Ahmet Sakalli

Fuzzy cognitive maps learning using Artificial Bee Colony optimization

Most of the dynamic systems are hard to express in mathematical models due to their complex, nonlinear and uncertain characteristics. Thus, advanced methodologies are needed, using human experience, present expert knowledge and historical data. Hence fuzzy cognitive maps are quite convenient, simple, powerful and practical tools for simulation and analysis of these kinds of dynamic systems. Yet, human experts are subjective and cannot handle relatively complex fuzzy cognitive maps (FCMs); hence, new approaches are required to develop for an automatic building of fuzzy cognitive maps. In this study, Artificial Bee Colony (ABC) global optimization algorithm is proposed for the first time in literature for an automated generation of fuzzy cognitive maps from historical data. An ERP management model is used as the illustrative example to obtain the data for training and validation. The obtained results show the success of the ABC learning for FCMs.

Analysis of the performances of type-1, self-tuning type-1 and interval type-2 fuzzy PID controllers on the Magnetic Levitation system

In this paper, we will compare the closed loop control performance of interval type-2 fuzzy PID controller with the type-1 fuzzy PID and conventional PID controllers counterparts for the Magnetic Levitation Plant. We will also compare the control performance of the interval type-2 fuzzy PID controller with the self-tuning type-1 fuzzy PID controllers. The internal structures of implemented controllers are firstly examined and then the design parameters of each controller are optimized for a given reference trajectory. The paper also show the effect of the extra degree of freedom provided by antecedent membership functions of interval type-2 fuzzy logic controller on the closed loop system performance. The real-time experiments are accomplished on an unstable nonlinear system, QUANSER Magnetic Levitation Plant, in order to show the superiority of the optimized interval type-2 fuzzy PID controller compared to optimized PID and type-1 counterparts.

Boundary function based Karnik-Mendel type reduction method for Interval Type-2 Fuzzy PID controllers

In this paper, we will present a Boundary Function (BF) based type reduction/ denazification method for Interval Type-2 Fuzzy PID (IT2-PID) controllers. Thus, we have presented a novel representation of the optimal Switching Points (SPs) of the Karnik Mendel (KM) method by first decomposing the IT2-FPID controller into SubControllers (SCs) and then derived Boundary Functions (BFs) to determine the optimal SPs of each SCs. Since the optimal SPs are calculated without an iterative algorithm, the explicit expressions of how the SPs are determined is represented in analytical structure via the proposed BFs. We have presented comparative studies where the computational time performance of the proposed BF-KM method is compared to the KM and the decomposition based KM methods. The presented results show that proposed method is superior in comparison to the other compared methods and feasible for especially real time control applications where there is a need of small sampling times.

Self-tuning PI Controllers via Fuzzy Cognitive Maps

In this study, a novel self-tuning method based on fuzzy cognitive maps (FCMs) for PI controllers is proposed. The proposed FCM mechanism works in an online manner and is activated when the set-point (reference) value of the closed loop control system changes. Then, FCM tuning mechanism changes the parameters of PI controller according to systems’ current and desired new reference value to improve the transient and steady state performance of the systems. The effectiveness of the proposed FCM based self-tuning method is shown via simulations on a nonlinear system. The results show that the proposed self-tuning methods performances are satisfactory.

Heuristic bubble algorithm for a linehaul routing problem: An extension of a vehicle routing problem with pickup and delivery

In this study, a further extension of the vehicle routing problem with pickup and delivery (VRPPD) is considered. The VRPPD problem is seen in many practical applications as logistic, distribution and transportation. However, a formal definition of the VRPPD cannot fully represent the real-life daily macro routing problem. For this reason, firstly, a new model of the very close to real-life problem is defined. Secondly, a novel heuristic algorithm with a new objective function is proposed to solve the daily macro routing problem. The proposed nature-inspired algorithm called as Heuristic Bubble Algorithm (HBA) is suitable for the proposed problem because of its particular new operators and fast response. The Matlab simulation results motivate that the proposed model and HBA is capable of solving real-life macro routing problems.

Concept by Concept Learning of Fuzzy Cognitive Maps

Fuzzy cognitive maps (FCM) are fuzzy signed directed graphs with feedbacks; they are simple and powerful tool for simulation and analysis of complex, nonlinear dynamic systems. However, FCM models are created by human experts mostly, and so built FCM models are subjective and building a FCM model becomes harder as number of variables increases. So in the last decade several methods are proposed providing automated generation of fuzzy cognitive maps from data. The main drawback of the proposed automated methods is their weaknesses on handling with large number of variables. The proposed method brings out a new strategy called concept by concepts approach (CbC) approach for learning of FCM. It enables the generation of large sized FCM models with a high precision and in a rapid way using the historical data.

