Synchronization of chaotic systems using time-delayed fuzzy state-feedback controller

This paper presents the fuzzy-model-based control approach to synchronize two chaotic systems subject to parameter uncertainties. A fuzzy state-feedback controller using the system state of response chaotic system and the time-delayed system state of drive chaotic system is employed to realize the synchronization. The time delay which complicates the system dynamics makes the analysis difficult. To investigate the system stability and facilitate the design of fuzzy controller, T-S fuzzy models are employed to represent the system dynamics of the chaotic systems. Furthermore, the membership grades of the T-S fuzzy models become uncertain due to the existence of parameter uncertainties which further complicates the system analysis. To ease the stability analysis and produce less conservative analysis result, the membership functions of both T-S fuzzy models and fuzzy controller are considered. Stability conditions are derived using Lyapunov-based approach to aid the design of fuzzy state-feedback controller to synchronize the chaotic systems. A simulation example is presented to illustrate the merits of the proposed approach

State estimation over non-acknowledgment networks with Markovian packet dropouts

In this paper, we investigate state estimation for systems with packet dropouts. According to whether there are acknowledgment (ACK) signals sent by the actuator to the estimator indicating the status of control packet dropouts or not, the systems are classified into two types: ACK systems, those with ACK signals, and non-ACK (NACK) systems, those without. We first obtain the optimal estimator (OE) for NACK systems with Markovian packet dropouts. However, the number of the components in the OE grows exponentially, making its stability analysis complicated and its computation time-consuming. Therefore, we proceed to design a computationally efficient approximate optimal estimator (AOE) using a relative-entropy-based approach. We prove that the proposed AOE has the same stability as the OE. We show that, even the separation principle does not hold for NACK systems, the stability of the OE can also be investigated separately; and discover that the OE for an NACK system has the same stability as the OE for the corresponding ACK system, even their structures are quite different. Finally, for strongly observable NACK systems, we establish a necessary and sufficient condition for the stability of the OE and the AOE.</p

Hierarchical fuzzy model-agnostic explanation: framework, algorithms and interface for XAI

Artificial intelligence (AI) has made remarkable achievements in extensive fields while its black box nature limited applications in many critical areas. Against this drawback, explainable AI (XAI), has emerged as a focal point of current research. Recently, fuzzy logic systems (FLSs) attract increasing attention in XAI because of their linguistic representation, which can be naturally understood by humans. However, the focus of these works is limited by simply relying on inherent rule-based structures for explanation. Motivated by further exploring the potential of FLS to overcome the challenges of XAI in terms of comprehensibility, scalability and transferability, in this work we propose Fuzzy Model-Agnostic Explanation (FMAE) as a post-hoc paradigm to explain the behavior of black box models. The innovations and contributions of this work provide a unified framework offering four levels of explanation, develop the associated algorithms to present the hidden knowledge behind the black box model in human-understandable form at different levels of granularity and create the interface to deliver explanations to users. First, we introduce the hierarchical FMAE framework to formulate explanations into four levels including sample, local, domain and universe. Second, the learning and explaining algorithms are developed to systematically construct FLS to model the behavior of black box models in the four levels where downscaling is performed by simplification to facilitate explanations with concise rules and upscaling is performed by aggregation to integrate explanations at a higher level. Third, the proposed explanation interface unifies two typical forms of expression in XAI by fuzzy rules: the semantic inference explanation revealing the decision mechanism of the black box model and the feature salience explanation reflecting the attribution and interaction of input features. Simulated user experiments are designed on the comprehensive explanatory metrics. Compared with mainstream methods, the result shows outstanding explanation performance on real-world datasets for both regression and classification tasks

Hankel Norm Model Reduction of Discrete-Time Interval Type-2 T-S Fuzzy Systems with State Delay

This article focuses on the model reduction problem of discrete-time time-delay interval type-2 Takagi-Sugeno (T-S) fuzzy systems. Compared with the type-1 T-S fuzzy system, the interval type-2 T-S fuzzy system has more advantages in expressing nonlinearity and capturing uncertainties. In addition, in order to simplify the analysis process, complex high-order systems can be approximated as low-order systems, which is called model reduction. In previous studies, there are few researches on model reduction of the interval type-2 T-S fuzzy system with time delay. Hankel norm is adopted to limit the error after model reduction. Based on Jensen's inequality, a linear matrix inequality (LMI) condition for the Hankel norm performance of the error system is obtained. A membership-function-dependent method based on piecewise linear membership functions is utilized to deal with mismatched membership functions where information of membership functions will be used for relaxing analysis results. Next, by a convex linearization design, the model reduction problem is formulated as a convex LMI feasibility/optimization condition. Numerical examples are given to verify the validity of the analysis. </p