Aiming at the attack and defense game problem in the target-missile-defender three-body confrontation scenario, intelligent game strategies based on deep reinforcement learning are proposed, including an attack strategy applicable to attacking missiles and active defense strategy applicable to a target/defender. First, based on the classical three-body adversarial research, the reinforcement learning algorithm is introduced to improve the purposefulness of the algorithm training. The action spaces the reward and punishment conditions of both attack and defense confrontation are considered in the reward function design. Through the analysis of the sign of the action space and design of the reward function in the adversarial form, the combat requirements can be satisfied in both the missile and target/defender training. Then, a curriculum-based deep reinforcement learning algorithm is applied to train the agents and a convergent game strategy is obtained. The simulation results show that the attack strategy of the missile can maneuver according to the battlefield situation and can successfully hit the target after avoiding the defender. The active defense strategy enables the less capable target/defender to achieve the effect similar to a network adversarial attack on the missile agent, shielding targets from attack against missiles with superior maneuverability on the battlefield.

In order to analytically evaluate the effects of different maneuvering strategies, we derive a series of closed-form solutions of the miss distance that are applicable to higher-order guidance system models. Instead of adopting the simplified zero-lag missile model, our solutions are closer to reality. First, based on the linearization of the guidance loop, the closed-form solutions of various guidance models are derived. For the first-order system, the confluent hypergeometric function is introduced to derive the solutions of the miss distance due to heading error and target maneuver; for the higher-order system in binomial form, the frequency and time domain expressions for the miss distance are obtained through frequency domain analysis and inverse Laplace transform; for the higher-order guidance systems with arbitrary forms, the power series solutions of the miss distance are given based on the adjoint system. Secondly, the effectiveness of step and weave maneuvers is analyzed based on the closed-form solutions, and the accuracy of these solutions is validated. Finally, an optimal maneuvering strategy based on the closed-form solutions is proposed. This strategy offers significantly better evasion performance than the conventional maneuvering strategy, as evidenced by both linear and nonlinear simulation results.

An investigation of the total pressure gain (TPG) in rotating detonation combustors (RDCs) with dilution holes is conducted by the experimental method in this study. The effects of pressure ratios (PR = 4.2–7.2) and equivalence ratios (ER = 0.5–1.5) on the total pressure gain are analyzed in four models, i.e., models A–D, of different throat areas A3.1 and dilution hole area A3.5. When the PR is small, the lowest ER causes the highest TPG, and when the PR is high, the highest ER leads to the highest TPG in Model A. While in models B–D, as ER increases, the TPG increases gradually in all the cases. Comparing the level of TPG between the four models, it is found that the increment of A3.1 and A3.5 results in the enhancement of the TPG. The present study's TPG shows superiority when compared with that of traditional RDC, which indicates that the RDC with dilution holes is more promising for achieving positive TPG in specific configurations. An empirical model considering the throat area A3.1, dilution hole area A3.5, outlet area A8, and heat (released by the fuel combustion) release rate Qv is proposed to better predict the performance of different RDC configurations. Positive total pressure gain is inferred to be promisingly attained at a high A3.1/A8, low A8/A3.5, and a high Qv. Total pressure measured by total pressure rake is verified by comparing with the data calculated by Mach-corrected-static-pressure and mass flow function methods, with relative errors in ±4% and ±15%, respectively.

This paper addresses the active target protection problem in a three-player (Target–Attacker–Defender, TAD) conflict by proposing a cooperative integrated guidance and control (IGC) strategy. Unlike previous studies that have designed guidance and control loops separately, this work establishes an IGC model by linearizing both the translational motion and the rotational motion of the vehicles, thereby generating actuator commands directly. This model integrates the kinematics and short-period dynamics, providing a more comprehensive and accurate representation of the vehicles’ characteristics. Based on the linearization and order reduction, differential game theory and the sweep method are employed to derive and analytically solve the Riccati differential equation, yielding an optimal control strategy with an explicit expression. The theoretical rigor of the proposed approach is ensured through a proof of optimality sufficiency. Furthermore, factors influencing the computational accuracy of the Riccati equation solution, including the singular values of the control matrix and condition numbers of the solution matrix, are analyzed. Taking into account the dynamic response and limitations of the actuators, numerical simulations demonstrate the effectiveness and superiority of the proposed IGC strategy in intercepting the attacker and protecting the target compared to traditional separated guidance and control designs.