Finite-Time Control Design Of Nonlinear Systems With Adjustable-Settling-Time

Based on finite-time stability theory, this thesis investigated the finite-time control design of nonlinear systems with adjustable-settling-time. First, we summarize the finite-time stability theory of nonlinear systems, including the subject background, the theoretical significance and the research status. Then by comparing various types and approaches of finite-time control, two commonly used methods have been given—the homogenous analysis approach and the backstepping constructive approach on the finite-time Lyapunov theory. For the following two types of nonlinear systems, we focus on the finite-time stabilization with adjustable-settling-time:(Ⅰ) The finite-time stabilization for a class of zero-dynamics uncertain nonlinear systems with adjustable-settling-time.In this part, the problem of finite-time stabilization is investigated for a class of uncertain nonlinear systems with zero-dynamics, and the method is proposed to design a more applicable finite-time stabilizing controller with adjustable-settling-time. Different from the existing results, the nonlinear system studied here is more general: (1) the system has the zero-dynamics which are unmeasured; (2) the control parameters are uncertain. Moreover, by using the Lyapunov theory of finite-time stability and the backstepping constructive methodology skillfully, the unmeasured zero-dynamics are effectively solved, and the design procedure of the finite-time stabilizing controller with adjustable-settling-time is presented. With the designed state-feedback controller in loop, the system is globally finite-time stable and the settling-time can be adjusted. Especially, when the initial conditions are known, the settling-time can be arbitrarily adjusted. Finally, simulation results are given to illustrate the effectiveness of design.(Ⅱ) The finite-time stabilization for a class of of high-order nonlinear systems with adjustable-settling-time.In this part, the problem of finite-time stabilization is investigated for a class of high-order nonlinear systems. Finite-time control is always (in the time-invariant sense) nonsmooth. For high-order nonlinear systems, various smooth feedback design methods are useless. Based on the Lyapunov theory of finite-time stability, by combining a suitable transformation and the adding a power integrator, the finite-time stabilizing controller with adjustable-settling-time is designed and the globally finite-time stability is achieved. Finally, simulation results are given to illustrate the effectiveness of the proposed approach.