The simplest interval type-2 fuzzy PID controller: Structural analysis

In this paper, we will present analytical derivations of the simplest the Interval Type-2 Fuzzy PID (IT2-FPID) controller output which is composed of only 4 rules. Thus, we will first propose a new visualizing method called Surface of the Switching Points (S-MAP) in order to better analyze the derivation of the Switching Points (SPs) of the Karnik-Mendel algorithms. We presented mathematical explanation of the S-MAP and showed that the SPs are determined by only two Boundary Functions (BFs) for the simplest IT2-FPID controller. We will then give the simplified analytical derivation of the simplest IT2-FPID controller around the steady state via the employed BFs and S-MAP. We have illustrated that the simplest IT2-FPID controller is in fact analogous to a conventional PID controller around the steady state. We presented the simplest IT2-FPID controller output in terms of the parameters of the antecedent IT2-FSs. We examined the effect of the design parameter over IT2-FPID control system performance. In the light of the observations, we presented a simple self-tuning mechanism to enhance the transient state and disturbance rejection performance.

Gradient Descent and Extended Kalman Filter based self-tuning Interval Type-2 Fuzzy PID controllers

In this paper, we will present two novel self-tuning structure based on the Gradient Descent (GD) method and Extended Kalman Filter (EKF) estimation to improve the control performances of Interval Type-2 (IT2) Fuzzy PID (FPID) controllers. In this context, we will derive the analytical expressions of the output of the IT2-FPID controller as a function of the design parameter, namely the Footprint of the Uncertainty (FOU) parameters. We will present the proposed GD based Self-Tuning IT2 (STIT2) FPID controller and the EKF based STIT2-FPID controller structures. These self-tuning structures update the FOU design parameter so that the size of the FOU of the IT2 fuzzy sets is tuned in an online manner. The adjustment of the FOU parameter results with a hybrid controller behavior combining the aggressive nature of the Type-1 (T1) FPID and the robust nature of the IT2-FPID controllers. We will present simulation results where the proposed GD-STIT2-FPID and EKF-STIT2-FPID controllers are compared with their IT2 and STT1 counterparts. The results will show that the self-tuning IT2-FPID controller has ability to improve overall reference tracking and disturbance rejection performances in comparison with its T1, self-tuning T1, and IT2 counterparts.

On the fundamental differences between the NT and the KM center of Sets Calculation Methods on the IT2-FLC performance

In this paper, we will present the fundamental differences of Nie-Tan (NT) and the Karnik-Mendel (KM) Center of Sets Calculation Methods (CSCMs) on the Interval Type-2 (IT2) Fuzzy Logic Controller (FLC) performance based on analytical derivations. We will derive the Fuzzy Mappings (FMs) of the IT2-FLCs and then investigate how the IT2-FMs are affected by the CSCMs in terms of the Footprint of Uncertainty (FOU) parameters. We will also present a special case where the resulting FM of the KM reduces to its NT counterpart and show that the NT CSCM can be seen as an approximation of the KM CSCM. We will examine three different FOU parameter settings to show that for certain FOU parameter settings the IT2-FLC where the NT CSCMs is employed loses its FOU from a mathematical point of view. We will also present two necessary conditions for the design of the IT2-FLC so that the resulting controller has a symmetrical control surface and is capable to eliminate the steady state error of the system response. Then, by taking account these conditions, we will investigate the gain variations of the IT2-FLCs in terms of the control performance objectives. Based on the observations, we will recommend design guidelines for the IT2-FLCs. The presented results will show that although the NT CSCM has a relatively easier design phase and a closed form representation which might be an enabler for theoretical analyses of the IT2 FLCs, the KM CSCM seems to be superior in overall since it is capable to generate smooth and aggressive control actions which cannot be accomplished by its NT counterpart.

Online fuzzy rule weighting method for fuzzy PID controllers via Big Bang-Big Crunch optimization

In this study, a novel online tuning method is proposed for fuzzy PID controllers via rule weighting. The rule weighting is performed with a fast evolutionary algorithm called Big Bang - Big Crunch (BB-BC) optimization algorithm which has a low computational time. In this study, the rule weights are selected as tuning parameter of fuzzy PID controller instead of structural parameter in order to improve the transient and steady state performance of the process. The BB-BC algorithm calculates the optimal rule weights that force the process output to follow the reference signal with an applicable control signal at each sampling period. The effectiveness of the proposed online rule weighting method is demonstrated on heat transfer process (PT-326 Process Trainer) in real time with comparisons. The results illustrate that the proposed online rule weighting method significantly improves the performance of the fuzzy PID controller structure.