The Complete System State Feedback Control And The Exponential Convergence

The control of nonholonomic dynamic systems has received considerable attention dur-ing the last few years. This particularly interesting class of nonlinear control system arises from control problems related to mechanical systems with nonholomic or nonintergrable constraints. Among several practical and technical reasons to study nonholomic control problems is the fact that such a class of nonlinear systems connot be asymptotic stabilized by only using continuous state feedback control laws.the researchers have done much work about the control and stabilization of non-linear mechanical systems with nonholonomic constraints. Traditional linear methods and existing non-linear control designs are not ap-plicable because of the uncontrollability of the first-order approximation of a nonholonomic system as well as the non-existence of a feedback linearizing transformation.This paper deals with the stabilisation problems of two classes of nonholonomic systems. The main results can be listed as follows.In the first part, the problem of global states feedback control problem is considered for a class of nonholonomic systems in generalized chained form with unknown virtual control parameters and nonlinear uncertainties. The problem we addressed is to design an states feedback controller such that the state of the closed-loop system is globally asymptotically stable. We get the design of the controller by the backstepping method. In order to overcome the uncontrollability of x-subsystem in the origin and a finite time escape for the given system, we use the input-state scaling technique and the switching control strategy which are similar to the first part. Meanwhile, we take the tuning function technique to overcome the phenomenon of the over-parameter. Numerical example is given to demonstrate the validity of the approach.In the second part,The multi-input systems in chained systems is considered.when the initional state become zero,we use constant control which is feasible in theory,however there is a lot of diffculty in real project systems.In this paper,we use the input-state scaling technique and the switching control strategy to succesful avoid this trouble.