Fundamentals of a fuzzy-logic-based generalized theory of stability

Smooth Compositions Made Stabilization of Fuzzy Systems: Easy and More Robust

Smooth fuzzy systems are the new structures of the fuzzy system which have recently taken attention for their capacity in system modeling. Hence, this article studies the stability of smooth fuzzy control systems and develops the sufficient conditions of the parameters for the stable closed-loop performance of the system. A major advantage of the presented conditions is that they do not call for a common Lyapunov function and therefore, no LMI is required to be solved to guarantee the stability of the fuzzy model. Besides, although they are the type-1 fuzzy model in nature, however, they show the high level of robustness to the noises and parametric uncertainties, which is comparable to the type-2 fuzzy models. Several comparative simulations demonstrate the capacity of the fuzzy models with the smooth compositions rather than the classical fuzzy models with the min-max or product-sum compositions.

Numerical solution of bipolar fuzzy initial value problem

Differential equations occur in many fields of science, engineering and social science as it is a natural way of modeling uncertain dynamical systems. A bipolar fuzzy set model is useful mathematical tool for addressing uncertainty which is an extension of fuzzy set model. In this paper, we study differential equations in bipolar fuzzy environment. We introduce the concept gH-derivative of bipolar fuzzy valued function. We present some properties of gH-differentiability of bipolar fuzzy valued function by considering different types of differentiability. We consider bipolar fuzzy Taylor expansion. By using Taylor expansion, Euler method is presented for solving bipolar fuzzy initial value problems. We discuss convergence analysis of proposed method. We describe some numerical examples to see the convergence and stability of the method and compute global truncation error. From numerical results, we see that for small step size Euler method converges to exact solution.

An Energy-Efficient and Obstacle-Avoiding Routing Protocol for Underwater Acoustic Sensor Networks

Underwater Acoustic Sensor Networks (UASNs) have become one of the promising technologies for exploring underwater natural resources and collecting scientific data from the aquatic environment. As obstacles hinder the communications among sensor nodes in UASNs, designing an effective bypass routing protocol to avoid obstacles is an urgent need. Moreover, the sensor nodes are typically powered by batteries, which are difficult to replace, restricting the network lifetime of UASNs. In this paper, an Energy-efficient and Obstacle-Avoiding Routing protocol (EOAR) is proposed not only to address the issue of marine animals acting as obstacles that interfere with communications, but also to balance the network energy according to the residual energy. In the EOAR protocol, when the current node perceives the existence of marine animals, the interference area of the animal-nodes is first calculated using the underwater acoustic channel model, and then the candidate forwarding relay set of the current node is obtained according to the constraint conditions. The optimal candidate forwarding relay is determined by a fuzzy logic-based forwarding relay selection scheme based on considering the three parameters of the candidate forwarding relay, which includes the propagation delay, the included angle between two neighbor nodes, and the residual energy. Furthermore, in order to solve the problem of energy waste caused by packet collision, we use a priority-based forwarding method to schedule the packet transmission from the candidate forwarding relay to the destination node. The proposed EOAR protocol is simulated on the Aqua-sim platform and the simulation results show that proposed protocol can increase the packet delivery ratio by 28.4% and 11.8% and can reduce the energy consumption by 53.4% and 32.7% and, respectively, comparing with the hop-by-hop vector-based forwarding routing protocol (HHVBF) and void handling using geo-opportunistic routing protocol (VHGOR).

On the stability and control of continuous-time TSK fuzzy systems

This paper introduces a new stability test and control design methodology for type-1 and type-2 continuous-time (CT) Takagi-Sugeno-Kang systems. Unlike methods based on a common Lyapunov function, our stability results apply for systems with unstable consequents, and our controllers can be designed for systems with unstabilizable consequents. The stability results are derived using the comparison principle with a discontinuous function and the upper right-hand derivative. The control results include CT fuzzy proportional controllers and fuzzy proportional-integral controllers that can be obtained by solving linear matrix inequalities. We provide several examples to demonstrate our stability testing and controller design and compare our results to available methods in the literature. Our results compare favorably with results available in the literature and provide stability tests and controllers where earlier approaches fail.

Fuzzy Complex Dynamical Networks and Its Synchronization

In this paper, the robust synchronization problem of fuzzy complex dynamical networks is investigated. A fuzzy complex dynamical network is an extension to an uncertain complex dynamical network in which all sources of parametric uncertainties are modeled with fuzzy numbers, i.e., all nodes' dynamics are described by fuzzy differential equations (FDEs) that permit a better description of a real process occurring in the presence of inaccuracy. To resolve the synchronization problem, this paper introduces new adaptive and impulsive controllers in which globally exponential synchronization of fuzzy dynamical networks under easily verified conditions is guaranteed. Moreover, we propose an efficient method that helps to find certain suitable nodes to be impulsively controlled via pinning, noting that these nodes, in general, vary at distinct impulsive time instants. Therefore, by using adaptive controllers and applying impulsive controllers to only a small portion of nodes, the whole network will completely be synchronized to a certain objective state. Finally, two numerical examples are given to illustrate the effectiveness of the proposed controllers.

Stability margin of linear systems with parameters described by fuzzy numbers

This paper deals with the linear systems with uncertain parameters described by fuzzy numbers. The problem of determining the stability margin of those systems with linear affine dependence of the coefficients of a characteristic polynomial on system parameters is studied. Fuzzy numbers describing the system parameters are allowed to be characterized by arbitrary nonsymmetric membership functions. An elegant solution, graphical in nature, based on generalization of the Tsypkin-Polyak plot is presented. The advantage of the presented approach over the classical robust concept is demonstrated on a control of the Fiat Dedra engine model and a control of the quarter car suspension model.