This paper investigates the prescribed performance attitude tracking control problem of a rigid spacecraft with uncertain dynamics and bounded disturbances. By suitable selection of the configuration error function, the trajectory tracking problem on SO(3) is transformed into a point stabilisation problem of an error dynamic system in the associated Lie algebra. The predefined transient performance indexes, which include the maximum steady-state error and overshoot, and the minimum convergence rate of the attitude error vector, are characterised as the inequality constraints. For the tracking controller design, the error transformation technique is utilised to transform the attitude error dynamics with inequality constraints to an equivalent ‘unconstrained’ error one. Then, a coordinate-free robust tracking controller is designed for the ‘unconstrained’ error dynamics to solve the prescribed performance attitude tracking control problem. A rigorous mathematical stability proof is given. Finally, numerical simulations are presented to demonstrate the effectiveness and robustness of the proposed controller.

This paper investigates the prescribed performance fixed-time tracking control problem for a class of second-order nonlinear systems with bounded disturbance and actuator saturation limit. In order to facilitate the controller development, we introduce the performance function and output error transformation technique to transform the tracking error dynamics with inequality performance constraints to an equivalent unconstrained error one. Different from the existing work on the guaranteeing prescribed performance control, we incorporate the fixed-time sliding mode surface into the control design procedure to cope with the disturbances and actuator saturation limit. Specifically, a robust adaptive fixed-time tracking controller, which requires no upper bound of the disturbance, is designed to solve the prescribed performance fixed-time tracking control problem. The rigorous mathematical stability proof is given. Finally, numerical simulations for the attitude tracking control are presented to demonstrate the effectiveness and robustness of the proposed controller.

In this paper, we investigate the finite-time attitude tracking control problem for a rigid spacecraft on the special orthogonal group ( $SO(3)$ ). The exponential coordinates, derived from the exponential and logarithmic maps of Lie group, are utilized to describe the attitude tracking error on $SO(3)$ almost globally unique except for a zero measure set on which the logarithmic map is double valued. To avoid this issue, a novel nonsingular sliding surface is designed to guarantee that the attitude tracking error will never reach the zero measure set and provide fixed-time stability during the sliding phase. Then, a novel continuous second-order sliding mode control scheme is developed to force the system state to reach the desired sliding surface in finite time. The salient feature of the proposed control scheme is that it significantly suppresses the chattering phenomenon. In addition, to address the lack of angular velocity measurements, a finite-time observer is proposed to recover the unknown angular velocity information in finite time. Then, an observer-based finite-time output feedback control strategy is obtained. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed control scheme.

This paper investigates the fixed-time tracking problem for uncertain nonlinear systems with input saturation constraint under the event-triggered scheme. An adaptive fixed-time controller is proposed to drive the tracking error to a residual set in fixed time, which can eliminate the problem of “explosion of complexity”. Furthermore, in order to decrease the communication burden between the controller and the actuator while maintaining the system control performance, we co-design the adaptive controller and the event-triggered strategy, which guarantees that the control input is injected into the actuator only when the predefined event occurs. In addition, the measurement error arisen from event-triggering mechanism is also compensated. Finally, a rigorous mathematical stability proof is given and simulation results are presented to illustrate the effectiveness of the proposed control scheme.