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.

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.

A novel finite-time tracking control algorithm with disturbances observer is investigated for agile missiles in the presence of mismatched and matched disturbances. A finite-time disturbance observer with the continuous super-twisting algorithm is designed to quickly estimate the mismatched and matched disturbances. An adaptive law on the basis of immersion and invariance theory (I&I) is proposed to estimate the uncertainty of aerodynamics and compensate for the inaccuracy of modeling. An adaptive dynamic scaling factor supervised by a designed supervision factor is implemented. Moreover, a novel sliding mode controller is designed, and a barrier Lyapunov function (CTV-BLF) containing the system state constraints is constructed, which can guarantee that the violation of the constraint will not appear. The finite-time stability of the new proposition is proven via Lyapunov-based analysis. Comparative simulation results illustrate the effectiveness of the proposed scheme.

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.

The reach-avoid game theory is an ideal tool to handle the conflicts among intelligent agents and has been previously studied assuming full state information and no time limits on the players in the past decades. In this article, we extend the problem by requiring the defender to detect the attacker and adding maximum operation time constraints to the attacker. The attacker aims to reach the target region without being captured or reaching its time limit. The defender can employ strategies to intercept the attacker only when the attacker is detected. A geometric method is proposed to solve this game qualitatively. By analyzing the geometric property of the Apollonian circle and the detection range, we give the barrier under the condition that the attacker is initially detected and the attacker’s shortest route which guarantees its arrival at the target region when it is initially outside the detection range. Then, a barrier that separates the game space into two respective winning regions of the players is constructed based on the shortest route and the time limit of the attacker. The main contributions of this work are that this paper provides the first attempt to introduce the abovementioned two concepts simultaneously, which makes the game more practical, and we provide the complete solution of the game in all possible situations.