In this paper, sliding-mode-control-based guidance laws to intercept stationary, constant-velocity, and maneuvering targets at a desired impact angle are proposed. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the missile's lateral acceleration to enforce terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. The conditions for capturability are also presented. In addition, by considering a three-degree-of-freedom linear-interceptor dynamic model and by following the procedure used to design a dynamic sliding-mode controller, the interceptor autopilot is designed as a simple static controller to track the lateral acceleration generated by the guidance law. Numerical simulation results are presented to validate the proposed guidance laws and the autopilot design for different initial engagement geometries and impact angles.

Sliding-Mode Guidance and Control for All-Aspect Interceptors with Terminal Angle Constraints

Terminal sliding mode control for the trajectory tracking of underactuated Autonomous Underwater Vehicles

This paper considers the problem of relative motion control for spacecraft formation flying (SFF). Using terminal sliding mode technique, a relative position/velocity tracking control based on the nonlinear model is developed. The presented controller enables rapid formation reconfiguration with feasible fuel cost and strong robustness in the presence of uncertain but bounded disturbances. A nonlinear model with J2 disturbance and bounded uncertainties is used for dynamic simulation.

Terminal Sliding Mode Control for Spacecraft Formation Flying

A global terminal sliding mode controller is proposed for higher order SISO nonlinear dynamic systems by employing the fast terminal sliding mode concept in both the reaching phase and the sliding phase. The inherent dynamical properties of the fast terminal sliding modes and the recursive mechanism for application in higher order systems are explored. A control design procedure is developed. It is shown that, by suitably choosing the parameters of the fast terminal sliding modes, the system state variables will reach the fast terminal sliding manifolds within a desired finite time, and stay in the sliding modes thereafter, resulting in the convergence to the equilibrium in a finite time which can also be prespecified. The control law designed, which is called "the global terminal sliding mode control", is nonlinear and continuous. It does not cause chattering in the reaching phase and sliding phase. The robustness analysis shows that the proposed global terminal sliding mode controller has superior robustness in system uncertainties and external disturbances. Simulation studies are presented to validate the proposed scheme.

Robust global terminal sliding mode control of SISO nonlinear uncertain systems

This paper addresses the relative position and attitude tracking control in the framework of geometric mechanics for autonomous rendezvous and docking of two spacecraft where the relative motion of the leader and follower spacecraft tracks a desired time-varying trajectory. Using exponential coordinates on the Lie group $$\mathrm {SE(3)}$$
 , which is the set of positions and orientations in three-dimensional Euclidean space, and the adjoint operator on the Lie algebra $$\mathfrak {se}(3)$$
 , the relative coupled translational and rotational dynamics is modeled. Based on the terminal sliding mode, a robust adaptive terminal sliding mode control scheme on $$\mathrm {SE(3)}$$
 is proposed to ensure the finite-time convergence of the relative motion tracking errors using limited control inputs despite the presence of unknown disturbances and moment of inertia uncertainty. The control scheme is then applied to a situation where the follower spacecraft synchronizes its attitude motion with the leader, while maintaining a constant relative position with respect to the leader. The robustness of the controller is established using Lyapunov stability theory. Simulation results of close range rendezvous and docking verify that the proposed control scheme can achieve faster and more accurate tracking performance while consuming less control energy than the conventional terminal sliding mode control method.

Robust adaptive terminal sliding mode control on SE(3) for autonomous spacecraft rendezvous and docking

The global stabilization of nonlinear minimum phase systems with partially linear strict nonminimum phase composite dynamics is discussed in this chapter using only the state variables of the linear composite part. The concept of the terminal sliding mode is employed for the control design. The advantage of the approach is that the finite time convergence of the proposed control strategy enables elimination of the effect of asymptotic convergence on the nonlinear systems, hence the peaking phenomenon does not occur. The global stabilization of the nonlinear systems under the developed controller is guaranteed.

Yuqiang Wu

Papers

On global stabilization of nonlinear dynamical systems