A numerical study is conducted to investigate the aerodynamic augmentation characteristics within a longitudinal V-shaped formation of hypersonic vehicles, using X-43A as the baseline geometry. Reynolds-Averaged Navier-Stokes (RANS) simulations, employing the Shear Stress Transport (SST) k-! turbulence model, are performed at Mach 6. The credibility of the numerical methodology is established through validation against available flight data and comprehensive grid-independence studies for both single-vehicle and multi-body configurations. The results reveal a dualistic aerodynamic interference mechanism. At low angles of attack (0 degrees-4 degrees), oblique shock waves from the lead vehicle impinge on the upper-echelon trailing vehicles, creating a high-pressure region that significantly enhances their lift-to-drag (L/D) ratios. However, this beneficial effect diminishes as the angle of attack surpasses 4 degrees due to the fixed formation geometry. Concurrently, the lower-echelon vehicles are persistently subjected to the lead vehicle's downwash field, resulting in a consistent degradation of aerodynamic performance across all tested angles of attack. These findings delineate the narrow performance-gain window for the fixed formation, highlighting its inherent limitations. The study concludes that while properly configured formations can yield substantial aerodynamic benefits, future research could focus on adaptive formation strategies to dynamically exploit favorable interference while mitigating adverse effects across a wider flight envelope.

Spacecraft pursuit–evasion in contested environments is complicated by strategic incompleteness: the evader can switch maneuvering modes and deploy multi-domain countermeasures that degrade the pursuer’s perception, leading to non-stationary information and distributionally ambiguous interference statistics. A dynamic time-window Nash equilibrium framework is developed for linearized Local Vertical Local Horizontal (LVLH) relative motion under interference-induced uncertainty. Perceptual degradation is modeled via an evidence–theoretic belief representation, and the Jensen–Shannon (JS) divergence is introduced to quantify discrepancies between nominal and interference-corrupted beliefs. The divergence metric drives an adaptive time-window partitioning policy and an uncertainty-aware running cost that balances nominal performance objectives with robustness regularization during high-degradation intervals. In each time window, sufficient conditions are provided for the existence of a local Nash equilibrium, and equilibrium strategies are characterized by the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation. A global consistency result is established: assuming state continuity, additive cost decomposition, and dynamic-programming compatibility at window boundaries, concatenating the window-wise equilibria yields a Nash equilibrium over the entire horizon. Unlike conventional receding-horizon differential games with a fixed replanning grid, the proposed policy partitions the horizon online in response to perceptual-degradation events and stitches adjacent windows through a continuation value. This boundary stitching enables the global consistency guarantee under additive costs and state continuity. To hedge against ambiguity in interference intensity, a variational distributionally robust optimization (DRO) problem with moment-constrained ambiguity sets is formulated, and the dual worst-case distribution is derived. The resulting Karush–Kuhn–Tucker (KKT) system is reformulated as a finite-dimensional variational inequality, for which an accelerated Alternating Direction Method of Multipliers (ADMM) operator-splitting solver is proposed for efficient real-time computation. Numerical simulations validate the framework and demonstrate improved robustness and computational scalability under time-varying interference compared with fixed-window baselines.

In the domain of autonomous unmanned aerial systems, pursuit-evasion games are critically challenged by adversarial information asymmetry and real-time operational constraints. Traditional methods often fail under the evader’s active multi-domain interference relying on fixed time-windows or passive noise assumptions which induces non-stationary perceptual uncertainty and strategic incompleteness. To address this, a dynamic time-window Nash equilibrium framework is proposed that adaptively adjusts strategy-update intervals based on real-time interference intensity, effectively balancing computational efficiency with strategic optimality. The evader employs a variety of multi-dimensional interference tactics, such as electromagnetic suppression, infrared decoys, and laser blinding. These tactics are modeled via Pignistic probability divergence and Jensen-Shannon metrics, which serve to characterize the extent of degradation in the pursuer’s situational awareness. Polar-coordinate kinematics are integrated to characterize UAV dynamics, while a variational distributionally robust optimization (VDRO) method is employed to resolve bounded uncertain parameters. The existence and consistency of local and global Nash equilibria is rigorously established under conditions of continuity, convexity, and bounded uncertainty. Numerical simulations demonstrate the framework’s superiority, achieving a 98.3% capture success rate and reducing the average interception time by 8.08% compared to fixed time-window methods, under high-interference scenarios. This work integrates game-theoretic equilibrium theory with adaptive robustness, offering a scalable solution for the pursuit-evasion games in highly contested environments characterized by significant interference.

