Research On Methods Of Performance-guaranteed Control For Uncertain Nonlinear Systems

With the increasingly rapid development of science and technology,the performance requirements for control systems become more and more demanding.It is well known that practical control systems are generally described as nonlinear ones with uncertainties including modeling errors,disturbances,and unmodeled dynamics.Designing performance-guaranteed controllers for such complex systems is genuinely challenging and there still exist many problems needing to be further studied and polished.This thesis,in combination with relevant mathematical tools in differential geometry,presents deep investigation about problems above and mainly focuses on the following aspects.First,PPC(the prescribed performance control)of SISO nonlinear systems with lumped uncertainties is considered.A homeomorphic transformation is proposed to relax the limitation brought by the prescribed performance requirements.Furthermore,controllability of the transformed system is proved unchanged.Through the error transformation,the original control objective is transformed into assurance of boundedness of the transformed system which greatly simplifies the design of the controller and guarantees the prescribed output tracking error performance.Second,this thesis investigates the prescribed performance control of MIMO nonlinear systems with uncertainties and input saturation.A novel error differential homeomorphic transformation is applied in prescribed performance control of MIMO system.The disturbance observer can efficiently estimate uncertainties for the transformed systems and thus eliminate their influence in the designing of the controller.Auxiliary system is used to analyze and compensate for the negative effects of the input saturation in the systems.The proposed method can not only simplify the controller structure,but also guarantee prescribed performance of output error and global boundedness of all signals in closed-loop systems.Third,the performance-guaranteed control of MIMO nonlinear systems with uncertain parameters is implemented.The feedback linearization is performed on the nonlinear model with uncertain parameters,and the original system is decomposed into a series of disturbed linear subsystems.The perturbation gain matrix is reduced to be constant,so that the influence of the uncertain parameters can be completely eliminated in the output channel.At the same time,the estimate of uncertain parameters can be obtained by Li derivatives.In addition,the original control performance of the nominal system can be guaranteed when there are no uncertain parameters,which is superior to the general robust control methods.Fourth,the prescribed performance control problem for nonlinear systems with parametric uncertainties and full state constraints is studied.The Barrier lyapunov Function method is currently the main method to solve the problem of full state constraints,which induces controllers with complex structure and thus difficult to construct.A novel method is proposed to solve the problem,based on the theory of differential homeomorphic transformation.In combination with adaptive control,this method can ensure that system states are within specified ranges and output tracking errors meet prescribed performance requirements even in circumstances of uncertain parameters.Fifth,the modeling and design of a class of uncertain nonlinear systems based on Lie group method is studied.The state space of nonlinear system is in essence differential manifolds and therefore,modeling the control system directly on manifolds can avoid the localization of the system model in vector space.In this paper,an adaptive invariant observer design method is proposed for the rotational attitude system equations of rigid bodies with group invariance on Lie groups.The designed observer has strong robustness and global exponential convergence.In summary,this paper systematically presents the controller to guarantee the system performance for nonlinear systems with uncertainties,using homeomorphic transformation,Lie derivatives,Lie groups and so on.Besides,controllability,input saturation and state-constrained problems are systematically and gradually studied,expanding some existing achievements.