In this paper, the stability of polynomial-fuzzy-model-based (PFMB) systems equipped with mismatched interval type-2 (IT2) membership functions is investigated. Unlike the ...membership-function-independent methods, the information and properties of IT2 membership functions are considered in the stability analysis and contained in the stability conditions in terms of sum-of-squares (SOS) based on the Lyapunov stability theory. Three methods, demonstrating their own advantages, are proposed to conduct the stability analysis for the IT2 PFMB control systems. In the first one, we divide the operating domain into subdomains and then conduct the stability analysis incorporating the information and properties of the IT2 membership functions in subdomains. Through this approach, the stability conditions can be further relaxed compared with the membership-function-independent analysis. Polynomial functions are adopted in the second method to approximate the IT2 membership functions. The advantage of this method compared with the first one is that richer information of IT2 membership functions is considered without increasing the number of SOS conditions. In the third one, we combine the advantages of both the first and the second method offering a new approach which utilizes the information and properties of the lower and upper IT2 membership functions in subdomains through simpler polynomial approximation functions. It can be shown that more relaxed stability conditions can be obtained compared with the first two methods. Numerical examples and simulations are presented to verify the effectiveness of the proposed methods.
This article focuses on the problem of sliding mode control (SMC) for polynomial fuzzy singular systems with the matched uncertainty, time‐varying delay and different control input matrices. An ...integral sliding surface with different control input matrices and polynomial matrices is established. The existence of the equivalent controller can be determined according to the given sum‐of‐squares conditions. By choosing an appropriate augmented Lyapunov–Krasovskii functional and utilizing a generalized free‐matrix‐based integral inequality, a less conservative admissibility condition of sliding mode dynamics is proposed in the form of sum‐of‐squares. It is noteworthy that due to the choice of augmented Lyapunov–Krasovskii functional, the traditional methods cannot transform the nonlinear terms in the admissibility condition of sliding mode dynamics into linear terms. Here, several inequalities are introduced to overcome this difficulty. Furthermore, the SMC law is proposed to ensure the reachability of the sliding surface. The simulation results show that the proposed method is less conservative and effective.
In this paper, the distributed set-membership filtering problem is investigated for a class of discrete time-varying system with an event-based communication mechanism over sensor networks. The ...system under consideration is subject to sector-bounded nonlinearity, unknown but bounded noises and sensor saturations. Each intelligent sensing node transmits the data to its neighbors only when certain triggering condition is violated. By means of a set of recursive matrix inequalities, sufficient conditions are derived for the existence of the desired distributed event-based filter which is capable of confining the system state in certain ellipsoidal regions centered at the estimates. Within the established theoretical framework, two additional optimization problems are formulated: one is to seek the minimal ellipsoids (in the sense of matrix trace) for the best filtering performance, and the other is to maximize the triggering threshold so as to reduce the triggering frequency with satisfactory filtering performance. A numerically attractive chaos algorithm is employed to solve the optimization problems. Finally, an illustrative example is presented to demonstrate the effectiveness and applicability of the proposed algorithm.
This article addresses the asynchronous control for singularly perturbed systems with nonhomogeneous Markov switching approximated by T-S fuzzy models. The transition probabilities of the ...nonhomogeneous Markov process are supposed to be time-varying and distinguished by of a polytopic set. As distinct from some reported works, to abate the effect of missing packets in unreliable communication network, a novel dropout compensation strategy is constructed, where the packet arriving rate is assumed to be uncertain. Meanwhile, to describe the asynchronizations of the dropout compensation strategy and the controller, the hidden Markov models are absorbed. By resorting to the fuzzy-rule-dependent and the parameter-dependent Lyapunov-Krasovskii functional, novel sufficient conditions of <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula> performance are formulated and the fuzzy-based asynchronous controller gains are realized. Finally, to testify the efficiency and applicability of the proposed results, a numerical example and practical tunnel diode circuit system are provided.
This paper is concerned with the event-triggered H ∞ control problem for discrete-time nonlinear networked control systems with unreliable communication links. First, an event-triggered scheme is ...proposed to determine whether the sampled data should be released into the network or not. Second, when the released data is transmitted in the network, a Bernoulli process is employed to model the phenomenon of data losses. Third, considering the instants at which the sampled data is not released or data losses occur, a new random process is first developed to model the input data sequence of the controller under the effect of the buffer. Consequently, a novel method is presented to address the stability analysis and control synthesis problems based on the polynomial fuzzy model approach. Finally, some simulation results are given to illustrate the effectiveness of the proposed method.
This article focuses on the design of a fuzzy adaptive event-triggered sampled-data control (AETSDC) scheme for stabilization of Takagi-Sugeno (T-S) fuzzy memristive neural networks (MNNs) with ...reaction-diffusion terms (RDTs). Different from the existing T-S fuzzy MNNs, the reaction and diffusion phenomena are considered, which make the presented model more applicable. A fuzzy AETSDC scheme is proposed for the first time, in which different AETSDC mechanisms will be applied for different fuzzy rules. For each fuzzy rule, the corresponding AETSDC mechanism can be promptly adaptively adjusted based on the current and last sampled signals. So the fuzzy AETSDC scheme can effectively save the limited communication resources for the considered system. By introducing a suitable Lyapunov- Krasovskii functional, new stability and stabilization criteria are established for T-S fuzzy MNNs with RDTs. Meanwhile, the desired fuzzy AETSDC gains are obtained. Finally, simulation results are given to verify the superiority of the fuzzy AETSDC scheme and the effectiveness of the theoretical results.