The evaluation of air combat decision-making has garnered significant attention due to its potential to effectively mitigate losses resulting from erroneous decisions. However, existing research primarily focuses on static evaluation methods. Therefore, this paper proposes a dynamic multi-round decision evaluation method based on the characteristics of multi-round unmanned aerial vehicle air combat under opponent's optimal strategy. In order to determine objective weights, an improved multi-attribute decision making method is proposed, which incorporates the proximity as a correction coefficient for evaluation indicators, utilizing the cosine similarity instead of Euclidean distance, and incorporating both actual and theoretical objective weights to prevent data mutations. Subsequently, the game theory is employed to reasonably adjust subjective and objective weights to obtain comprehensive weights. To address the issues related to the ambiguity and randomness during the evaluation process, a reverse cloud generator is utilized to determine the center of gravity of the cloud model using comprehensive weights while employing the weighted deviation degree for evaluating air combat decision-making effectiveness. By activating the cloud generator through the cloud model, the optimal strategies for each round of air combat are determined, thereby completing the dynamic evaluations for multi-round sequential decision-making processes. Finally, the feasibility and effectiveness of the proposed method are verified through simulations.

This paper addresses the critical challenge of adversarial decision-making in multi-UAV systems under the condition of incomplete information about the strategies of opponents. While existing methods largely assume complete knowledge of opponent behavior, real-world applications often involve significant uncertainty, making such assumptions impractical. To bridge this gap, we propose a distributionally robust optimization (DRO) framework tailored for multi-UAV adversarial decision-making, where strategic uncertainty is explicitly accounted for using the Wasserstein distance. Our approach integrates a novel adversarial game situation assessment model that incorporates angular relationships, significantly enhancing the accuracy of situational awareness compared to traditional methods. The model constructs a game-theoretic decision framework using the artificial potential field (APF) method, where the property of zero resultant force at equilibrium ensures stability and rapid convergence in dynamic environments. To address the uncertainty introduced by incomplete strategies, we leverage the DRO framework, optimizing the game decisions against the worst-case scenario within a distributional robustness context. The resulting problem is reformulated into a convex optimization program, enabling the computation of Nash equilibria through efficient numerical methods. Extensive simulations, conducted under varying adversarial scenarios, validate the proposed approach’s ability to deliver robust decision-making strategies that outperform conventional methods, ensuring the Red side’s superiority even in the face of strategic uncertainties. This work contributes a novel methodology for multi-UAV adversarial decision-making, expanding the applicability of game-theoretic models in uncertain and dynamic environments.

To address the confrontation decision-making issues in multi-round air combat,a dynamic game decision method is proposed based on decision tree for the confrontation of unmanned aerial vehicle (UAV) air combat.Based on game theory and the confrontation characteristics of air combat,a dynamic game process is constructed including the strategy sets,the situation information,and the maneuver decisions for both sides of air combat.By analyzing the UAV’s flight dynamics and the both sides’information,a payment matrix is established through the situation advantage function,performance advantage function,and profit function.Furthermore,the dynamic game decision problem is solved based on the linear induction method to obtain the Nash equilibrium solution,where the decision tree method is introduced to obtain the optimal maneuver decision,thereby improving the situation advantage in the next round of confrontation.According to the analysis,the simulation results for the confrontation scenarios of multi-round air combat are presented to verify the effectiveness and advantages of the proposed method.

Due to the unique architectural structures between buildings, wind disturbances often exhibit unmeasured nonlinear characteristics, posing significant challenges to maintaining the stability of quadrotor unmanned aerial vehicles (QUAVs) operating in such environments. This study proposes an adaptive disturbance observer-based trajectory tracking control method designed to handle complex, nonlinear, time-varying disturbances that are not fully measurable. By integrating a radial basis function neural network (RBFNN) into the observer, this method effectively captures and estimates the unquantifiable nonlinear disturbances during operation. Additionally, the embedded model control (EMC) technique is incorporated into the RBFNN, allowing the weight updating law of the network to automatically self-tune. To ensure robust stability of the closed-loop system, hierarchical sliding mode control (HSMC) is applied. The numerical simulations and flight experiments validates that the proposed method is effective.

This paper models the vibration of hypersonic vehicles based on Hamilton’s principle. By treating the vibration of a hypersonic vehicle as equivalent to that of a free-free beam, the Hamiltonian function of the system is derived. A nonlinear potential energy term is then introduced to yield the modified Hamiltonian function. Using modal decomposition, the equation for the vibration amplitude is derived. Considering only the first-order mode, the Hamiltonian function is expressed accordingly, and Hamilton’s equations are established. The Rayleigh dissipation function, control inputs, and generalized aerodynamic forces are incorporated into the Hamiltonian equations, ultimately transforming them into the system’s state-space equations. In this paper, the state equations obtained are nondimensionalized, and computer simulations are subsequently conducted on the nondimensionalized state equations.

