In this study, a composite robust control approach with non‐singular terminal sliding mode control and fixed‐time disturbance observer (FxTDO) is proposed for a class of second‐order non‐linear systems in the presence of matched uncertain disturbances. A bi‐limit‐weighted homogeneous FxTDO is designed based on the efficient utilisation of power functions obtained by the differentiation error amplification strategy. The FxTDO enjoys a fast convergence rate and simple parameters tuning process. By introducing the disturbance estimation to directly compensate the total disturbance in the composite control law, only a particular small gain‐based discontinuous control term is needed to guarantee the existence of sliding mode, and chattering phenomenon can be attenuated. The simulation results revealed the effectiveness of the proposed method.

In this paper, non-recursive fixed-time convergence (FxTC) observers were proposed to deal with missions such as state estimation and tracking differentiation. The observers were designed based on the time-scale paradigm such that the parameters tuning process could be greatly simplified. The FxTC observers have fast convergence rate, and the convergence time is uniformly bounded by a fixed constant independent of the initial observation errors. Based on the extended state idea, the FxTC observers were redesigned into extended state observers for total disturbance estimation. Some practical rules of thumb were also presented to dispose of the big overshoot of observers’ states. Numerical simulations were carried out to verify the feasibility of the observers and the extended state observers.

This paper studies a cooperative encirclement interception guidance law against a maneuvering target that utilizes a leader–follower control scheme. The control design is decoupled into two parts. In the line-of-sight (LOS) direction, a fixed-time distributed disturbance observer is presented to estimate the maneuvering of the target. Based on the proposed disturbance observer, the guidance law is designed for the followers to guarantee that each follower’s total flight time achieves consensus with that of the leader. In the normal direction of the LOS, the control command is designed to realize the encirclement interception with a predefined-time consensus protocol. The convergence of the guidance algorithm is proven by the Lyapunov stability theory. Numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed cooperative-guidance law.

In this paper, the hit-to-kill strategy is introduced to solve the three-dimensional (3D) robust head-pursuit (HP) interception problem considering the line-of-sight (LOS) angle constraints. Firstly, a target based relative dynamic model is proposed to be the nominal model for designing the robust HP guidance laws, where the HP interception problem is formulated as a target passively chases after the interceptor missile. Secondly, the 3D retro-proportional navigation (RPN) guidance law is reinterpreted from the point of control theory, which forces the corresponding guidance system asymptotically stable. Meanwhile, the concept of nullifying the LOS angular rates is successfully introduced to solve the 3D robust HP guidance problem via the sliding mode control. Thirdly, the LOS angles constrained robust HP guidance law is proposed based on the nonsingular terminal sliding mode control. The stabilities of the presented guidance laws are analyzed via the Lyapunov approach. The simulation results are in agreement with the theoretical statements.