Research On Adaptive Control Methods For Unknown Nonlinear Systems Under Multipe Constraints

Most physical systems exhibit highly nonlinear and strong coupling characteristics,such as robots,unmanned vehicles,unmanned ships and unmanned aerial vehicles,etc.,and it is difficult or hardly possible to obtain accurate mathematical models due to hostile and variable environments,which makes solving control problems challenging.In addition,the system states are required to suffer from some constraints during the operation due to the limitation of physical conditions and the consideration of safety,and the system performance becomes poor if the constraints are violated.Fucosing on the above challenges,this paper aims to investigate adaptive tracking control problems of uncertain nonlinear systems with output and state constraints as well as performance constraints,respectively.Specified contents are as follows:1)For uncertain strict feedback nonlinear systems,originating from practical needs,finite-time asymmetric output constraints(FTAOCs)are proposed based on the existing output constraints(constraints exist all the time,i.e.,infinite-time constrained cases,ITCC),that is,the constraints imposed on the system output start from the initial time and end at a certain time(the ending time is known and can be changed according to actual needs).For addressing the FTAOCs,with the fact that barrier Lyapunov functions(BLFs)cannot be applied directly,a novel transformation function is proposed,which converts the FTAOCs for errors into the ITCC for an auxiliary variable.Then,barrier functions and adaptive algorithms are used to constrain the auxiliary variable and estimate the unknown model parameter,respectively.In the end,the stability of the closed-loop system is demonstrated.It should be pointed out that the ending time of the FTAOCs is adjustable,such that the controlled system can be transformed into constrained or unconstrained cases by ingeniously changing this time.2)For uncertain multi-input multi-output(MIMO)nonlinear systems under unknown time-varying disturbances,with complex application scenarios as the background,a more general constraint called output constraint existing in a limited time interval(OCOLT)is proposed based on the FTAOCs,i.e.,the constraint imposed on the system output starts from a certain time after the system operation and ends at a certain time(the ending time is known and can be changed according to actual needs).In order to deal with the OCOLT,a new transformation function is proposed,which transforms the unconstrained and constrained phases of the OCOLT into the ITCC for an auxiliary variable.For estimating unknown model parameters and disturbances,adaptive algorithms and disturbance observers are designed based on Backstepping,respectively.Finally,it is proved that the tracking error of the closed-loop system is uniformly bounded and constrarined by the OCOLT.In the controller design,dynamic surface control(DSC)methods are used to avoid heavy computation loads caused by repeatedly differentiating virtual controllers.For the OCOLT,the start and ending time of constraints are exceedingly impotant and can be changed according to the need of performances or users,such that the OCOLT can be further extended to addressing the cases of the FTAOCs,unconstrained and constrained requirements,without need to revise controller stuctures.In addition,the OCOLT avoids the difficulty that there does not exist feasible control gains to render the controlled system stable due to small values of constraint boundaries for the ITCC.It is worth noting that,under a unified control framework,the OCOLT can provide a feasible solution for the requirements of both time-varying and constant constraints.3)For uncertain MIMO nonlinear systems subject to time-varying disturbances under prescribed performace constraints,a high-accuracy control method is proposed for adaptive tracking problems and applied to the control of an unmanned aerial vehicle.To estimate unknown time-varying disturbances,an extended state observer is designed,which features estimating non dissipative disturbances.To further enhance the accuracy and robustness of the vehicle under complex environments,performance constraint functions are designed to shape the transient and steady-state behaviours of tracking errors using barrier functions,and the thrust of the vehicle is designed.In the end,the Euler angular velocity controller is designed using Backstepping,and the simulation and experimental results verify the effectiveness of the algorithm.Compared with existing methods,the designed prescribed performance algorithm assumes the mass of the vehicle and disturbances to be unknown and non dissipative,respectively,which is an impressive merit.4)For uncertain cascaded MIMO nonlinear systems under dynamic performance constraints,a high-accuracy control method is investigated for adaptive tracking problems and applied to the control of quadrotor-slung-load systems(QSLSs).Essentially,the QSLSs consists of both load and quadrotor subsystems that are connected by a cable.Firstly,in order to make the load quickly track the reference trajectory and stabilize in the vertical direction,using the traditional predetermined performance control,a new performance constraint boundary(PCB)is designed whose values are not only dependent on time,but also related to the tracking error.The designed PCB is applied to the load and the direction of the cable by using barrier functions,respectively,which improves the response rate of the closed-loop system.For the case of the unknown load mass,an adaptive algorithm is designed.In the end,the closed-loop system is proven to be stable,and the effectiveness of the algorithm is verified by simulations.This thesis enriches the research on adaptive control theory of uncertain nonlinear systems,gives a new insight for solving control problems of constrained nonlinear systems,and further provides a feasible solution to addressing complex engineering chanllges.