To address the maneuver decision-making problem in multi-round air combat game confrontation of unmanned aerial vehicles(UAVs), a multi-algorithm voting feature selection-based lightweight gradient boosting learning algorithm(MV-LightGBM) is proposed. This algorithm applies an innovative hybrid decision-making framework that decouples the complex maneuvering decision process into two hierarchical levels: strategic judgment and tactical execution. For the strategic judgment level, a two-player zero-sum game model based on incomplete information is constructed. By solving for the Nash equilibrium, it accurately determines whether maneuvering is necessary in the current situation, thereby avoiding unnecessary actions when in an advantageous state. For the tactical execution level, when the game model indicates the need for maneuvering, a LightGBM model trained with robust feature selection (using a multi-algorithm voting mechanism) is activated to efficiently select the optimal specific maneuvering action. The proposed algorithm is validated via simulations, demonstrating its high accuracy and efficiency in UAVs air combat decision-making.

The optimisation of manoeuvring strategies for unmanned aerial vehicles (UAVs) in air combat has become a crucial concern as UAV technology continues to advance. This paper proposes an evolutionary game-based decision-making method to guide the manoeuvre behaviour of UAVs in air combat. Initially, a kinematic freedom UAV model and an air combat manoeuvre model are established. Subsequently, the evolutionary game process is described in terms of replicated factor dynamics, and the evolutionary stabilisation strategy in evolutionary game theory is employed to optimise the UAV's manoeuvre strategy. Finally, through comparison with traditional methods, the effectiveness of this approach in enhancing both survivability and combat effectiveness of UAVs is verified. The experimental findings demonstrate that this proposed method significantly enhances the survivability and combat effectiveness of UAVs in air combat, which holds great practical significance.

To investigate the influence of stochastic processes and flight attitude on the structural reliability of hypersonic vehicles, a novel dynamic reliability approach is proposed based on a vibration model with stochastic processes. By analyzing the aerodynamic forces of the five surfaces for a hypersonic vehicle, a vibration model of the cantilever beam equivalent to the structure of vehicle is constructed with considering both aerodynamic and stochastic aerodynamic forces. Then, using the stochastic averaging method, the vibration equation is transformed into an ITÔ equation of the vibration amplitude. Based on the equation, a dynamic structural reliability model of the vehicle is established by applying the backward Kolmogorov equation, which can be calculated using the implicit difference method. The simulation results are presented to verify the effectiveness of the proposed dynamic reliability method.

In the field of calculating the attack area of air-to-air missiles in modern air combat scenarios, the limitations of existing research, including real-time calculation, accuracy efficiency trade-off, and the absence of the three-dimensional attack area model, restrict their practical applications. To address these issues, an improved backtracking algorithm is proposed to improve calculation efficiency. A significant reduction in solution time and maintenance of accuracy in the three-dimensional attack area are achieved by using the proposed algorithm. Furthermore, the age-layered population structure genetic programming （ALPS-GP） algorithm is introduced to determine an analytical polynomial model of the three-dimensional attack area, considering real-time requirements. The accuracy of the polynomial model is enhanced through the coefficient correction using an improved gradient descent algorithm. The study reveals a remarkable combination of high accuracy and efficient real-time computation, with a mean error of 91.89 m using the analytical polynomial model of the three-dimensional attack area solved in just 10 -4 s, thus meeting the requirements of real-time combat scenarios.

Structural reliability analysis of hypersonic vehicles is of paramount importance in the field of aeronautics and astronautics. This study is dedicated to exploring the impact of aerodynamic heating on the reliability of a hypersonic vehicle, with a particular focus on calculating the thermal stresses induced by aerodynamic heating. Building on the Eckert reference temperature method, a heat transfer iterative method is developed to calculate the wall temperature and heat flux in order to determine the dynamic wall temperature distribution of the vehicle. Utilizing this distribution, the thermal stresses on the vehicle’s body are calculated through the application of equivalent load theory and integrated into a hypersonic vehicle dynamic reliability model, thereby effectively assessing the impact of thermal stresses on structural reliability, where the aerodynamic forces are computed using shock expansion wave theory and piston theory. Ultimately, the study presents simulation results for three distinct flight scenarios, offering substantial support and reference for related research endeavors.

