# Nonlinear Dynamics and Machine Learning for Robotic Control Systems in IoT Applications
## 1 Introduction  
The integration of robotic systems with advanced control methods and machine learning has become a key research focus, particularly in the context of the Internet of Things (IoT) [1, 2]. As IoT applications continue to expand across various industries [3, 4], from smart agriculture to autonomous transportation [5, 6], the demand for adaptive, real-time control systems that can handle complex, dynamic environments has grown significantly [7]. These systems must be capable of interacting with diverse sensors, processing vast amounts of data, and making intelligent decisions to optimize performance [8]. In this regard, the combination of nonlinear dynamics, machine learning, and IoT technologies offers a promising approach [9, 10]. Nonlinear control systems are well-suited for managing the complex dynamics of robotic platforms, especially those with multiple degrees of freedom [11, 12]. Traditional control techniques, such as PID and adaptive control, have been widely applied in robotics [13]. However, these approaches often struggle in environments characterized by high nonlinearity, uncertainty, and time-varying conditions. Recent advancements in machine learning, particularly deep learning and recurrent neural networks, provide new opportunities to enhance control accuracy and adaptability [14, 15, 16, 17]. By leveraging the universal approximation capability of neural networks, it is possible to model the intricate relationships between input control signals and system behavior, enabling more precise control in real-time scenarios [17]. In parallel, the integration of the IoT allows for the seamless exchange of information between robotic systems and distributed networks, facilitating real-time monitoring, control, and decision-making across large-scale environments [18; 19]. The IoT infrastructure supports the collection of sensor [20; 21; 22] data from various sources, which can be fed into machine learning models for the continuous adaptation of control parameters. This adaptability is essential in applications such as smart farming, where environmental conditions can change unpredictably, requiring the control system to respond promptly. This paper introduces a hybrid control architecture that combines nonlinear dynamics and machine learning (ML) techniques to optimize robotic control systems, specifically designed for a 20 degrees of freedom (DOFs) robotic platform [23]. The integration of ML into this system enables real-time adjustments, improving the adaptability and precision of the control strategy. This research builds on previous work by integrating nonlinear dynamic modeling with machine learning and the IoT, focusing on practical implementation and real-time adaptability in various IoT-driven scenarios [24; 25; 26; 27; 28; 29; 30; 31]. Recent studies have demonstrated the potential of machine learning techniques in robotic control. For instance, [PERSON] et al. [11] utilized a deep learning-based Model Predictive Control (MPC) framework to enhance the trajectory tracking of a three DOFs robotic leg, highlighting the advantages of data-driven models over traditional analytical methods in real-time control scenarios. Similarly, [PERSON] et al. [24] explored the application of auxiliary physics-informed neural networks to solving the forward and inverse problems of nonlinear integro-differential equations, demonstrating the efficacy of adaptive learning models in complex environments. [PERSON] and [PERSON] [32] explored the application of multi-layer neural networks in industrial robot trajectory tracking, while [PERSON] et al. [33] and [PERSON] et al. [34] applied recurrent neural networks to trajectory tracking for high-dimensional robotic systems, demonstrating the efficacy of adaptive learning models in complex environments. Moreover, the integration of the IoT with robotic control systems has been discussed extensively, particularly in smart farming applications [35; 36; 37] where real-time data processing and environmental adaptability are crucial.