Practical Finite-time Tracking Control For Uncertain Nonlinear Systems

In dynamical systems theory,the concepts of asymptotic and exponential stability mean that the system trajectory or state converges to an equilibrium state as time approaches infinity.However,in many applications,it is desirable for a dynamical system to have the property of a trajectory that converges to a Lyapunov stable equilibrium state,which must converge in finite time,not just asymptotically.Compared with the control method based on asymptotic stability,the finite-time control strategy provides faster transient response,higher precision tracking performance and faster convergence rate.In particular,the finite time control scheme has better dynamic performance when there are uncertainties and disturbances in the system.Finite-time control has been used in many practical applications in recent years,such as unmanned vehicles,robotic manipulators,permanent magnet synchronous motors,and rigid spacecraft.At the same time,finite time control always been one of the hot and difficult issues in the field of control.This research focuses on the practical finite time control of a class of uncertain nonlinear systems.The main work is as follows:(1)This chapter studies the practical finite time target tracking control problem of Euler-Lagrange system with an unknown target trajectory.Fourier series and radial basis function neural network(RBFNN)are utilized to reconstruct the target trajectory,which is mathematically linked with the actual camouflaged target trajectory and facilitates the design and analysis.An error transformation function is introduced and embedded with the Lyapunov function,with which an adaptive tracking control scheme is developed.It is shown that such strategy is able to ensure the tracking error converging to a prescribed compact set containing the origin at a self-defined convergence rate.The simulation results verify the effectiveness of the proposed control method.(2)This chapter focuses on the practical fixed-time fault-tolerant control of fully constrained nonlinear systems with structural faults.Different from most of the linear fault schemes adopted,this chapter introduces a nonlinear fault,which is more in line with the actual situation.Then,the barrier Lyapunov function(BLF)and the fixed-time control theory are combined to design the full-state constraint.At the same time,a first-order filter is introduced to avoid the problem of "differential explosion".By introducing full-state constraints,the system can still proceed safely under structural failure,and the tracking performance is ideal.Meanwhile,the fixed time control is used to solve the problem of finite time dependence on the initial state,which is also verified by the simulation results.(3)The practical finite time control problem of adaptive neural networks for strict feedback systems with spatiotemporal constraints is developed.Adaptive neural network is used to deal with modeling uncertainty and external interference.In addition,the spatiotemporal constraints are introduced and combined with the practical finite time control theory to ensure that the system tracking error has a preset performance boundary(spatial constraints).Moreover,for uncertain nonlinear systems,a new method of time-varying scaling function is adopted to make the system converge to the position pointed by a time-varying scaling function in finite time(temporal constraint).Finally,the designed control law guarantees the spatiotemporal constraints of the system tracking error.(4)The practical prescribed time tracking control problem of strict-feedback uncertain systems under time-varying full state constraints is investigated.A nonlinear transition function dependent on rate function,error variable,and dummy error is constructed,and the constrained problem of the system state is transformed into the boundedness problem of the nonlinear transition function.According to the practical prescribed time control theory,combined with Backstepping method and adaptive control technology,a practical prescribed time tracking algorithm for strict feedback uncertain systems with full state constraints is designed.Compared with BLF,the method in this chapter eliminates the problem of “feasibility condition” existing in BLF,and the constraints can be in asymmetric form,which reduces the complexity of the system analysis process.