Aiming to enhance autonomous air combat capabilities for armed helicopters, a novel dynamic integrated weapon/flight control design method is proposed in the presence of disturbances based on a heuristic dynamic programming (HDP) algorithm. Driven by the underactuated, highly coupled, nonlinear characteristics of helicopters, the proposed mathematical model incorporates weapon delivery rotation to achieve precise aiming and reduce controller complexity. To realize dynamic gaming of the target and the helicopter, two critical indexes are introduced: aiming deviation and attack occupation. While general situation assessment focuses on current air combat information, the proposed situation trend assessment integrates both current data and future maneuver trends, influencing the subsequent movements of both the helicopter and the target. Based on this theoretical framework, near-optimal strategies for both the target and the helicopter are derived. Furthermore, for better air combat performance, this paper proposes an optimal control policy for helicopters based on an identification and an HDP algorithm under disturbances. The identification process effectively eliminates training estimation errors, while the HDP algorithm ensures boundedness, monotonicity, convergence, and optimality. Simulation experiments confirm the efficacy and practicality of the proposed control methods in addressing the challenges of integrated weapon/flight control design, demonstrating significant improvements in autonomous air combat performance.

In this article, to address the issue of accelerating convergence performance and eliminating the tracking error, an advanced optimal control method for nonlinear discrete-time systems is investigated based on an improved N-step [( ${N} +1$ )-step] gradient learning algorithm. Independent of the discount factor, this article introduces a novel tracking error index without quadratic input terms for the steady-state and convergence performances, which obtains the optimal control policy without calculating the reference control input. Compared with classic N-step gradient learning algorithms with infinite future reward assumption, the proposed algorithm investigates the (N +1)-step return with a fixed N and a step forward for finite tracking problems based on a long-term weighting parameter. Based on the above theory, value iteration (VI) and policy iteration (PI) methods are utilized to derive the convergence, monotonicity, optimality, and stability properties of the proposed algorithm, which can be conducted without the traditional assumption of zero initial functions. In the implementation of the algorithms, the actor-critic structure, constructed by four neural networks, is established to approximate the states, the value functions, and the control policy, respectively. Three simulation experiments on a helicopter system validate the efficacy and practicality of the control methods in addressing nonlinear optimal tracking challenges.

The highly nonlinear and strongly coupled flight characteristics of hypersonic aircraft systems present formidable challenges for flight attitude control. This paper proposes a nonlinear model predictive control (NMPC) method for the MIMO (Multiple-Input Multiple-Output) non-affine nonlinear attitude model of a hypersonic aircraft. Initially, the characteristics of the MIMO non-affine nonlinear attitude model for a hypersonic aircraft is investigated. Subsequently, an NMPC method based on the interior point method is proposed to formulate a flight attitude control system. Simulation results demonstrate that the proposed method exhibits rapid response, excellent stability, and effectively meets the stringent requirements for the attitude control of hypersonic aircraft.

This study proposes a decision-making model for unmanned aerial vehicle aerial combat wargaming based on an improved Lanchester equation combined with matrix game theory. The model accounts for the dynamic confrontation between multiple types of UAVs by improving the traditional Lanchester equation with visibility ratios, consumption coefficients, and probabilistic targeting. A dynamic programming approach is employed to simulate multi-stage combat scenarios, while the Min-Max algorithm is used to derive optimal strategies at each stage. The model enables real-time tactical decision-making under uncertain and fast-changing combat conditions. Simulation results demonstrate the model's effectiveness and practicality, offering a theoretical foundation for intelligent UAV swarm operations in future air combat environments.

To investigate the vibration control of hypersonic waveriders subjected to shock wave interference, the structure of a hypersonic waverider is simplified as an axially moving cantilever beam. The external force load induced by shock wave interference is incorporated to establish the corresponding vibration model of the cantilever beam. Furthermore, considering the uncertainties in airflow density and damping coefficient, appropriate adaptive update laws are designed. Subsequently, based on a double-layer sliding surface structure, a specific generalized force control law is developed to regulate both the amplitude and vibration velocity of the cantilever beam. Finally, the effectiveness of the proposed vibration model and control strategy is validated through simulation analysis.

Racing drones have attracted increasing attention due to their remarkable high speed and excellent maneuverability. However, autonomous multi-drone racing is quite difficult since it requires quick and agile flight in intricate surroundings and rich drone interaction. To address these issues, we propose a novel autonomous multi-drone racing method based on deep reinforcement learning. A new set of reward functions is proposed to make racing drones learn the racing skills of human experts. Unlike previous methods that required global information about tracks and track boundary constraints, the proposed method requires only limited localized track information within the range of its own onboard sensors. Further, the dynamic response characteristics of racing drones are incorporated into the training environment, so that the proposed method is more in line with the requirements of real drone racing scenarios. In addition, our method has a low computational cost and can meet the requirements of real-time racing. Finally, the effectiveness and superiority of the proposed method are verified by extensive comparison with the state-of-the-art methods in a series of simulations and real-world experiments.