Today, most existing mobile agents are controlled manually using remote controls that operate on radio channels. However, this manual control poses several challenges, including the need for specialized operator training, limited operational range, and dependency on weather conditions [1,2].
A mobile agent can be a software or hardware entity capable of performing various tasks within a network or on a device, such as carrying information, conducting computations, and interacting with other agents or the environment [3,4].
Controlling mobile agents requires qualified specialists. For example, in the U.S. military, experienced Air Force pilots undergo a full year of training to become proficient mobile agent operators -a task that, in some cases, can be more demanding than piloting an aircraft. Operator errors and mechanical failures account for most mobile agent accidents [5,6].
A new technological trend involves the development of mobile agents equipped with an even number of rotors that rotate diagonally in opposite directions. Mobile agents are just one component within a complex, multi-functional system [7,8]. Unlike manned aircraft, operating mobile agents requires additional support system components, including the agent itself, the operator's workstation, software, data lines, and other elements necessary to achieve mission objectives. Current development trends favor compact mobile agents, with a focus on simplicity of control, reliability, and maneuverability [9,10].
In model aviation and professional applications such as the civil sector, agriculture, military, law enforcement, and other fields, mobile agents are in high demand. Selecting the optimal models and control systems is crucial for effectively monitoring ground-based targets [11,12].
Thus, pilotless mobile agents present a more efficient and economical alternative to manned aircraft for many tasks [13][14][15].
The main challenge in controlling mobile agents lies in the reliance on centralized control systems, where the control center serves as a vulnerable element; if communication with it is lost, further control becomes impossible. In contrast, decentralized control faces issues with coordinating and circulating large volumes of information, leading to slower response times. A promising alternative is a network-centric approach, which allows control to be transferred to an alternative center when needed [16][17][18].
An analysis of recent scientific literature reveals that, although modern information technologies have advanced considerably, the network-centric approach to control remains underdeveloped compared to centralized and decentralized methods.
Three main approaches to the control of mobile agents can be identified: centralized, decentralized, and network-centric. In centralized control, a single command center issues control signals to all mobile agents. If this center is disabled or compromised, all mobile agents lose connectivity and cannot be controlled. Decentralized control, while reducing dependence on a single command point, has the drawback of coordination challenges. For example, if mobile agents need to rapidly reconfigure, a large amount of information must be transmitted to them, significantly reducing the overall speed of the control system [19,20].
The network-centric approach is designed to address the limitations of the previous models. This approach integrates all forces and resources into a single information system, enabling control objectives to be met even in dynamic, complex environments that are subject to unpredictable interference. Such interference can be irregular, intermittent, and variable, yet network-centric control is still effective under these conditions [21,22].
Consider a control network that a subset of mobile agents follows. Among the entire group of mobile agents, approximately 10% are selected as nodes that hold partial control information (Fig. 1). These nodes, equipped with control functions, form a network, and from them, one is designated as the primary control center [23,24].
Only the node mobile agents (NMA) are coordinated directly by the control center; these nodes, in turn, control the remaining mobile agents (MA). This setup minimizes communication interference since individual control of each node could overwhelm communication channels. For example, if the command is to change direction quickly, adjusting the coordinates for each mobile agent individually would require significant time. Furthermore, if there is only one primary control agent and it suddenly stops responding, is damaged, or is compromised, all mobile agents would lose direction, become vulnerable to interception, or cease to operate [25][26][27].
A network-centric system consists of a primary control mobile agent (MMA) that continuously sends commands to other mobile agents, setting parameters such as movement direction [28,29]. Alongside commands, it also relays information from the control center to the node mobile agents. If the primary control agent fails for any reason, copies of all information, including control data for all mobile agents, are preserved within the node mobile agents. In this way, an adversary would need to disable every node agent to compromise the entire network -a challenging task since the enemy cannot readily identify which agents' function as nodes. This network organization enhances the resilience of the control system. A key feature of a network-centric system is its "wandering center." If the primary control mobile agent is identified and disabled by an adversary, the stability of the system remains unaffected, as control can quickly be reassigned. A new control agent is selected from the remaining active node agents, allowing for seamless continuity. This flexibility means that control can be handed over to another node at any moment, ensuring sustained operation. In this network-centric mobile agent control system, two types of information are managed: control: this includes global coordinates transmitted from the control center to the main control agent. command: this includes the coordinates transmitted by the control agent to node agents, which then relay local coordinates to other agents. Thus, mobile agents navigate based on local rather than global coordinates, as provided by the node agents. In summary, a key strength of the network-centric approach is the use of a roving control center. If connections to the current center are lost, a new center is assigned to maintain control. This design ensures system survivability, thereby greatly enhancing the overall effectiveness of mobile agent control.
Based on the network-centric control algorithm model for mobile agents in dynamic environments and the simulation model of interacting mobile agents, it is essential to conduct experimental studies to assess parameters and evaluate the effectiveness of network-centric control.
To validate the scientific and methodological framework developed, we performed mathematical modeling to analyze the effectiveness of network-centric control for mobile agents in a dynamic environment.
