A novel adaptive finite-time controller (NAFTC) is proposed for flexible air-breathing hypersonic vehicle (FAHV) with actuator saturations, composing of two controllers designed for velocity and height subsystem respectively. Firstly, an adaptive dynamic inversion control is presented for velocity subsystem. The influence of actuator saturation is solved by an improved auxiliary adaptive law (IAAL). Compared with conventional adaptive law, the IAAL can achieve faster convergent speed of tracking error and weaken dramatical change for control signal effectively. Secondly, an adaptive continuous sliding mode control is designed for height subsystem, in which integral sliding surface is established based on a continuous fast higher-order sliding mode algorithm (CFSMA). Compared with conventional finite-time high-order regulator, CFSMA can drive states to converge faster and adjust respond speed of system conveniently without complicated parameters selection. Meanwhile, IAAL is combined to deal with the influence of elevator saturation. Ultimately, with the aid of NAFTC, FAHV subject to actuator constraints can also achieve faster convergent speed. In addition, NAFTC can realize higher tracking precision and faster respond speed compared with existing conventional adaptive controllers.

This article proposes a predefined-time non-singular terminal sliding mode controller (PNTSMC) for multi space transport robot system, which is suitable for complex on-orbit assembly tasks. Firstly, a composite Lyapunov function predefined-time stability criterion (CLF-PSC) is proposed to simplify the stability analysis and controller design. Comparing with traditional predefined-time stability criterion, the CLF-PSC offers a simpler form. More importantly, combining with chain rule of the composite Lyapunov function, the CLF-PSC can be composed and decomposed flexibly, which makes it more convenient for application. Secondly, a unified framework for non-singular terminal sliding mode surfaces is proposed. By integrating the CLF-PSC with the framework, a general method for predefined-time non-singular terminal sliding mode surface (PNTSMF) design is presented, which can effectively avoid the singularity problem without violating strict predefined-time stability. In addition, two PNTSMFs are proposed as specific examples. Additionally, a predefined-time reaching law with varying power is designed based on the CLF-PSC. Due to that the power can change with the sliding variable, the reaching law can weaken chattering, reduce control input, and strictly guarantee predefined-time convergence. Thirdly, combining the PNTSMF with the reaching law, a predefined-time disturbance observer and a distributed cooperative PNTSMC are designed for the system, which exhibit excellent performance of predefined-time convergence, high precision, chattering suppression, and robustness against disturbances. Finally, simulations are provided to verify the performance of the proposed PNTSMF and PNTSMC.