Adaptive Finite-time Control Of Nonlinear Systems And Its Application

The control problem of nonlinear systems has been widely concerned by scholars for a long time.With the progress and development of science and technology,in order to meet the requirements of engineering applications,some practical engineering problems exist in reality commonly,such as uncertainty,actuator failure,dead-zone,saturation and so on,has been considered in many researches.In addition,for practical systems,finite-time stabil-ity tends to have a higher application value compared to infinite-time stability.Besides,finite-time-stable closed-loop systems might have better robustness and disturbance rejec-tion properties.Therefore,it is of great theoretical and engineering significance to study the finite-time control problem of nonlinear systems with uncertainties.So far some relevant research works have been done.However,the finite-time control problem for nonlinear sys-tems with unknown input constraints,more serious uncertainties and more general system structure needs to be further studied and discussed.By using neural networks,adding a power integrator technique and Lyapunov function method,the problem of adaptive finite-time control for uncertain nonlinear systems is inves-tigated in this thesis.Some effective control schemes are proposed.Based on these control schemes,the problem of finite-time consensus for uncertain multiple mechanical systems is studied.The main contributions of this doctoral dissertation are summarized as follows:1.For non-smooth but continuous nonlinear systems with parametric uncertainties,by us-ing the parameter separation technique and the adaptive control method,the problem of adaptive finite-time control is investigated.A recursive design scheme of an adap-tive finite-time control law is developed in the framework of adding a power integrator technique.With the help of Lyapunov function method,the finite-time stability of the closed-loop system is proved.2.The problem of adaptive neural network finite-time control for nonlinear systems with unknown control coefficients and non-parametric uncertainties is studied.Based on the approximation theory of neural networks and the adaptive control method,a recursive design scheme of an adaptive finite-time control law is developed.By using finite-time Lyapunov stability theory,it is proved that if the designed parameters in the controller and adaptive laws are suitably chosen,then all the signals in the closed-loop system are bounded and the system state can converge to the origin in finite time.3.The problem of adaptive neural network finite-time control for uncertain non-strict feed-back nonlinear systems with input saturation is investigated.Because of the existence of non-strict feedback structure,the recursive design method cannot be used to construct the controller directly.In order to solve this problem,by assuming that the unknown nonlinear functions have strictly increasing smooth bounding functions,an adaptive finite-time control scheme is proposed with the help of variable separation approach and adding a power integrator technique.By employing Lyapunov function method,it is proved that if the designed parameters in the controller and adaptive laws are suitably chosen,then the state of the corresponding closed-loop system is finite-time bounded.4.The problem of adaptive finite-time control for uncertain non-strict feedback nonlinear systems with input dead-zone is investigated.First,by introducing characteristic func-tion,the input dead-zone model is transformed into a simple linear system with a static time-varying gain and bounded disturbance.Second,a recursive design scheme of an adaptive finite-time control law is developed by using adding a power integrator tech-nique.In each step of the recursive design,RBF neural network is used to approximate the unknown nonlinear function.Finally,it is proved that the state of closed-loop sys-tem can converge to a small neighborhood of the origin in finite time by using Lyapunov function method.5.The problem of adaptive finite-time fault-tolerant consensus protocol design for uncer-tain multiple mechanical systems with actuator faults is studied.Compared with the existing results,the restrictive conditions imposing on the unknown nonlinear function-s are relaxed.In the presence of both partial loss of effectiveness and bias types of actuator faults,by combining graph theory and neural network,a distributed adaptive finite-time fault-tolerant consensus protocol is developed based on the recursive design method.With the help of Lyapunov function method,it is proved that the position errors and the velocity errors between any two mechanical systems will converge to a small neighborhood of zero in finite time.6.The problem of adaptive finite-time consensus tracking for uncertain multiple mechani-cal systems with input saturation and dead-zone under switching topology is studied.By using adding a power integrator technique and graph theory,a distributed observer-based finite-time consensus tracking protocol is presented.By using finite-time boundedness lemma,it is proved that the tracking errors are finite-time bounded.Besides,the pro-posed consensus tracking protocol can also be applied to the case of switching directed topology,and the topology graph is not required to satisfy the detail-balanced condition.