This paper proposes a nonsingular terminal sliding mode control scheme with fast fixed-time convergence for a class of second-order nonlinear systems in the presence of matched uncertainties and perturbations. First, based on fixed-time stability theory, a novel stable system is proposed. Then, using the fixed-time stable system, a fast fixed-time nonsingular terminal sliding surface is derived. The settling time is independent of the initial system state and can be set in advance with the design parameters; the upper-bound of convergence time is derived from the Lyapunov theory. Moreover, the proposed control scheme has an advantage in convergence rate over existing results and achieves better control performance with low control energy cost. The simulation results for a tracking system with a single inverted pendulum are presented to validate the effectiveness and superiority of the proposed control method. INDEX TERMS Fixed-time stability, nonsingular terminal sliding mode control, nonlinear system.

In this paper, a three-dimensional (3D) impact-angle-control guidance law is proposed based on the approaches of nonsingular terminal sliding mode control and fixed-time convergence theory to intercept a maneuvering target. The guidance law is derived based on the coupled 3D engagement dynamics. To intercept the target with an expected impact angle, the nonsingular terminal sliding mode control is designed to ensure that the line-of-sight (LOS) angles and rates rapidly reach the desired values. Furthermore, the fixedtime convergence algorithm is proposed to guarantee that the LOS angles and rates are convergent in fixed time. The upper bound of the settling time can be obtained by presetting the parameters of the proposed guidance law, and it is independent of the initial conditions. The stability of the guidance system is proven via Lyapunov stability theory. The simulation results are presented to validate the efficiency and superiority of the proposed guidance law.INDEX TERMS Fixed-time convergence, nonsingular terminal sliding mode control, three-dimensional guidance, maneuvering target, impact angle.

This article proposes a new terminal cooperative guidance law with impact time constraint in three-dimensional (3D) engagement. Two parts are comprised by this guidance scheme to control the impact time and fulfill the interception. The guidance law along the line-of-sight (LOS) direction is first designed based on finite time consensus protocol to share time-to-go values among missiles and reach the consensus. Meanwhile, the guidance law on the LOS normal direction is developed based on the fast finite time control method to achieve the interception. The stability analysis of the proposed guidance law based on the Lyapunov theory is also demonstrated in detail. Moreover, the maneuvering target can be intercepted successfully under the presented control algorithm, and the guidance system can fulfill stability within finite time. Additionally, the effectiveness and applicability of the proposed guidance scheme are explicitly verified through simulation tests.

To address the need for flexible energy management and impact angle control in the midcourse guidance of modern long-range antiballistic interceptors, an impact time and angle guidance law is designed for the exoatmospheric midcourse flight of antiballistic interceptors, which covers two pulse sections and two coast sections. The problem is described as an optimal control model with discontinuities in the system equations at interior points, and an iterative guidance method is used to efficiently solve the two-point boundary value problem. Simulation results demonstrate the effectiveness of the proposed guidance law; the obtained miss distance accuracy has an order of magnitude of 1 m, and the impact angle accuracy has a 1° order of magnitude while the angle can be achieved.