorithmic and parametric uncertainties of the model parameters ( Δθ p +Δθ b ) are included in Table 2. At the beginning, it is supposed that the parametric and algorithmic uncertainties are equal; thus, the membership parameters can be calculated using methods proposed in (Alipouri and Poshtan, 2016) (see equations (48) and (49) in Alipouri and Poshtan, 2016).…”

“…Using type-2 fuzzy set, the uncertainties are picked up from the data; therefore, Δ st ( k ) → 0 can be supposed. Therefore, the minimum variance bound of prediction error is (see Alipouri and Poshtan, 2016)…”

Uncertain Method for Optimal Control Problems With Uncertainties Using Chebyshev Inclusion Functions

“…Some different methods have been proposed to guarantee the robustness of OCPs in the presence of uncertainties [8]. In recent years, some completely different methods have been introduced to solve this deficiency, for instance, fuzzy programming, stochastic methods, and interval arithmetic methods [9][10][11][12]. For using stochastic methods, we need to know about the probabilistic distribution and for using the fuzzy methods, we need sufficient information about system changes.…”