## 1 Introduction  
Different control systems have been used in structures for many years to reduce the structural responses due to dynamic loads such as earthquakes and wind, which can cause destructive and permanent damage to the structures. These control systems are applied in various forms of passive, semi-active, and active, depending on the properties of the structure and the dynamic effect. It is known that active control systems absorb more energy than other control systems. The main reason for high energy absorption is the placement of actuators that generate the control force in every step of the seismic excitation. Generally, the use of active control systems in the structures can be provided in two different ways. The first way is the usage of an active tendon system applied on the first or each floor of the structures. The other way is the implementation of an active mass damper placed on the top floor of the structures. In the research, the active tendon control is examined. The actuators, which create the control force to absorb the energy in the structure according to the value determined by the sensors, are cross-linked to the pre-stressed tendons to realize active tendon control. The idea about the active control of structures was first introduced by [PERSON] [1] and was subsequently expanded with analytical or experimental studies. The utilization of active mass dampers and active tendons to reduce structural reactions in tall structures [2, 3], the relationship between the control forces and the structural responses [4], time delay effect [5], and the investigation of various feedback strategies for active-controlled structures [6, 7]can be examples among these studies. In addition, many studies are available in the literature either to determine the parameters of various control techniques such as H2, Hinf, linear quadratic regulator (LOR), neural network control, fuzzy logic control, sliding mode control (SMC) and proportional-integral-derivative (PID) controller or to improve the weaknesses of these techniques by comparing them with each other. For instance, a proposal of an instantaneous optimal control algorithm with a modification to reduce the time delay effect [5] was proposed. The attainment of effective solutions in the nonlinear active-controlled structures with artificial neural networks and the use of the metaheuristic algorithms to calculate the parameters of the PID, H2, and Hinf are the other stochastic based methods in the active control [8; 9; 10]. The utilization of a modified linear quadratic regulator (MLQR) was investigated to determine the degree of the system stability before the earthquake [11]. The prevention of the chattering effect with the help of a fuzzy sliding-mode control algorithm [12] was studied by [PERSON] and [PERSON]. The determination of the PID parameters with a numerical algorithm [13] was conducted by [PERSON] and [PERSON] for the control of irregular structures. The analysis of nonlinear active-controlled structures was carried out by combining a dynamic fuzzy wavelet neural emulator and the floating-point genetic algorithm [14]. The use of neural-based sliding-mode control with genetic algorithms was developed by [PERSON] and [PERSON] [15]. The comparison of the sliding mode controller without a chattering problem with PID was performed by [PERSON] [16]. The comparison of the block pulse functions with the linear quadratic regulator was proposed by [PERSON] and [PERSON] [17]. The comparison of a wavelet-based adaptive pole assignment with the linear quadratic regulator was proposed and the system was optimized via active tuned mass dampers via metaheuristics [18]. The conventional mathematical methods are sufficient to overcome some engineering problems. However, the traditional methods can cause both a loss of time and an increase in the error rate when it comes to solving some complex engineering problems. Therefore, the algorithms which contain the mathematical expressions are needed to achieve successful results in the appropriate time frame.