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.

Aiming at improving the autonomy of hypersonic entry vehicles, a rapid trajectory optimization algorithm, which has the potential to be implemented online and onboard, is proposed in this paper. The nonlinear and nonconvex hypersonic entry trajectory optimization problem is transformed into a series of convex subproblems through a proper combination of the pseudospectral method and an improved successive convexification method; thus, the high discretization accuracy of the pseudospectral method and the fast and deterministic convergence properties of the convex-optimization-based algorithm can be simultaneously exploited. The resulting subproblems can be solved efficiently by matured interior-point methods, and the solution converges rapidly by adopting a novel dynamic trust-region updating approach. The optimality of the solution is verified by the optimal control theory. The effectiveness of the algorithm is demonstrated by numerical experiments.