Nonholonomic System Output Feedback Control Problem

This paper deals with the stabilization problems of three classes of nonholonomic systems. The main results can be listed as follows.In the first part, the problem of global output feedback stabilization of the nonholonomic systems with strongly nonlinear uncertainties is considered, and the uncertainties are bounded by a linearly growing condition. The problem we addressed is to design an output 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, we introduce the input-state scaling technique. In the absence of the disturbances, for this question of stabilization of nonholonomic systems, most commonly used control strategy is to use constant control in some initial time interval. Then, at a time instant, the constant feedback law is switched to a nonlinear control law which is also based on discontinuous coordinate transformation. However, if there exist nonlinear functions, the above choice of control strategy may lead to a finite time escape for the given system. Some solutions blow up before the given switching time. In order to prevent this phenomenon from happening, for the system with uncertainties, a kind of novel nonlinear switching schedule based on the value of x₀ but not time was used. It guarantees that too large control cannot come in some initial time interval. Numerical example is given to demonstrate the validity of the approach.In the second part, the problem of global output 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 output 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 third part, the problem of global adaptive output feedback control problem is considered for a class of nonholonomic systems with nonlinear uncertainties and unknown parameters. The problem we addressed is to design an adaptive output 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 uncontrolla-bility 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.