Abstract
Stabilization is one of the most fundamental issues in systems and control, and the objective of stabilization controller design is to find a controller for a concerned system such that the resulting closed-loop control system is asymptotically/exponentially stable. Even though stabilization is sufficient for most academic studies and industrial applications, yet for some more demanding situations, the systems are required to reach their desired targets within a finite-time interval, finite-time control needs to be adopted. However, most existing finite-time control approaches are not applicable to complex nonlinear systems. Considering the fruitful results achieved by fuzzy control approaches to complex nonlinear systems, finite-time control of T-S fuzzy models could provide an effective alternative to handle finite-time control of complex nonlinear systems. It is thus desirable to develop finite-time control of nonlinear systems based on T-S fuzzy models.In this thesis, the state feedback finite-time control, output feedback finite-time control and adaptive finite-time control problems of nonlinear systems are studied based on T-S fuzzy models. Some novel finite-time control approaches to nonlinear systems based on T-S fuzzy models are developed. The main advantages of these proposed approaches are summarized as follows: (i) the proposed finite-time controllers together with their corresponding Lyapunov functions can be obtained simultaneously via solving a set of linear matrix inequalities (LMIs), which can be easily facilitated by available software packages; (ii) the nonlinear systems considered in the thesis are much more general than their counterparts in most existing works.
The first part of the thesis studies the state feedback finite-time control problem of two classes of nonlinear systems based on T-S fuzzy models. By using the finite-time Lyapunov theorem, approaches to finite-time control via state feedback are developed. It is shown that the fuzzy control systems can be finite-time stabilized with/without a guaranteed H∞ performance by the proposed controllers. Moreover, constructive procedures to obtain such controllers are also provided in the form of LMIs, and upper bounds on the time required for finite-time convergence of the nonlinear systems based on T-S fuzzy models are estimated. In addition, a continuous piecewise Lyapunov function is designed based on the piecewise Lyapunov function technique so that boundary conditions can be removed.
In the second part of the thesis, the output feedback finite-time control problem of a class of nonlinear systems based on T-S fuzzy models is investigated. First, a continuous observer with a predefined time-delay is developed to estimate unmeasurable state variables accurately within a finite-time interval. Then, a control law consisting of the observer and a finite-time controller similar to the one shown in the first part of the thesis is developed such that finite-time control of the closed-loop control system can be achieved. An upper bound on the time required for the finite-time convergence can be estimated.
In the final part of the thesis, the adaptive finite-time control problem of a class of nonlinear systems based on T-S fuzzy models with parametric uncertainties is investigated. The adaptive finite-time controller design is an intricate problem because finite-time Lyapunov theorems cannot be directly used to verify finite-time stability of adaptive control systems. Moreover, Barbalat’s lemma, as an essential tool in stability analysis of adaptive control systems, may not be applicable to such scenarios. It is shown that finite-time control of the adaptive control system under study can be achieved by the proposed controller. Constructive procedures to obtain the controller are provided, and an upper bound on the time required for the finite-time convergence can be estimated.
| Date of Award | 15 May 2017 |
|---|---|
| Original language | English |
| Awarding Institution |
|
| Supervisor | Lu LIU (Supervisor) |