Robust Stabilization Based On Impulsive Observers And Adaptive Impulsive Observers Design

The concept of impulsive observer was put forward firstly by German scholars Raff and Allgower in2007with the aim of achieving state estimation by utilizing the outputs of system at discrete sampled instants. As a result, the bandwidth usage can be reduced in the context of network-based control. In recent years, significant progress has been made in designing impulsive observer and its application. But there are still many problems remain to be solved. Based on the recent research on impulsive observer, this thesis focuses on following two problems:impulsive observer-based output feedback stabilization for systems and the design of adaptive impulsive observer. Regarding the first issue, it seems that there is no result available in the literature. Regarding the second question, although a design method for adaptive impulsive observers has been proposed by Iran scholars Ayati and Khaloozadeh, it was later proved that their design method is infeasible. In this thesis, aiming at the first problem, both design schemes and design criteria for impulsive observer-based output feedback control are presented for a class of nonlinear system and for linear systems with uncertain parameters. Aiming at the second problem, a novel design method for adaptive impulsive observers is developed. The proposed adaptive impulsive observers are capable of estimating the state of system as well as the unknown parameters. The main work and results are as follows:(1) The issue on impulsive observer-based output feedback stabilization for a class of continuous-time nonlinear systems is investigated. Using the time-varying Lyapunov function, which depends on the impulse time sequences, and the constant variation formula, the exponential stability of the closed-loop system is analyzed. Furthermore, by convex combination technique, a design criterion on impulsive observer-based output feedback stabilization control law is given in terms of linear matrix inequalities (LMI). This criterion relies on the upper and lower bounds of the impulse interval. The simulation on flexible robotic arm model has verified the validity of the proposed control method.(2) The problem of impulsive observer-based stabilization of linear systems with parameter uncertainties was addressed. Firstly, the impulsive observer-based feedback control system was deduced by introducing the state estimation error and possess of the characteristic of hybrid systems. Secondly, by using a novel time-varying weighted Lyapunov function and the convex combination technique, the exponential stability of the closed-loop system is performed and the design problem can be cast into the feasibility problem of a set of LMIs, while control gain and observer gain can be obtain by solving above LMIs. Two examples show that the robustness of the proposed impulsive observer-based control is not weaker than that of the continuous-time observer-based control. (3) The design of adaptive impulsive observer (AIO) for nonlinear systems has been discussed. The dynamics of observer state of the proposed AIO is modeled by an impulsive differential equation, by which the observer state is updated in an impulsive fashion. The parameters estimation law is modeled by an impulse-free time-varying differential equation associated with the impulse time sequence for determining when the observer state is updated. Unlike the previous work, the convergence analysis of the estimation error system is performed by applying a time-varying Lyapunov function based method, in conjunction with the application of a generalized version of Barbalat lemma. A sufficient condition for the existence of AIO is derived. For some special case, it is shown that the sufficient condition can be formulated in terms of LMIs, and the observer matrices can be achieved by solving a set of LMIs. Furthermore, with an additional persistence-of-excitation-type constraint, it is proved that the sufficient condition can guarantee the convergence of parameters estimation. Chua’s circuit and Lorenz system are provided to illustrate the design procedure of the proposed AIO.