On Finite-Time Adaptive Control For Several Classes Of Uncertain Restricted Nonlinear Systems

With the development of science and technology,controlled objects or industrial processes are becoming increasingly complex,multi-objective,multi-decision,high-performance and high-precision requirements,as well as various uncertainties and constraints such as large time delays,dead time,saturation,preset performance,quantization,hysteresis,etc.,are widely present in practical systems.On the one hand,the stability control of nonlinear systems with various uncertainties and constraints has become one of the hot and central issues in the study of control theory at home and abroad.On the other hand,people are no longer satisfied with the asymptotic stability of the system and want the control objective to be achieved as fast as possible when the controller is being designed,such as rapid rendezvous and docking of spacecraft and space stations,rapid formation of attack UAV swarms,or stopping a high-speed car as soon as possible in an emergency situation,etc.,all require the system to stabilize in a finite amount of time.Based on the above reasons,finite-time control schemes are proposed.Up to now,some important and meaningful achievements have been made in finite-time control of nonlinear systems.However,the study of finite-time control of nonlinear systems with unmodeled dynamics,full-state constraints,input saturation,and other constraints still has important theoretical interest and a wide range of practical applications.In this dissertation,merging the dynamic surface control(DSC)and command filtered backstepping design,the adaptive finite-time control method is proposed for several classes of uncertain restricted nonlinear systems.The unknown continuous function is approximated by radial basis function neural networks(RBFNNs).The dynamic signal processing system generated by the filter is not modeled dynamics,and the nonlinear mapping(NM)is designed to convert the restricted system into an unrestricted system.The controller design problem of the coupling between agents and the non-strict feedback formal system is solved by means of the properties of the Gaussian function and Young’s inequality.With the help of Lyapunov finite-time stability theory,it is strictly proved that the closed-loop system is semi-globally practical finite-time stable(SGPFS).The main work is summarized as follows:(1)Finite-time control problems have been studied for a class of nonlinear systems with restricted parameters.Using the properties of logarithmic functions,a one-to-one NM is constructed to transform the restricted system into an unconstrained one;By constructing a nonlinear filter to replace the traditional firstorder linear filter,the requirements for the filter time parameters are reduced.Based on the finite-time stability theory,a finite-time controller is designed using modified DSC.It is proved that all signals in the system are SGPFS,and all states satisfy the constraints.Simulation results validate the effectiveness of the proposed method.(2)The finite-time control is studied for a class of uncertain non-strict feedback systems including unknown dead-zone,full-state constraints and unmodeled dynamics.An adaptive finite-time control strategy is provided based on the linearized representation of dead zone,the DSC technology and the properties of Gaussian function.The logarithmic function is introduced to design a reversible NM,which solves the problem of full-state constraints;The dynamic signal generated by the low-pass filter is used to process the unmodeled dynamic.Based on the finite-time stability theory,it is proved that all signals are semiglobally practical finite-time stable,and all state constraints are not violated.Two numerical examples verify the effectiveness of the proposed finite-time control strategy.(3)The finite-time control problem is studied for uncertain constrained pure feedback systems with actuator faults,and the system states must satisfy timevarying constraints.The unknown dynamic uncertainties of the system is processed by auxiliary dynamic signal;The NM is introduced to deal with all state constraints of the system.For the transformed unconstrained system,an adaptive finite-time fault-tolerant control strategy is designed based on the command filtered backstepping method.In the stability analysis,by introducing the compensation signals and adding them into the whole Lyapunov function,and with the help of the defined compact set in stability analysis,it is strictly proved that all signals are SGPFS,and all the states are restricted to the predefined boundary.Simulation results demonstrate the effectiveness of the proposed method.(4)The finite-time consistent tracking control problem is discussed for uncertain multi-agent systems with preset performance and input saturation.By introducing a new finite-time performance function,the tracking error is ensured to converge to a predefined decay range in finite time;By using tanh(·)function and mathematical transformation,the effect of input saturation is solved.The unmodeled dynamics and dynamic disturbances of the system are solved by means of measurable dynamic signals.By using Young’s inequality and the properties of Gaussian functions,the coupling problem between multi-agents and the system controller design problem in non-strict feedback form are successfully dealt with.Furthermore,a finite-time adaptive neural controller is designed based on command filter,which not only guarantees the finite-time stability of the system,but also makes the tracking errors reach a predefined bound in a finite-time.Stability analysis proves that the proposed method is feasible,and simulation verifies its effectiveness.