Special Issue “Application of Fuzzy Control in Computational Intelligence”

Due to the fitted structure of fuzzy logic, neural networks and evolutionary computing, neuro-fuzzy systems, evolutionary-fuzzy systems, and evolutionary neural systems, we can study computational intelligence. It is very common in the field of machine control to use fuzzy logic. However, the meaning of “fuzzy” is still lacking clarity or definition. The benefit of fuzzy logic is that the result can be expressed in a way that operators can comprehend more easily than genetic algorithms and neural networks. Therefore, the experiences of the operators can be useful when designing the controller. Therefore, the tasks that have been performed artificially to date can become even more effortless to mechanize. As a systematic method, fuzzy control, an intelligent control technology, can combine the human experience and implement nonlinear algorithms that are characterized by a series of linguistic statements into the controller. Within the applications of process control, some studies have found that, in machine-driven applications, fuzzy control can be very useful. It is crucial for the experts in the field to take a very close look at fuzzy control applications because it is a current trend. The goal of this Special Issue, “Application of Fuzzy Control in Computational Intelligence”, is to curate the new development and application of fuzzy control in the field of computational intelligence to cope with obstacles in artificial intelligence and automation technology. The Special Issue is available online at: https://www.mdpi.com/journal/processes/special_issues/fuzzy_control_computational_intelligence.

1. Model-Based Fuzzy Control Development for Stochastic Systems

Recently, researchers have been paying attention to approaches of model-based fuzzy control for stochastic systems. The model-based fuzzy control was developed using the Takagi–Sugeno fuzzy model, which can be used efficiently to approximate physical nonlinear systems. In accordance with a modeling method, a Takagi–Sugeno fuzzy model, established on a stochastic family of differential equations and membership functions, was represented for nonlinear stochastic systems in [1]. According to this type of fuzzy model, the technology of parallel-distributed compensation was applied to [1] establish the static output controller. A line-integral Lyapunov function was applied to derive several non-insufficient conditions to achieve the mean square of asymptotical stability. In the line-integral Lyapunov function, a possible conservatism that was produced by the derivative of the membership function was removed in order to improve the sufficient conditions that are related to relaxation. By using the projection lemma, those conditions were transmitted to the linear matrix inequality form that will be able to deal with by the convex optimization algorithm.

Taking into consideration multiple performance constraints in the model-based fuzzy control approach, a powerful fuzzy controller designed for stochastic nonlinear systems was investigated in [2]. For the purpose of solving the obstacle of stochastic behaviors in nonlinear systems, the covariance control theory and passive control theory were chosen based on the aspect of energy. Additionally, the pole placement method was noted as obtaining better system reactions for transient behaviors. Nevertheless, as the settling time or converge rate of the system is required to be faster, it is known that the control inputs and maximum overshoot of the system responses may both increase simultaneously. Because of this, the fuzzy controller design approach also takes the input constraint into account when determining the maximum value for the control gain. Furthermore, the perturbation of the nonlinear systems was addressed by applying an efficient robust control strategy.

Usually, the COVID epidemic, ship stabilizers, network systems, chemical changers, and hydraulic machines are several examples of physical systems where time delay is a prevalent consequence that degrades control performance during signal transmission. In relation to passivity performance, a delay-dependent stability criterion for Takagi–Sugeno fuzzy systems with multiplicative noise was addressed. For the practical control problem, the general situation of an interval time-varying delay was taken into consideration. In order to obtain some suitable relaxed conditions and prevent the derivative of the membership function, an integral Lyapunov–Krasovskii function was presented for the criterion in [3]. In addition to handling the delay terms and ensuring that the available derivative of the time-varying delay is greater than one, a free-matrix inequality was used.

2. Extending the Model-Based Fuzzy Control to Type-2 Fuzzy Models

For a class of nonlinear systems, the Type-2 Takagi–Sugeno fuzzy model is more capable of fully explaining the parameter uncertainties than the Type-1 Takagi–Sugeno fuzzy model. Based on the Interval Type-2 Takagi–Sugeno fuzzy model for stochastic nonlinear systems subject to actuator saturation, a fuzzy controller design methodology was proposed. Stochastic behaviors frequently appear in many practical cases and should be taken into account while designing the controllers. The controller may expand even further than what is practical to secure the system’s functioning when stochastic behaviors are at play. As a consequence, the controller design should also take the actuator saturation issue into account. In [4], utilizing Lyapunov theory, a stability analysis and a few related necessary conditions for the Interval Type-2 Takagi–Sugeno fuzzy model were conducted.

The uncertainty problem, which would significantly worsen the performance of the entire system, must be taken into account for the control of practical multi-agent systems. Owing to this, the Type-2 Takagi–Sugeno fuzzy model was applied in [5] to represent the nonlinear multiple systems with uncertainties. Type-2 Takagi–Sugeno fuzzy formation and confinement controllers were created using the fuzzy model and an imperfect premise matching technique. Hence, for nonlinear multiple systems, the Type-2 Takagi–Sugeno fuzzy control method design may be more adaptable. When solving the formation problem, the control approach examined in varies from other research in that it does not include communication between leaders. Leaders can drive followers into the defined range they created because they achieved the formation purpose. By means of the lower principles of fuzzy controllers, they can be used to accomplish a more cost-effective control goal in addition to developing an even more flexible procedure of the controller design approach to address the problem of the uncertainties admirably.

