Bases teóricas especializadas sobre el tema

In the past few decades, the Takagi-Sugeno (T-S) fuzzy model has been proven to be an ef- fective model to describe many nonlinear complicated real systems such as multiple nonlin- ear systems, switched nonlinear hybrid systems, and second-order non-holomonic systems [171–174]. In [175], a discrete-time switching fuzzy system is developed, which inherently contains the features of switched hybrid systems and T-S fuzzy systems. Therefore, fuzzy logic theory has been widely applied in the control area [176–179].

An fuzzy congestion control mechanism is proposed to control the network flow based on a variable length virtual output QL [180]. In this scheme, the fuzzy logic control is used to provide the properties of controlling of the nonlinear time-varying systems due to its capability of dynamically adapting its parameters. In contrast, the other control strategies would have to be held a constant value even under the network environment with time- varying traffic load, round trip times, etc. The existing methods are developed based on the linearised model, which is linearised around a certain network condition, such as the number of TCP sections, the targeted QL, and the round-trip time. Fuzzy control avoid this to achieve a global nonlinear performance. In [181], fuzzy-logic control is developed without a precise model. Some research on fuzzy logic in telecommunications networks are presented in the literature [182].

A fuzzy control based RED (FCRED) is investigated to adjust the parameter of the RED algorithm [183]. This work presents a brief summary of fuzzy logic control theory in communication network. There are three main parts in the fuzzy controller design: the fuzzification unit, fuzzy-inference engine with fuzzy-rule base and defuzzification unit. The fuzzification unit is to map the input values to be controlled to a fuzzy set, such as the mem-

bership functions. In addition, the fuzzy-rule base is to provide the connection between the input data and the appropriate output values. It is constructed according to a combination of trial and error [184]. The fuzzy model consists of a set of IF-THEN rules. Furthermore, the defuzzification unit maps this fuzzy output variable to a crisp controller output. Accord- ing to the results in [185], defuzzification methods include: centre of area (CoA), centre of maximum (CoM) and mean of maximum (MoM) that the plant understands.

A fuzzy based RED is proposed to generate the control of the packet dropping probabil- ity subject to the average QL and the packet loss rate based on a fuzzy logic method [184]. Moreover, another improved fuzzy RED algorithm is investigated to dynamically tune the maximum drop probability parameter (Pmax) of the RED. It use the Pmax and the error sig- nal as the input data in the controller, then the output value of the controller is the change of Pmax in RED. An adaptive fuzzy based RED (AFRED) AQM control is developed to adapt the fuzzy rule and parameters in membership functions for improving the stability [181]. Thus, AFRED features an adaptive adjust module with the input variable of the instanta- neous QL to produce the control of packet drop probability. The fuzzy rules of AFRED are changed based on the real packet drop ratio measured in AQM. A fuzzy logic controller based REM (FUZREM) is designed in [186]. In addition, an adaptive fuzzy REM (AFREM) is developed to adapt its fuzzy rules for the REM mechanism [69]. Furthermore, a fuzzy GREEN is proposed in [185]. Moreover, a DEEP BLUE [187] is designed by combining the BLUE AQM algorithm with the fuzzy extension of Q-learning, a reinforcement learning technique, to achieve the online model-free optimization. Also, a fuzzy logic congestion detection (FLCD) algorithm is investigated in [188].

A fuzzy-based PID AQM strategy is developed by to operate in conjunction with a con- ventional PID controller via a fuzzy switching mechanism [189]. The fuzzy PID controller consists of two inputs, such as the error QL and the error of its change rate. In order to consider the error of the link input rate, a enhanced fuzzy controller is studied to generate

the output variable of dropping probability in [190]. In the fuzzy-logic control strategy, the maximum QL of virtual output queues that is adjusted by the controller can induce packet drops in the real queue [191]. Thus, a self-adaptive fuzzy controller [192] is developed to calculate the learning rate for a neural-network-based PID controller [193]. The further work on fuzzy control for network traffic management can be found in the literature [194– 197].

Some observation strategies are proposed to be implemented in routers to improve the performance in AQM schemes and to monitor the traffic flow in TCP networks [48–50]. A fuzzy observer was designed to build an observer-based fuzzy controller to implement a T-S fuzzy control algorithm for the congestion control [68]. Another fuzzy observer was applied to constitute an AQM controller for a TCP/IP network to track the desired QL accurately and avoid network congestion [69]. To achieve the performance in the presence of unknown signals or uncertainties in the networks, the fuzzy observer was presented by using T-S fuzzy system which is consisted of a number of linear time-invariant models to approximate the nonlinear plant. However, the issues of the local linear observation in the subsystem of the fuzzy system are still hardly to force the estimation errors to zero [68, 69].