Finite-time Control Under Constraints With Applications In Tilting Quadrotor Control

The control systems always suffer from uncertainties and external disturbances.Compared with the asymptotic control,finite-time control can achieve better robustness and disturbance rejection,but also improve the convergence performance.Analysis and synthesis of finite-time control is of significance to nonlinear control.The Euler-Lagrange systems can describe most control systems,such as satellite,unmanned aerial vehicle,manipulator,etc.Finite-time control on these systems is the theoretical basis of the highorder systems.Moreover,there exist various constraints in control systems,including saturation,prescribed performance constraints,and actuator faults.Considering these constraints in control design could be of theoretical and practical importance to improve the robustness and generalization abilities of control.We in this paper address the finite-time control problem under constraints for the Euler-Lagrange systems and MIMO nonlinear systems on the basis of finite-time stability.The main contributions are as follows:Firstly,we address the finite-time convergence performance problem for the EulerLagrange systems,and propose finite-time stability analysis for three conditions,including known uncertainties boundaries,unknown boundaries and chattering alleviation.We propose finite-time adaptive robust control to compensate for the known uncertainties boundaries.adaptive laws are designed to estimate the unknown coefficients in boundaries reducing the design conservatism.By designing the derivative of control inputs with discontinuous sign functions,we propose a second-order finite-time control to alleviate the chattering phenomenon,where the actual control inputs are the integral output of the discontinuous feedback control.A modified finite-time stability theory is further proposed to improve the convergence speed by adding fractional items in the conventional theory.Secondly,we consider state and output feedback control with input saturation and measurement constraints for Euler-Lagrange systems.We propose backstepping-based finite-time control for the Euler-Lagrange systems under saturation.By using the deviation signals of control inputs,we construct an auxiliary system to compensate for the saturation nonlinearities.Based on the second-order finite-time control,a novel saturation mechanism is designed for the derivative of control inputs,and an auxiliary system is constructed according to the deviation of the derivative control signals to compensate for the saturation nonlinearities.Additionally,we propose a finite-time output feedback control with considering actuator faults and measurement constraints.Fuzzy logic systems are utilized to estimate unknown nonlinearities and fuzzy state observer is constructed to approximate unmeasurable system states.Thirdly,we study the finite-time output feedback control and saturation-tolerant prescribed control under system ability and performance constraints for the MIMO nonlinear systems.To improve the generalization ability,we extend Euler-Lagrange systems to a more general MIMO nonlinear systems,and propose finite-time output feedback control with considering saturation,actuator faults and measurement constraints.We further consider performance constraints and propose a Tunnel Prescribed Performance(TPP)without the dependence of the initial tracking errors,which can not only simplify the control design,but also achieve smaller overshoot performance.To accomplish a trade-off between input saturation and prescribed performance,we design a novel auxiliary systems by introducing nonnegative modified signals into TPP as Saturation-tolerant Prescribed Performance(SPP).Namely,SPP possesses the ability of enlarging or recovering the performance boundaries flexibly,which can dramatically reduce the design conservatism.The closed-loop state errors are guaranteed to a small neighborhood around the equilibrium in finite time under saturation-tolerant prescribed control and always evolved within SPP constraints.Finally,a novel tilting quadrotor conception is proposed,where the dynamics are established based on the Euler-Lagrange equations and then analyze the uncertainties and disturbances effects.We design finite-time control for known uncertainties boundaries,unknown boundaries and alleviating chattering.We further verify the effectiveness of the above finite-time control under the conditions of input saturation,actuator faults,measure constraints and performance constraints.