摘要
本文主要研究了两类复杂系统的自适应控制问题.全文分为以下两部分：1.带有iISS未建模动态非线性系统的鲁棒输出反馈控制.
该部分考察了一类具有动态不确定性的非线性系统的输出反馈渐近跟踪问题.最近诸多的研究表明,iISS比ISS严格弱,能够包含更广泛的、非线性更强的一类非线性系统.该类系统的动态不确定性子系统即满足积分输入状态稳定(iISS)属性.在处理未建模动态状态时,我们应用了改变函数供能函数对的方法,有效处理了动态不确定性带来的困难。考虑到系统的状态未知,不能用于反馈设计,我们根据系统结构,构造了一动态观测器,借助于这一观测器,并应用返步(Backstepping)递推方法,设计了一个输出反馈控制器,实现了内部状态和输出对任意常数信号的全局渐近跟踪.设计过程中采用的调节函数方法有效避免了过度参数化(overparameterization).
2.相对阶为4的多变量系统的直接模型参考自适应控制.
在这一部分中,我们将利用Kp=SDU的分解思想,把n*=2推广到n*=4的情况.对于相对阶n*=4的多输入多输出系统(MIMO),我们若仿照相对阶n*=2的多变量系统来设计反馈控制器,则在控制器中出现不可量测的(?)与(?),这样的控制器将无法实现,因此再延用n*=2的设计方法不可行.对于相对阶n*=4的多输入多输出系统,我们基于稳定性考虑,在控制器中引入了“非线性阻尼项”,通过设计“非线性阻尼项”来抵消控制器中的不可量测项,这样在保证稳定性的前提下,得到了一个闭环系统.对于该系统,我们给出了一种自适应输出反馈控制器的设计方案.
This paper mainly deals with two kinds of adaptive control problem,which is divided into the following two parts.
1. The robust output feedback control problem for a class of nonlinear systems with iISS unmodeled dynamics.
In this part, we consider the problem of output feedback tracking problem with dynamic uncertain systems. Recently, many research show that iISS is strictly weaker than ISS. It presents a class of much more general nonlinear systems. The uncertain dynamics subsystem of it satisfies integral input-to-state stability. In order to deal with unmodeled state, we apply the method of changing supply function to overcome the difficulties of dynamic uncertainties. In view of the unknown state, it cannot be applied in the feedback design. Based on the structure of the system, we construct a dynamic observer. And then with Backstepping method, we design an output feedback controller to achieve the global asymptotic tracking to arbitrary constant of internal state and output. The tuning function design is also applied which effectively avoids overparameterizatin.
2. The design and analysis of the direct model reference adaptive control with relative degree four stable control.
In this part, we use the method of Kp= SDU to enlarge n*= 2 to n*= 4. To the system with relative degree four,there are some difficulties. If we imitate the control law of the system with relative degree two,which involvesθandθ,which is not available for measurement. Consequently the control law cannot be implemented and the choice of control law is not feasible. To the system with relative degree four,we introduce nonlinear damping two times based on stability considerations. By designing nonlinear damping, a closed-loop system is obtained, based on the system,a design scheme of adaptive output feedback controller is given. A simulation is given to show the effectiveness of the proposed scheme.
引文
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