In [6], the authors compared Type-2 fuzzy logic with the traditional Perturb and Observe Method in three different scenarios to track the photovoltaics’ maximal power point, and environmental variables, such as irradiance and temperature, were considered. Systems with a high level of uncertainty (complex and nonlinear systems) are not suitable for Type-1 fuzzy logic. Type-2 fuzzy logic is more capable of addressing with linguistic uncertainties by modeling the haziness and unreliability of knowledge, hence lowering the ambiguity in a system. This technique delivers high levels of efficiency, reliability, and robustness, as shown by the results for three situations in terms of the four variables effectiveness, settling time, tracking time, and overshoot. The outcome of the algorithm developed in [6] is additionally examined and contrasted with the Perturb and Observe procedures, the other two tracking strategies. The findings of the incremental conductance approach and particle swarm algorithm demonstrated that Type-2 fuzzy logic control is superior to the three methods previously described.

3. Advanced Fuzzy Control by Combining Other Control Methods

In order to solve the complex nonlinear system problems of the fuzzy controller design, the fuzzy control method can be usually employed combined with other control approaches. For example, exchange rate forecasting is an important, but difficult, undertaking because of the fuzziness and uncertainty of the related data brought on by various influencing factors. Nonetheless, the ambiguity of the data itself is ignored by the majority of conventional forecasting techniques. Accordingly, in [7], to be used in forecasting exchange rates, a unique fuzzy time series forecasting system was presented, and it was found to have an excellent capacity to handle the inconsistencies and ambiguities in the data. This system is based on a combined fuzzification method and an advanced optimization algorithm. Clearly, the data “decomposition and ensemble” scheme was practiced in carrying out the preparation of the data process. The observed data were fuzzed using the combined fuzzification approach, and the best model parameters were found using a sophisticated optimization algorithm.

The authors of [8] introduced an adaptive fuzzy sliding-mode control architecture for complex nonlinear systems with specified performance. Firstly, the constrained variable was first converted into an unconstrained one using an error transformation. Then, to approximate the unknown dynamics, a fuzzy logic system was built. Following this model, a nominal adaptive linearizing controller was created, improving the overall closed-loop system’s tracking performance by including a composite algorithm based on a serial-parallel model. In order to solve the so-called “loss of controllability” problem, an inbuilt smooth-switching technique transfers control to an additional sliding-mode controller until the threat has been safely avoided. The closed-loop signals were guaranteed to be semi-globally, uniformly bound, and stable using the combined design strategy proposed in [8].

The fault diagnosis of the electronic control unit establishes the fault point and the fault type using the network’s completion information for the vehicle controller unit gateway and then displays the precise fault information through the meter/virtual terminal or alert to finish the troubleshooting process. At present, fuzzy logic algorithms, neural network algorithms, support vector machine techniques, and other intelligent algorithms are frequently employed. In [9], the fuzzy logic algorithm was discussed with the fault diagnosis problem regarding the creation of a knowledge base, the inference engine’s efficiency, and professional experience.

In [10], for a class of undisclosed separate nonlinear systems with iteration-varying original error, iteration-varying system parameters, iteration-varying external load, iteration-varying expected outputs, and iteration-varying control direction, an iterative learning control problem was taken into consideration. The iteration-varying uncertainties simply needed to meet a few boundedness requirements; no specific structure, such as the high-order internal model, was required. In [10], the law of an iterative learning control was proposed with an adaptive iteration-varying fuzzy system to master all of the uncertainties and succeed in the learning control goal. Additionally, it demonstrated a necessary condition for creating adaptive gains and demonstrated that the learning error would converge to a small value as long as the trial number is significant enough.

4. Applications of Model-Based Fuzzy Control to Practical Nonlinear Systems

In the majority of useful industrial systems, including those found in aircraft, ships, robotics, and power plants, the fuzzy control method has been wildly investigated by researchers. Two papers in the Special Issue presented fuzzy control applications to robot systems. In [8], for omnidirectional mobile robots with specified performance, an adaptive fuzzy sliding-mode control scheme was suggested. The aim of [11] was to design a fuzzy motion control algorithm for a monocular vision system that was developed based on the coordinated movement of two humanoid robots. The proper gait mode was chosen using the fuzzy motion control technique. The two humanoid robots may work together to collaboratively advance toward the front of the target object while actively searching for it, lifting it, and taking it to the platform. Through the control terminal, fuzzy procedures were used to manage the synchronized movement job.

The generation and control problem of nonlinear multi-boiler systems was resolved in [5] by the development of an interval Type-2 fuzzy control design approach. In [5], the simultaneous control of several boiler systems was accomplished using an effective fuzzy control theory based on the leader-following multi-agent system. In [12], based on data from the Automatic Identification System (AIS), the Takagi–Sugeno fuzzy observers gain design algorithm was created to estimate ship motion. The path of ships must be precisely estimated in order to address the safety issue. To estimate the shipping path using AIS data, nonlinear observer design methods have been researched in the literature. However, since some dynamic ship systems are more complicated than others, it was difficult to directly establish the nonlinear observer design method. In [12], the nonlinear ship dynamic systems were represented by the Takagi–Sugeno fuzzy model. A fuzzy observer design approach was created to address the issue of estimating utilizing AIS data based on the Takagi–Sugeno fuzzy model. In addition, a unique algorithm can strategically alter the fuzzy observer’s observing gains. By using the suggested algorithm, the estimation goals can be met with a more appropriate or superior observer.