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Two novel predefined‐time control algorithms for a nonlinear strict‐feedback system are proposed in this short communication. It is required that the upper bound of system convergence time is exactly a positive constant parameter in each algorithm, and it can be selected arbitrarily by users. Composite state tracking errors are introduced to the backstepping design process by using some novel smooth time‐varying tuning functions. In order to address the problem of explosion of complexity in the first algorithm, the second algorithm extends the predefined‐time control strategy to a dynamic surface control (DSC) case. Furthermore, the proposed predefined‐time DSC algorithm can guarantee global stability rather than semi‐global stability for the closed‐loop system compared with traditional DSC algorithms. Simulation results show the effectiveness of the two control schemes.

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Probabilistic swarm guidance enables autonomous microsatellites to generate their individual trajectories independently so that the entire swarm converges to the desired distribution shape. However, it is essential to avoid crowding for reducing the possibility of collisions between microsatellites. To determine the collision-free guidance trajectory of each microsatellite from the current position to the target space, a collision avoidance algorithm is necessary. A synthesis method is proposed that generate the collision avoidance trajectories. The idea is that the trajectory planning is divided into macro-planning and micro-planning; macro-planning guides where the microsatellites move step by step from the initial cube to the target cube by probabilistic swarm guidance with Centroidal Voronoi tessellation, while the micro-planning is to generate the optimal path for each step and finally reach the specified position in the target cube by model predictive control. Simulation results are presented for the collision-free guidance trajectory of microsatellites to verify the benefits of this planning scheme.