This paper gives a new systematic framework to solve the asynchronous sliding mode control (SMC) problem for the semi-Markovian jump systems with singular perturbations, which can effectively remove ...the dependence on the unavailable system mode of SMC controller in some existing works. By considering the effect of the singular perturbation, this paper introduces a novel ε-dependent common sliding function, and then an asynchronous SMC law is developed by just using the detected mode signal. In order to overcome the difficulties in analyzing the stability of the sliding mode dynamics and the reachability of the specified sliding surface, a novel matrix decoupling technique and a novel semi-Markovian Lyapunov function method are introduced. Besides, genetic algorithm (GA) is employed to solve two meaningful optimization problems arising from designing a desired asynchronous SMC scheme. Finally, an operational amplifier circuit with a switching positive temperature coefficient thermistor is simulated to show the practicability of the proposed asynchronous SMC approach via GA.
This paper is concerned with the problems of dissipativity analysis and synthesis for discrete-time Takagi-Sugeno fuzzy systems with stochastic perturbation and time-varying delay. First, a novel ...model transformation method is introduced to pull the time-varying delay uncertainty out of the original system. Consequently, the transformed model is composed of a linear time-invariant system and a norm-bounded uncertain subsystem. By using this model transformation method combined with the Lyapunov-Krasovskii technique, sufficient conditions of the dissipativity are established. Then, a fuzzy controller is designed to guarantee the dissipative performance of the closed-loop system. Finally, three examples are presented: one shows the effectiveness of model transformation method, the second performs the comparison with alternative approaches, and the third illustrates the applicability of the proposed dissipative control methods.
•Convolutional Neural Networks can be improved in terms of the classification performance and robustness by using variable weight structures.•Analysis of different data processing methods, models’ ...robustness and statistical properties.•Comparative analysis of variable weight convolutional neural networks and other widely used machine learning techniques.•Medical applications to the classification of seizure phases and types.
Deep learning techniques have recently achieved impressive results and raised expectations in the domains of medical diagnosis and physiological signal processing. The widely adopted methods include convolutional neural networks (CNNs) and recurrent neural networks (RNNs). However, the existing models possess static connection weights between layers, which might limit the generalization capability and the classification performance of the models as the weights of different layers are fixed after training. Furthermore, to deal with a large amount of data, a neural network with a sufficiently large size is required. This paper proposes the variable weight convolutional neural networks (VWCNNs), which are a type of network structure employing dynamic weights instead of static weights in their convolutional layers and fully-connected layers. VWCNNs are able to adapt to different characteristics of input data and can be viewed as an infinite number of traditional, fixed-weight CNNs. We will show that the proposed VWCNN structure outperforms the conventional CNN in terms of the classification accuracy, generalization capability, and robustness when the inputs are contaminated by noise. In this paper, VWCNNs are applied to the classification of three seizure phases (seizure-free, pre-seizure and seizure) based on measured electroencephalography (EEG) data. VWCNNs achieve 100% test accuracy and show strong robustness in the classification of the three seizure phases, and thus show the potential to be a useful classification tool for medical diagnosis. Furthermore, the classification of seven types of seizures is investigated in this paper using the world’s largest open source database of seizure recordings, TUH EEG seizure corpus. Comparisons with conventional CNNs, RNN, MobileNet, ResNet, DenseNet and traditional machine learning methods including random forest, decision tree, support vector machine, K-nearest neighbours, standard neural networks, and Naïve Bayes are being conducted using realistic test data sets. The results demonstrate that VWCNNs have advantages over other classifiers in terms of classification accuracy and robustness.
In this article, the sliding mode control (SMC) problem is addressed for a class of Markovian jump systems via the T-S fuzzy model. First, in order to reduce the frequency of state transmission for ...alleviating congestion phenomenon in the bandwidth-limited communication network, a dynamic event-triggered (DET) strategy is introduced into the sensor-to-controller channel, in which an additional internal dynamical variable is employed to adjust the event-triggered condition adaptively. A fundamental issue resulting from the event-triggered strategy is that the controller cannot obtain the information about system mode during the triggering interval. Aiming at the phenomenon, this work utilizes a mode detector to estimate the unavailable system mode. Then, this article proposes a detected-mode-dependent event-triggered sliding mode controller whose membership grades are determined only via the transmitted state at the triggering instant. By constructing a relation on the membership functions (MFs) between the fuzzy model and the controllers for MF-dependent analysis, the conditions on the reachability and stability conditions are relaxed. Furthermore, an optimization algorithm is provided for the minimum control power via a high-dimensional grid searching for the coefficients of the internal dynamic variables, which, together with the designed detected-mode-dependent sliding mode controller, constitutes the novel SMC scheme under the DET strategy. Finally, the simulation results via the single-link arm system are provided to illustrate the efficiency of the proposed method.