# UAV Cluster Behavior Modeling Based on Spatial-Temporal Hybrid Petri Net
## 1 Introduction  
The increasing application of the new generation of artificial intelligence technology and autonomous technology rapidly in the battlefield will give birth to a new type of combat force and overturn the traditional mode of war [1; 2; 3; 4; 5]. The future war will be intelligent war. The application of a UAV cluster in a battlefield is an important part of intelligent warfare. The UAV cluster is a kind of large and complex real-time feedback system that integrates the calculation process, the communication network, the physical process, sensor network, and control system. We need a comprehensive description and analysis on the model of the UAV cluster due to the various forms of complex behavior between heterogeneous UAVs. Using the modeling and simulation method to study the relevant issues of UAV cluster combat can provide theoretical support for the development and application of this new combat style, which has important practical significance [6; 7; 8]. [PERSON] [9] proposed the hybrid stochastic timed Petri net (HSTPN) modeling method for hybrid systems featuring discrete, continuous, conflicting, time-delay, and stochastic characteristics simultaneously. [PERSON] [10] used an extended Petri net to model the obstacle avoidance system of the unmanned vehicle, and such models were converted into corresponding Simulink models. The dynamic behaviors and attributes of the obstacle avoidance system was analyzed through the simulation of MATLAB T. In [PERSON]'s [11] proposal, they labeled a hybrid Petri net model and proposed an automatic extraction technique that could simplify the model handling the state space explosion problem, which can be used for CPS modeling and verification. [PERSON] [12] proposed a compression algorithm to convert OGSPN into a generalized stochastic Petri net (GSPN), throughwhich the CPS was abstracted into several types of objects and its logical structure and working process was visually described. Considering the uncertainty of CPS, [PERSON] used a fuzzy mathematics-based method to process the compressed model of GSPN to improve the accuracy of the performance analysis. A variety of CPN (colored Petri net) models were established to represent fleet maintenance activities and maintenance management, taking into consideration the factors that have a significant impact on fleet maintenance including fleet operation, aircraft failure logic, and component failure processes [13]. [PERSON] [14] built a transition timed Petri net using the heuristic A\({}^{*}\) algorithm to deal with the scheduling in remanufacturing scheduling. [PERSON] [15] developed a Petri net model that can well deal with all AMS characteristics, and proposed a Banker's algorithm, like deadlock avoidance policy. [PERSON] [16] used hybrid Petri nets to model and analyze the operating mechanism of adaptive cruise control system and verified the feasibility of the proposed model. [PERSON] [17] proposed a CPS model based on AOP spatial-temporal Petri net, which was successfully applied in the fault detection and repair of a robot system. [PERSON] [18] proposed a CPS real-time event model based on spatial-temporal hybrid Petri nets and analyzed the reliability of the method by modeling a medical control system. [PERSON] [19] used spatial-temporal hybrid Petri nets to build and verify a CPS model. Based on formal modeling methods, [PERSON] [20] analyzed and detected the logic flaw of poor synchronization. To avoid this kind of logic flaw, [PERSON] presented a novel optimized modeling solution based on the synchronization theory of Petri nets and further improved the calculation method of the synchronic distance. Petri net is a formal graphical model, which can intuitively reveal the essence of the system operation process with a suitable modeling scheme [21; 22; 23]. Heterogeneous UAV cluster modeling is characterized by deep integration of the discrete process and continuous process, physical process, and computational process.