Prescribed-Time Control for Nonlinear Systems With Sensor Faults and Unknown Control Directions

This paper investigates the prescribed-time control for nonlinear systems with sensor faults and unknown control directions. Firstly, the prescribed-time control is realized based on scale function and descending power coordinate transformation. Then, effective nonlinear terms are designed in the controllers to compensate for state pollution caused by sensor faults. Furthermore, the Nussbaum gain function is introduced and it can be proven that the derivative of its variable is bounded, which is of significance to analyze the invariant set. The proposed control scheme guarantees that system states converge to zero within the specified time in advance and all signals of the closed-loop system are bounded. Finally, a numerical simulation and a practical simulation based on the Nomoto ship model intuitively show the feasibility of the scheme. Note to Practitioners—This study is motivated by achieving the prescribed-time control for nonlinear systems with sensor faults and unknown control directions. With the improvement of automation, the prescribed-time control that the convergence time can be arbitrarily specified in advance has been applied to many time-critical fields, such as missile guidance, emergency braking, and so on. It is noted that hypersonic weapons, uncalibrated visual servo control, and other practical models have the characteristic of unknown control direction, and most of the existing prescribed-time control schemes are not suitable for these practical systems. In addition, since the hovercraft power systems and aircraft systems are in a harsh environment for a long time, it can easily lead to sensor faults resulting in major accidents. In this study, based on the descending power coordinate transformation, the prescribed-time controllers with unique nonlinear terms are designed to deal with the above challenges.