In this article, an improved event-triggering-learning (ETL)-based adaptive dynamic programming (ADP) method for the post-stall pitching maneuver of aircraft is proposed to achieve the robust optimal control and reduce the computational cost. First, a feedforward control with the nonlinear disturbance observer (NDO) technique is designed to attenuate the adverse effects caused by the unsteady aerodynamic disturbances. Subsequently, the ADP method with a critic neural network which is constructed to approximate the value function in the Hamilton–Jacobi–Bellman equation is employed to conduct the optimal control of aircraft. In addition, to reduce the computational cost of learning, the event-triggering (ET) mechanism with an improved ET condition is applied. The Lyapunov stability theory is utilized to prove that all signals in the closed-loop control system are uniformly ultimately bounded. Finally, simulation results are presented to illustrate the effectiveness of the proposed ETL-based ADP method.

To guarantee the collision avoidance of the quadrotor unmanned aerial vehicles (QUAVs) with limited network resources and external disturbances in a complex environment, a distributed event-triggered (ET) collision avoidance formation controller is proposed in this article. To improve the robustness of the QUAVs, the parameter adaptive method (PAM) is used to tackle the influence of the external disturbance. The virtual tube (VT) is designed individually for each QUAV to avoid the collision between the QUAVs. As long as the distances between the VTs are greater than the minimum safe distance for the QUAVs, and no QUAV exceeds the boundary of the corresponding VT, the collision will not occur. Furthermore, to restrict the QUAV in the corresponding VT, the fuzzy artificial potential field with coefficients adjusted by predicting the future position of the QUAV by using both the relative position and velocity, is established and distributed around the boundary of the VT. Thus, the QUAVs are restricted to the VT and the collisions are avoided. Then, the distributed ET collision avoidance formation controller is designed by the VT and the PAM. A dynamic ET mechanism is presented to release the network load, the triggered frequency being heavily related to the distance between the position of the QUAV and the boundary of the VT. Furthermore, the closed-loop system boundedness has been certified by the Lyapunov theory. Finally, comparative flight experiments are performed to verify the effectiveness and the superiority of the proposed controller.

In this paper, to develop a backstepping-based finite-time control (BFTC) method for the three-dimensional integrated guidance and control (IGC) system with target maneuvers and disturbances, a novel decoupled finite-time approximation auxiliary system (DFTAAS) is proposed together with a finite-time disturbance observer (FTDO). To accurately estimate the target maneuvers and the disturbances, the FTDO is designed. To approximate the virtual control law derivative and avoid the explosion of complexity problem, the DFTAAS is proposed. To solve the singularity issue and guarantee the boundedness of the virtual control law derivative, the piecewise functions are designed to derive the DFTAAS and the virtual control. Besides, to make the controller parameters independent of the norms associated to the control matrices, the control matrices are introduced into the DFTAAS so that the conservatism of the controller parameters is restrained. Furthermore, the finite-time stability properties of the system state stabilization and the disturbance estimation are integrated into the Lyapunov stability to guarantee the finite-time stability of the whole closed-loop IGC system. Finally, the hardware-in-the-loop experiment is implemented to verify the effectiveness of the proposed method. Note to Practitioners —The aim of this paper is to design a BFTC scheme for the three-dimensional IGC system with target maneuvers and disturbances. In the practical IGC application, to solve the explosion of complexity problem, the finite-time dynamic surface control is designed to implement the BFTC. Nevertheless, the boundedness of the virtual control law derivative, which is essential for the system stability, can not be guaranteed due to the singularity. Besides, the parameter conservatism is inevitable due to the control matrices. In addition, the finite-time stability properties of the system state stabilization and the disturbance estimation, which interact and influence each other in the control process, is rarely integrated in practical. In view of the above actual issues, the piecewise function is designed to develop the DFTAAS and the guidance law to solve the explosion of complexity problem and ensure the boundedness of the virtual control law derivative. The control matrices are introduced into the DFTAAS to solve the problem of parameter conservatism. The finite-time stability properties of the system state stabilization and the disturbance estimation are integrated into the Lyapunov stability, which is more in line with the practical needs to sufficiently consider the coupling of them.

In order to achieve a straight ballistic trajectory of missile and reduce the update frequency of the missile normal acceleration for the interception of maneuvering target, a backstepping-based parallel approaching guidance method is designed with nonlinear disturbance observer (NDO) technique and event-triggered (ET) mechanism in this paper. In order to suppress the adverse effect of target maneuver, the NDO is designed to estimate the target maneuvering acceleration. Then, the NDO-based backstepping method is used to obtain the normal acceleration of missile and realize the parallel approaching guidance. In order to reduce the update frequency of missile normal acceleration, the ET mechanism is employed in the parallel approaching guidance method. If the missile trajectory is relatively straight, the normal acceleration of missile remains unchanged. On the contrary, if the missile trajectory is not straight, the normal acceleration of missile is updated to make the missile trajectory straight. In this way, the ET-based parallel approaching guidance can be obtained. Furthermore, a determined method for the initial missile flight-path angle is proposed to keep the normal acceleration of missile at zero in the initial stage of interception. Besides, Lyapunov stability analysis method is used to prove that all signals in the closed-loop guidance system are uniformly ultimately bounded. Finally, simulation results show the effectiveness of the proposed guidance method.

To intercept a maneuvering target in a two-dimensional plane, the inverse optimal guidance law based on zero effort miss (ZEM) and disturbance observer (DO) is studied in this paper. Firstly, the relative kinematics equation is simplified to obtain the missile-target ZEM and its dynamics. In order to enhance the robustness of the inverse optimal guidance law, the integral of the ZEM is introduced as a new state to form an augmented system with the original system based on the idea of proportional integral (PI) control. Then, the target maneuver acceleration is assumed as the unknown external disturbance of the guidance augmented system, which is estimated by the DO. Based on the estimated value of DO and the backstepping method, the inverse optimal guidance law is designed to reduce the adverse effect of the disturbance on the guidance system. Finally, simulations are designed to verify the effectiveness of the inverse optimal guidance method based on DO.