## 1 Introduction  
High-rise buildings, towers, and long-span bridges need to be designed safely and reliably under the dynamic loads of earthquakes, wind, and vehicles. Modern structures have become longer and higher, and beautiful and economical designs have also become possible with the development of new materials and construction techniques. However, such modern structures are susceptible to excessive structural vibrations, which may induce problems in structural damage or even the loss of lives. Many approaches to structural vibration control (passive control, active control, hybrid control, etc.) have been proposed over the past decades. The passive control techniques generally dissipate the vibration energy of a structural system or change its dynamic characteristics. The passive control systems provide a reliable performance. However, it cannot be adapted by various load conditions. On the other hand, the active control techniques reduce the structural vibration using external control forces. The active control systems can be adapted by various external forces. However, the active control systems have several problems, such as stability and power requirements. The hybrid control techniques are control methods that combine passive and active control to improve control performance and safety. Among these, structural active control techniques using artificial neural networks (ANNs) were introduced in the mid-1990s. During this period, researchers used the learning ability of neural networks in the design of a controller to control structural vibration during earthquakes. Many researchers [1; 2; 3; 4; 5; 6; 7; 8; 9] have presented active control algorithms using neural networks in civil engineering. [PERSON] et al. [1] presented artificial neural networks to control the structural response of a 10-story San Jose apartment building to an earthquake simulated using real measured data. [PERSON] and [PERSON] [2] conducted a computer simulation on the active control of a three-story frame structure subjected to ground excitations. They used an emulator neural network to forecast the future response of the structure from the response in the previous steps. Then, a controller neural network was used to assess (train) the relation between the immediate history of the response of the structure and the actuator. [PERSON] and [PERSON] [3] applied an emulator neural network and a trained neuro-controller of a linear structure to active control of the nonlinear structure. Nonlinearly controlled neural networks were also used to control the response of the nonlinear structure. They then compared the effectiveness of the nonlinearly trained neuro-controller with that of the linearly trained neuro-controller and found that a trained neuro-controller can successfully control the response of nonlinear structures. [PERSON] and [PERSON] [4] applied the previously developed neuro-control algorithms to the benchmark problem of an active tendon system. [PERSON] et al. [5] showed the applicability of neural network control of civil structures subjected to seismic excitations using the force-matching concept. [PERSON] and [PERSON] [6] proposed a new ANN learning algorithm using an objective function and sensitivity to solve the problems of the conventional ANN, which has shortcomings such as a longer learning time and the need to predetermine the desired structural response. [PERSON] et al. [7] presented an algorithm for selecting the optimal number of neurons in the hidden layer of a neural network controller based on a measure of the network performance and applied neural controllers to single-degree-of-freedom (SDOF) and two-DOF systems subjected to the El Centro earthquakes. Generally, a supervised learning algorithm was adopted for ANN learning since an ANN was used to control the response of structures during the earthquakes. However, [PERSON] [8] suggested a possible alternative approach to learning in a neural network for the active control of structures without the supervision of a teacher.