Research On The Stabilization Of Several Classes Of Uncertain Nonlinear Systems

The feedback stabilization of nonlinear systems is a hot research field in control the-ory, which is widely used in robot systems, aerospace systems, power systems, economic systems and so on. Compared with the linear systems, the nonlinear systems are more accurate in describing the practical systems, but their research is more complicated. It is proved that there are not universal design methods for all nonlinear systems. On the other hand, due to the measurement errors and the external disturbances, the uncer-tainties unavoidably exist in the practical systems. The existence of these uncertainties usually leads to the deterioration of system performance and increases the difficulties of control design, and presents challenges to the existing control theory. In view of the above facts, this dissertation focuses on the stabilization of several classes of uncertain nonlinear systems with different structures. The main results and contributions of this dissertation can be summarized as follows:(1) The problem of global state feedback stabilization is studied for a class of high-order nonlinear systems with general structure. The general structure here means that the considered systems have both high and low order nonlinear terms and the state-dependent growth rates. By introducing sign functions, and by skillfully utilizing the adding a power integrator method, a continuous state feedback controller is successfully constructed to render the states of the resulting closed-loop system globally asymptoti-cally to zero.(2) The problem of global output feedback stabilization is investigated for a class of high-order nonlinear systems with multiple time-varying delays. Under the condition that the nonlinear terms can cover both high-order and low-order nonlinearities, an output feedback stabilizing control scheme is successfully designed with the help of the adding a power integrator method and the homogeneous domination approach. Due to the versatility of the homogeneous domination approach , the proposed method is also utilized to the control design of feedforward nonlinear systems.(3) The problem of global finite-time stabilization by state feedback is considered for a class of stochastic high-order nonlinear systems with time-varying nonlinearities.First, the time-varying version of stochastic Lyapunov theorem on finite-time stability is developed by extending the existing time invariant one. Then, based on the generalized theorem, and by skillfully using the adding a power integrator method, a continuous state feedback controller is successfully constructed to guarantee that the closed-loop system is globally finite-time stable in probability.(4) The problem finite-time stabilization is addressed for a class of uncertain non-holonomic systems with state constraints. A nonlinear mapping is first introduced to transform the state-constrained system into a new unconstrained one. Then, by em-ploying the adding a power integrator method and switching control strategy, a state feedback controller is successfully constructed to guarantee that the states of closed-loop system are regulated to zero in a finite time without violation of the constraint. As an application of the proposed theoretical results, the problem of finite-time parking a car is solved. Simulation results are given to demonstrate the feasibility and effectiveness of the proposed method.(5) The problem of finite-time stabilization is discussed for a class of feedforward nonholonomic systems with inputs saturation. First, the kinematic model of the feed-forward nonholonomic system is established by studying the motivating example of a hopping robot. Then, rigorous design procedure for saturated finite time state feedback control is presented by using the adding a power integrator and the nested saturation methods. The development of saturated finite-time controller is also presented briefly for a class of dynamic feedforward nonholonomic systems. An application for the kinematic hopping robot is provided to illustrate the effectiveness of the proposed approach.