On Finite Time Control For Non-Strict Feedback Nonlinear Systems

As is widely recognized,the swiftness of a system is a crucial parameter that reflects its performance,and finite-time control(FTC)is a control scheme that intuitively showcases the rapidity of a system.As a result,it is increasingly used in real-world engineering applications such as emergency braking of cars,precision guidance of missiles,and real-time tracking of drones.The conventional control scheme only focuses on how the designed controller stabilizes the system while ignoring the time taken for the system state to reach stability or boundedness.FTC,however,solves this deficiency,leading to a surge of interest in FTC research in recent years.This paper proposes several adaptive FTC strategies for diverse nonlinear systems.The primary contents of this study are summarized as follows:Firstly,a fixed time control method for a non-strict feedback system is investigated based on the dynamic event-triggering control strategy.Dynamic surface control(DSC)technology is adopted to eliminate the computational complexity problem generated during backstepping design.The dynamic event-triggering controller reduces the data transmission burden,and the dynamic event trigger controller has fewer triggers than the static event trigger controller.An effective combination of DSC technology and fixed-time adaptive control technology using nonlinear filters guarantees that all signals in the closed-loop system are stable in practical fixed-time.Finally,two numerical simulation examples are used to validate the proposed approach.Secondly,a predefined-time control scheme based on command filtering is proposed for a class of non-strict feedback nonlinear systems with unmodeled dynamics.A known dynamic signal is employed to eliminate the impact of unmodeled dynamics.Unlike fixed-time control,the convergence time of predefined-time control is a more precise user-designed constant.The introduced command filtering technique not only overcomes the computational complexity problem caused by backstepping technology,but also avoids the process of finding variables contained in the black-box function during dynamic surface design.Through theoretical analysis,it is finally proved that the designed command filter predefined-time controller can make all signals in the closed-loop system converge to a small neighborhood within a predefined time.Finally,numerical simulation demonstrates the effectiveness of the proposed method.Thirdly,a controller is designed for an interconnected large system with unmodeled dynamics based on the predefined-time control technology.Dynamic signals are used to process unmodeled dynamics,and command filtering techniques are introduced to avoid the hassle of finding variables.The predefined-time control technology is applied to the controller design of the interconnected large system,which overcomes the shortcomings of the previously designed controller.Theoretical analysis confirms that the command filtering predefined-time controller can make all signals in the closed-loop system converge to a small neighborhood within a predefined time.At the same time,the actual output of all subsystems can track the desired output within the predefined time.Finally,numerical simulation validates the effectiveness of the proposed method.