Robust Control For Nonlinear Non-affine-in-input Systems

During the recent decades,control design for nonaffine-in-input nonlinear dynamics and pure-feedback dynamics attracts increasing attention from control scientists.From the point of mathematical model,nonaffine-in-input systems and pure-feedback systems render a complex form in which the system states and inputs are nonlinearly coupled.Therefore,comparing to affine-in-input systems and strict-feedback systems,nonaffine-in-input and pure-feedback systems are more comprehensive and exquisite in modeling real physical dynamics.Generally speaking,the control inputs either in nonaffine-in-input or purefeedback systems act no direct effect on the evolution of states,thus designing such an indirect control strategy for those systems is still a challenging yet interesting problem.On one hand,due to the inherent nonaffine behaviour,the control input is of little possibility to be derived inversely,even by giving the exact form of its equivalent input.On the other hand,in some extreme cases,the control direction of control input,referring to the sign of control effectiveness,is not attainable to our knowledge.Besides,when the interested dynamics is stirred by some unmodelled dynamics or external disturbances,the robustness of the closed-loop system should necessarily be kept eyes on,for to some extent ensuring the security and stability.Concerning the aforementioned obstacles,this dissertation systematically investigates the robust control design for nonaffine-in-input dynamics and pure-feedback dynamics,striving to pave the way for a better tracking performance for these kind of dynamic systems.The main contributions of this dissertation are summarized in the following four parts.1)A NN-based direct learning control design for a class n-order integrator nonaffine dynamicsFirst,I consider the tracking control problem for a general class of n-order integrator nonaffine-in-input system with uncertain dynamics.By implicit function theorem,it is proved that the solution to the nonaffine dynamics with respect to specific determined convergent performance exists and is unique.To obtain this solution,a structure of neural network using concurrent learning algorithm is utilized.A varying-gain supertwisting sliding mode control is used as a derivative observer here to conduct the design process.Lyapunov based analysis demonstrates the uniformly ultimately bounded result of the output tracking error.By increasing control gain or the number of neurons,the ultimate error could be regulated as small as desired.2)Continuous asymptotically tracking control for a class of nonaffine-in-input system with non-vanishing disturbance Second,we explore the possibility of designing a continuous controller for a class of nonaffine-in-input system to achieve asymptotically tracking results with robustness to system uncertainties,unvanishing disturbances,and unknown control effectiveness.A Robust Integral of the Sign of the Error(RISE)design is formulated to search a robust control for the nonaffine dynamics,while a timevarying gain of Nussbaum-type-function(NTF)is augmented to estimate the unknown direction and magnitude for control effectiveness.A second order filter is employed to proceed the design when the NTF gain is involved without using any unmeasurable signals.Rigorous analysis shows that the proposed controller can asymptotically stabilizes the closed-loop system and the output tracking error.Simulation results on a DuffingHolmes chaotic system demonstrate the effectiveness of the proposed approach.3)A composite output feedback control algorithm for pure-feedback systems: a neural adaptive methodThird,the problem of output feedback control for a class of nonlinear systems in pure-feedback form is considered in this paper.A composite control algorithm is developed using a finite high-order derivative observer and a novel adaptive neural-network controller.By introducing a point-to-segment error and a Nussbaum-type function,the issue of multiple unknown control direction is solved,and the tracking error of output can be steered into a pre-determined neighbor of 0.Convergence analysis is studied using Lyapunov stability analysis and shows that the residue error of output can be regulated as small as desired.Simulation on a three-order pure feedback dynamics illustrates the effectiveness of the proposed algorithm.4)Continuous robust tracking control for magnetic levitation system with unidirectional input constraintFinally,the exponentially tracking control problem for a magnetic levitation system(MLS)in the presence of parameter uncertainties and external disturbances is investigated.The disturbance/uncertainties-rejecting problem for the MLS is addressed from the view of a continuous nonlinear robust control development.Another problem of the concern is the common unidirectional input constraint in the MLS.By utilizing a input transformation and augmented dynamics,a virtual control input,which removes the unidirectional constraint,is affinely emerged in the dynamics.A second-order filter is introduced to provide feedback signals for the control development.A novel Lyapunov function guarantees the exponentially tracking stability of the close loop dynamics.Finally,some numerical simulation and real-time experimental results for tracking of time-varying trajectories are presented to validate the performance of the proposed control design.