## 1 Introduction  
Researchers solving problems in engineering, computer science, biological, and physical sciences are developing advanced mathematical methods for control purposes. Technological advances have had a significant impact on the implementation of new analytical methods for solving nonlinear problems [1]. In most cases involving nonlinear control systems, states may not be completely measurable, which makes it difficult to solve complex control engineering problems. Other major difficulties in the area of control design are the use of a range of different models and concepts, a lack of standardization in the parameters, a lack of adequate control techniques, external disturbances, and the high level of nonlinearity of the equations that govern processes. A further issue is a lack of knowledge of important variables, since the states of the system can directly reflect the nature of the control design process allowing for high performance to be achieved [2]. It can therefore be stated that it is necessary to use advanced estimation, control, and optimization techniques to guarantee optimal nonlinear system performance. Knowledge of the system is important to understand its control requirements; however, the nonlinearities are often so complex that the control design for an adequate performance of the system is difficult [3; 4; 5; 6]. Over time, new control strategies have emerged to ensure optimal system performance, and the estimation of states is vitally important for the development of feedback laws that allow for the avoidance of interruptions, stops, or process failures. For these reasons, it is important to develop devices called observers to estimate the missing states, and at the same time, to address the lack of online sensor measurements, the high cost of sensors, and the long laboratory analysis times [7; 8]. Artificialneural networks have successfully demonstrated their feasibility and excellent performance in terms of describing highly nonlinear systems [9; 10]. This is mainly due to their simplicity of deployment flexible architecture, robustness, and online learning. Several researchers have focused on the applications of neural networks applications to the identification, performance evaluation, and control of nonlinear plants [11; 12]. However, most of these schemes require a complete knowledge of the variables of the mathematical model, which is not always possible. For this reason, Recurrent High Order Neural Networks (RHONN) have proven to be very useful for identification and control problems, and artificial neural networks and control strategies have been proposed to increase the system performance [13; 14]. One of the main challenges in optimal control of nonlinear systems is tuning its parameters for an optimal solution. This problem has been addressed in the past by using metaheuristic techniques, since they have proved to be effective when dealing with complex systems. Metaheuristic optimization algorithms are well suited for problems with unknown search spaces, unlike deterministic algorithms. These optimization techniques find an optimal solution from a set of candidate solutions and have been used in almost every branch of science, technology, and engineering. In the last few years, a subset of metaheuristic algorithms inspired from nature, called swarm intelligence, have become more popular due to their simplicity, versatility, and flexibility [15]. Ant Lion Optimizer (ALO) has been successfully used in modeling, control, scheduling, and management with application in distributed generation, mechanics, thermal systems, and renewable energy, among others [16; 17; 18; 19]. In [20; 21], an ALO was used for parameter identification of the controller gains in a two-area thermal power system. The objective was to obtain optimal values for the control law, speed regulation, and frequency for both areas in presence of disturbances. A comparison of ALO performance with other algorithms based on standard deviations and objective functions was reported.