Finite-Time Stabilization of Nonlinear Systems With Actuator Saturation

This paper deals with finite-time stabilization (FTS) of nonlinear systems subject to actuator saturation. We present an analytical method to design the finite-time controller such that the FTS of the system can be guaranteed in the presence of actuator saturation. Moreover, a certain interrelation among the saturation bound, the system structure, and the controller parameters is established. Based on such a relationship, the settling time (ST) and the domain of attraction (DA) can both be estimated in an easily verifiable manner, which are ignored in many existing results of actuator saturation. Moreover, it is shown that the parameter of the designed controller can provide a tradeoff between the estimations of the ST and the DA by adjusting the controller parameters. All the results are illustrated in simulations. Note to Practitioners—Actuator saturation, a phenomenon where the control input exceeds the limits of an actuator, plays a crucial role in control theory and its applications. In control systems, actuator saturation can lead to performance degradation, instability, and even system failure if not properly addressed, such as Chornobyl nuclear power plant accident and the YF-22 crash incident. Note that in the presence of actuator saturation, most existing results focus on Lyapunov stability or finite-time boundedness, which makes it challenging to guarantee that the system converges to equilibrium within a finite time. This paper was motivated to break through this bottleneck and solve the FTS problem. Unlike the existing saturation results, we first decompose the system based on controllability. Then a straightforward controller design is proposed for the controllable part, while constraints on the system structure are provided for the uncontrollable part. Based on such conditions, not only is the estimation of the DA easily obtained, but the corresponding ST estimation is also derived. The obtained results in this paper are of great significance for providing a more general and easily achievable design for saturated control input. And these results are applied to various industries, such as aerospace, automotive, mobile robotics technology, and industrial automation.