The software tools used in this study include: Simulations were performed on a personal computer with an Intel® Celeron® processor (3. The minimum required percentage of node mobile agents % (nodePercentage) needed to reach the target was calculated as follows. A target is considered "hit" if both of the following conditions are met: The percentage of mobile agents that reached the target (targetHitPercentage) must be at least equal to the required percentage of mobile agents needed to hit the target (targetHitPercentage). Among the mobile agents that reached the target, there must be at least one node mobile agent (targetReachedCount > 0).
To evaluate these conditions, 100 experimental trials were conducted, using the following parameters: Number of mobile agents (numberOfAgents): 100. Minimum percentage of mobile agents required to hit the target (targetHitPercentage): 5%. Percentage of node mobile agents (nodePercentage): ranging from 1% to 20% of the total number of mobile agents. Initial (startLatitude, startLongitude) and target (targetLatitude, targetLongitude) geographic coordinates for node mobile agents. Percentage of mobile agents that lost communication (lossPercentage), randomly generated between 50% and 90%. For each agent that lost communication, the geographic coordinates were set to NULL.
The experimental results were used to plot graphs illustrating the relationship between the percentage of node mobile agents % (nodePercentage) and the probability of hitting the target (targetHitPercentage) in each experiment (Fig. 2). Based on the experimental results, the average effectiveness of target hits with varying numbers of node mobile agents was analyzed (see Table 1 and Fig. 3). From the above, it can be concluded that to achieve effective target damage (80% and above), the minimum required number of node mobile agents (nodePercentage) is between 7% and 9%. Therefore, using more than 9% of node mobile agents out of the total number of mobile agents is not advisable.
Evaluating effectiveness of network-centric control for mobile agents in a dynamic environment, using neural networks, plays a crucial role in determining the suitability of this approach for various tasks. The main stages of this method can be described as follows:
use the test set to assess the network's accuracy and efficiency under real-world conditions. analyze the results in the context of specific tasks and environmental constraints.
use the results to refine the network architecture and its parameters. adapt the network to changes in environmental dynamics and control tasks. The process of training and creating the neural network was carried out using the Deductor Studio Academic analytical platform, which provides highly efficient tools for data analysis and processing. A critical step in this process was utilizing a specially created and carefully prepared dataset to train the network.
The dataset included information from solving 1,000 different problems, which played a key role in enhancing the adaptability and accuracy of the neural network. This approach to data preparation contributed significantly to the network's ability to solve diverse tasks and ensured its high efficiency across various contexts.
For the parameters listed in Table 2, a mechanism for estimating the probability of target damage (%) based on the neural network can be applied. The number of mobile agents with which communication was lost, units. targetHitProbability Probability of hitting the target, %
The parameters from Table 2 were provided as input data for building a neural network (Fig. 4). Based on the results of the correlation analysis of the raw data, it was determined that not all fields should be used for neural network training. Only the fields listed in Table 3 are relevant, as the remaining fields have an insignificant impact on the resulting value (Fig. 5). The number of mobile agents with which communication was lost, units. targetHitProbability Probability of hitting the target, % targetHitProbability Probability of hitting the target, % The obtained dataset was used to train a multilayer perceptron neural network. The following network structure was established: five layers of neurons, with the first (input) layer containing 7 neurons, three hidden layers containing 7, 3, and 5 neurons respectively, and the fifth (output) layer containing 1 neuron. The activation function used is sigmoid. The architecture of the networkdefined by the number of layers, their sizes, and the activation function -determines its ability to solve specific tasks. This framework demonstrates how data moves through the network, from the input to the output layer, with each layer performing calculations using weights and the activation function. The backpropagation method was employed for training.
The schematic representation of the neural network structure is shown in Figure 6, where the line colors indicate the values of the weighting factors. The output of the neural network is the probability of a target being hit (%). By applying the parameters of a different task to the input, the network generates a predictive output for the probability of hitting the target (%). During the training of the neural network, the probability values of hitting the target (%) were obtained. On average, the deviation across 1,000 experiments was 3.8%. This suggests that the neural network trained using this methodology yields results that closely match the efficiency of the mobile agent control system (Table 4). The structure of the neural network selected for training resulted in the smallest relative calculation error, while errors for other network configurations exceeded 5%. Therefore, the constructed neural network can be effectively used to solve similar problems, as it accurately reflects the results and allows for the estimation of the probability of hitting the target (%) in dynamically changing environments. Additionally, the use of the neural network helped identify input parameters with minimal impact on the outcome.
This study reviews the network-centric approach as a method for enhancing the efficiency of mobile agent control systems. The key distinction of this approach, compared to others, is the use of a "wandering center." If communication with the current center is lost, a new center is appointed, ensuring the continuity of the control process. This structure guarantees the system's survivability and, as demonstrated, offers significant potential for improvement, ultimately increasing the overall efficiency of mobile agent control. The research highlights the effectiveness of network-centric control when compared to centralized control (in which no nodal mobile agents are used). It was found that as the number of nodal mobile agents increases, the effectiveness of hitting the target improves. Notably, effective performance (80% or higher) is achieved with just 9% of the total number of mobile agents functioning as nodal agents, suggesting that exceeding this threshold would not provide additional benefits.
Finally, the results from the mobile agent control system were compared with the output from the neural network training, which estimates the probability of hitting the target with a relative deviation of 3.8%. This confirms that the neural network, trained using the proposed methodology, produces results that closely align with the efficiency of the mobile agent control system.