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Abstract The differential games have been widely used to analyze the conflicts between intelligent agents. Motivated by the fact that the agents always have finite energy or time requirements, a novel reach‐avoid game with time limits is investigated in this work. The attacker aims to reach the target region without being captured or reaching its time limit, while the defender strives to intercept the attacker or delay it. This game is beyond the scope of the classical Hamilton‐Jacobi‐Isaacs (HJI) approach. To make the problem possible to solve, we introduce the concept of reaching region and provide the optimal strategies of the players based on it. Using these strategies, we construct a hypersurface, called the barrier, in the game state space which partitions it into two parts that lead to different outcomes of the game. In this work, the complete analytical expressions of the barrier in all possible situations are provided. The game results can be obtained by substituting the initial states into the related expression and there is barely any computational burden. Compare to the existing works, the game with time limits is more practical. Also, this work provides the foundation for analyzing general multiple‐attacker‐multiple‐defender games.

To improve the trajectory tracking accuracy, the anti-jamming performance, and the environment adaptability of a quadrotor, the paper proposes a new adaptive trajectory tracking algorithm with multilayer neural network and sliding mode control method. The major difference between other related approaches is that the paper uses the multilayer neural network in the system and the neural network is online computing in the whole process. Firstly, the paper establishes the quadrotor dynamic model and introduces the conception of Sigma-Pi neural network. Then, the paper adds the neural network to the attitude and trajectory tracking control loop. Moreover, the paper designs the adaptive neural network control law. At last, to illustrate the stability of the adaptive control law, the paper gives the Lyapunov stability analysis. Finally, to demonstrate the effectiveness of the method, the paper gives different types of simulation. Comparing with different cases, when increasing the layer of the neural network, the trajectory tracking performance becomes better. In addition, introducing multilayer neural network into the system could improve the anti-interference ability of the system and has a high-precision in tracking the desire trajectory.

In this paper, adaptive tracking control is applied to improve performances of an underactuated quadrotor helicopter with respect to attitude and position control. Firstly, the dynamic model is presented. Then a new trajectory tracking algorithm is designed by using the sigma-pi neural network and backstepping. The paper designs the sigma-pi neural network compensation control law and gives the Lyapunov-type stability analysis. Then the corresponding numerical simulations are performed by using MATLAB. Simulation results are shown to demonstrate the effectiveness of the proposed control strategy, which could reduce tracking error, decrease tracking time, and improve the anti-interference ability of the system.

Objective Bone marrow mesenchymal stem cells (BMSCs) show significant potential for osteogenic differentiation. However, the underlying mechanisms of osteogenic capability in osteoporosis‐derived BMSCs (OP‐BMSCs) remain unclear. This study aims to explore the impact of YTHDF3 (YTH N6‐methyladenosine RNA binding protein 3) on the osteogenic traits of OP‐BMSCs and identify potential therapeutic targets to boost their bone formation ability. Methods We examined microarray datasets (GSE35956 and GSE35958) from the Gene Expression Omnibus (GEO) to identify potential m6A regulators in osteoporosis (OP). Employing differential, protein interaction, and machine learning analyses, we pinpointed critical hub genes linked to OP. We further probed the relationship between these genes and OP using single‐cell analysis, immune infiltration assessment, and Mendelian randomization. Our in vivo and in vitro experiments validated the expression and functionality of the key hub gene. Results Differential analysis revealed seven key hub genes related to OP, with YTHDF3 as a central player, supported by protein interaction analysis and machine learning methodologies. Subsequent single‐cell, immune infiltration, and Mendelian randomization studies consistently validated YTHDF3's significant link to osteoporosis. YTHDF3 levels are significantly reduced in femoral head tissue from postmenopausal osteoporosis (PMOP) patients and femoral bone tissue from PMOP mice. Additionally, silencing YTHDF3 in OP‐BMSCs substantially impedes their proliferation and differentiation. Conclusion YTHDF3 may be implicated in the pathogenesis of OP by regulating the proliferation and osteogenic differentiation of OP‐BMSCs.