Research On Adaptive Backstepping Control For An Uncertain Nonlinear System With Full-state Constraints

With the rapid development of nonlinear system control theory,more and more attention has been paid to the control of uncertain nonlinear systems.Full-state constraints,predetermined performance and actuator faults bring lots of challenges to the control of uncertain nonlinear systems.In this work,according to the predefined-time control problem of uncertain nonlinear systems under the influence of full-state constraints/predetermined performance/actuator fault,this paper proposes an adaptive tracking backstepping control strategy.The main contents are as follows.Firstly,an adaptive predefined time backstepping tracking control strategy is developed for the control problem of an uncertain nonlinear system with full-state constraints.An adaptive predefined-time filter is constructed to handle the "explosion of complexity" problem of backstepping method,in which the unknown upper bounds of time derivatives of the virtual inputs can be estimated,and filter error can be bounded in a predefined time.State transformation function is constructed to deal with many types of full-state constraints problem.Then,the unknown nonlinear function is dealt with RBFNN.Furthermore,the adaptive predefined time controller is proposed.Based on Lyapunov stability theory,the closed-loop system is proved to be bounded stable in a predefined time and all states don’t transgress the constraints.The simulation of a single-link robotic manipulator system is given to show the validity of the proposed control scheme.Secondly,an adaptive predefined-time prescribed performance backstepping tracking control strategy is proposed for an uncertain nonlinear system with time-varying full-state constraints and prescribed performance of the output error.The time-varying full-state constraints problem is dealt with state transformation function.Meanwhile,by combing the predefined-time prescribed performance function and error transformation function,the tracking error meets the prescribed performance requirements within the predefined time.Then,the adaptive predefined-time predetermined performance controller is constructed.Furthermore,based on Lyapunov theory,the predefined-time bounded stability of the closed-loop system is verified.All states satisfy their constraints,the output error enters into the preset range in a predefined time.Simulation result of a single-link robotic manipulator system is given to show the validity of the proposed control scheme.Finally,an adaptive fault-tolerant backstepping tracking control strategy is proposed for an uncertain nonlinear system with asymmetric time-varying full-state constraints and time-varying actuator faults.A fuzzy logic based-membership function is constructed to realize the local expanded constraint boundary.At the same time,as the reference command is slightly beyond the border,the output can still track the reference command via locally expanding the constraint boundary.In addition,the boundaries of other states can be expanded automatically.State constraint problem is solved by constructing a transformation function.Time-varying actuator faults are handled by adaptive technique.On this basis,the adaptive fault-tolerant controller is developed.Based on Lyapunov stability theory,the closed-loop system is bounded stable.The validity of the proposed control scheme is verified by the simulation of a single-link robotic manipulator system.