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The problem of robust nonlinear fault estimation for discrete-time Takagi-Sugeno fuzzy systems is investigated by proposing a depth partitioning approach. Compared with those existing results, the working space spanned by the updated normalized fuzzy weighting functions can be partitioned into any number of non-overlapping subspaces in a systematic way and thus a new gain-scheduling fault estimation observer is developed with proprietary gain matrices concerning the current operating mode. More importantly, the conservativeness will become less and less if the prescribed number of non-overlapping subspaces varies from small to large. In other words, it provides a chance to achieve much better performance of fault estimation while a smaller degree of the homogenous matrix polynomial can be chosen, which is very important for practical applications of theoretical results. Finally, the given depth partitioning approach is applied to deal with the fault estimation of the tunnel diode circuit and its advantages are validated via simulation comparisons. [ABSTRACT FROM AUTHOR]

In this paper, a new switching sequence convex optimization (SSCO) algorithm is proposed for solving non-convex optimization problem with complex time-varying relaxation matrix structures that arises during output feedback design. Firstly, the introduced time-varying relaxation matrix combines the membership functions and the designed switching mechanism to adjust the positive and negative terms of the inequality constraints. As a result, relaxed controller design conditions with complex matrix structures are established. The proposed SSCO algorithm employs switching optimization variables and inner approximation strategy, which is able to compute non-convex optimization problems with complex matrix structures more flexibly and converge quickly. It is worth noting that the implementation of the SSCO algorithm requires a set of strictly feasible initial solutions. Therefore, an initialization iterative algorithm is proposed, which overcomes the difficulties of transforming the solving problem into a typical non-convex optimization problem and linearizing multiple different concave parts, by which a set of optimized feasible solutions are obtained. Finally, simulation examples are used to demonstrate the superiority of the design scheme proposed in this paper. [ABSTRACT FROM AUTHOR]

• A dynamic trade-off between conservatism and complexity is established via a online evaluator. • More efficient fuzzy stabilization conditions are developed in this paper. • The recent multiple-sums-based method is improved evidently in the study. This paper is concerned with the problem of developing more efficient stabilization conditions for discrete-time Takagi-Sugeno fuzzy systems, i.e., not only reducing the conservatism but also (at the same time) alleviating the complexity of fuzzy control synthesis. Firstly, under the framework of traditional fuzzy stabilization, the recent multiple-sums-based method reported in the literature is improved by removing all the redundant variables, and thus the same feasible stabilization range can be obtained at the cost of more economical computational burden. Secondly, in order to further enhance the control efficiency, a dynamic trade-off between conservatism and complexity is established by proposing a new online evaluator of the updated system variation information across two adjacent sampling instants, and thus the so-called resilient stabilization is developed for reducing the conservatism without increasing or even alleviating the complexity. Moreover, all the determined matrices at the farthest sampling instant can be entirely removed without introducing any conservatism due to the proposed substitution technique. Finally, the superiority and effectiveness of our proposed methods are illustrated by a set of simulation comparisons with relevant research results reported in recent literature. [ABSTRACT FROM AUTHOR]

The problem of relaxed state estimation design of multi-instant fuzzy switching observer for discrete-time nonlinear systems is studied by proposing a deep division approach. Firstly,both the enhancement factor and the attenuation factor for each normalized fuzzy weighting function are for the first time introduced synchronously in order to derive much finer subdivisions of the whole spanning space constituted by all the normalized fuzzy weighting functions. Consequently, a more advanced ranking-based switching mechanism can be proposed over the previous results. Secondly, a new multi-instant fuzzy switching observer with different gain matrices for each finer subdivision is designed with the help of the given switching mechanism and thus much more freedom can be brought for reducing the conservatism of existing designs of fuzzy observers. More importantly, it is worth noting that the calculation of all the involved gain matrices belongs to a feasible off-line process. Finally, two simulation examples including tunnel diode circuits are provided to validate the progressiveness of the proposed deep division approach. [ABSTRACT FROM AUTHOR]

In this paper, a new two-dimensional gaussian hierarchical priority fuzzy system (TGHPFS) is proposed to handle interval-valued data. TGHPFS first performs hierarchical clustering of the average value of interval-valued data in each dimension to generate two-dimensional gaussian membership functions of two-level rules. The two levels of rules are associated by calculating the activation strength of the second-level rules to the first-level rules and setting the connection threshold. The regularized least squares method is used to optimize the consequents of the second-level rules. The two-dimensional gaussian membership function designed in this paper is used to model the antecedents of interval-valued data, solving the correlation problem between the left and right values of interval-valued data. The effectiveness of TGHPFS is validated using real-world datasets, and the proposed method is compared with other latest methods to show the superiority of TGHPFS. [ABSTRACT FROM AUTHOR]

This paper proposes a variable-type hierarchical fuzzy system (VTHFS) with high accuracy and strong interpretability. An improved rear-part direct-connected structure is used in the VTHFS, which eliminates the intermediate variables of the hierarchical fuzzy system (HFS). A new feature sorting method is proposed to find suitable input variables for each layer of subsystems of VTHFS. Under the proposed topology structure, layer by layer training of VTHFS can be achieved by changing the expected output of each layer, thereby reducing residual errors layer by layer and improving the prediction accuracy of VTHFS. Three fuzzy set distribution constraints are used in parameter optimization of VTHFS to improve the interpretability, including integrity, distinguishability, and footprint of uncertainty. The type of fuzzy set is automatically adjusted according to the uncertainty characteristics of input data measured by fuzziness, which further enhances the semantic interpretability of the VTHFS and solves the problem of requiring prior knowledge to define the fuzzy set type in existing research. Finally, the proposed VTHFS is tested on the regression data sets in the real world. Experimental results demonstrate the effectiveness of the feature sorting method and the fuzzy set type adjustment method. Through a large number of quantitative indicators, it can be confirmed that VTHFS has stronger interpretability and higher prediction accuracy compared to other fuzzy systems. [ABSTRACT FROM AUTHOR]

This paper proposes a novel gradient-boosting-based ensemble system with a fuzzy regression tree (FRT) as its base component for regression tasks. FRT first initializes the rule space as a whole. In each division round, the rule space is supervised to be divided into smaller subspaces using a novel guaranteed membership division method. The consequent parameters are optimized using fuzzy weighted regularized L2 least squares. The FRT corresponding to the minimum MSE is kept as the initial model for the next division round. The above operation is repeated until the FRT reaches the maximum division rounds. Using gradient boosting to train subsequent FRTs to build hierarchical fuzzy regression tree (HFRT). The HFRT can guarantee the high accuracy while ensuring the low complexity of computation, particularly suitable for solving high-dimensional problems. HFRT performed ablation analysis experiments and compared with state-of-the-art algorithms on 28 data sets. The results confirm the effectiveness of the HFRT. [ABSTRACT FROM AUTHOR]

In this paper, the ability of disturbance rejection is considered for nonlinear systems presented by Takagi-Sugeno (T-S) fuzzy model with time-varying delay. First, a membership function dependent Lyapunov-Krasovskii functional is designed to handle the time-varying delay and an observer-based switching controller is designed to cope with the time derivative of membership function. For each switching signal, an invariant set is estimated corresponding to the switching controller, and the subset of the intersection is also an invariant set if the number of switching is finite with energy bounded disturbance. Then, for the trajectory starting from the origin, the ability of disturbance rejection is measured by H ∞ performance and for other cases, two sets are designed such that any trajectories beginning with the smaller one will remain in the larger one. Finally, the merits of the proposed method are demonstrated by two examples. [ABSTRACT FROM AUTHOR]