非线性自适应迭代学习控制研究
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摘要
近二十多年来,非线性系统控制理论是自动化控制领域研究的热点问题之一。基于Backstepping技术的自适应控制作为非线性控制理论的一种研究方法,可以使不满足匹配条件的时不变参数不确定性非线性系统,实现跟踪误差渐近收敛于零,但无法处理含有时变参数不确定性的情形。当系统中控制方向未知和含有混合参数(时变参数和时不变参数)不确定性以及目标轨线发生变化时,单一的自适应控制算法远不能解决这些问题。而Nussbaum增益技术是处理控制方向未知问题的一种有效方法;传统迭代学习控制是处理重复性跟踪问题的一种有效控制方法,经过若干次迭代能以较高的精度在给定有限时间区间内实现给定目标轨迹的完全跟踪,但现有的这种方法还存在很大的缺陷,如要满足全局Lipchitz连续,跟踪目标轨迹一致(与迭代次数无关)等。因此,如何将基于Backstepping技术的自适应控制、Nussbaum增益技术、迭代学习控制相结合,来解决控制方向未知问题和非一致目标轨迹跟踪问题是值得研究的课题。
由以上研究思想,本文工作主要包括以下几个方面:
第一,针对一类具有参数不确定性和多个控制方向未知的非线性时滞系统,提出了一种基于观测器的输出反馈稳定化设计方案。利用Nussbaum增益技术处理未知控制系数,利用Backstepping技术设计自适应控制器。通过构造一个Lyapunov-Krasovskii泛函,证明了闭环系统的稳定性,实现了系统状态渐近收敛于零,且保证了所有信号有界;第二,针对一类控制方向未知的一阶混合参数化非线性时滞系统,提出一种自适应迭代学习控制方案。利用Nussbaum增益技术处理未知控制系数;设计微分-差分型参数自适应律以及迭代学习控制律,解决非一致目标跟踪问题。通过构造一个Lyapunov-Krasovskii泛函,证明了跟踪误差的平方在一个有限时间区间上的积分收敛于零,同时保证所有信号均在有限时间区间内有界;第三,针对一类控制增益未知的在有限时间区间上可重复运行的高阶混合参数化非线性系统,利用改进Backstepping技术,将参数重组技巧和分段积分机制相结合,提出一种由参数微分-差分型自适应律和学习控制律组成的混合自适应迭代学习控制算法,处理非一致目标轨迹跟踪问题。通过构造一个Lyapunov-like泛函使得跟踪误差的平方在一个有限时间区间上的积分收敛于零,同时保证所有信号均在有限时间区间内有界;第四,对文中所提的算法都做了计算机仿真研究,进一步验证了算法的可行性和有效性。
In last two decades, the control theory of nonlinear systems becomes one of hot topics in the fields of automatic control. The adaptive control based on Backstepping technique as a method of nonlinear control theory ensures the stability and asymptotic tracking convergence of unmatched nonlinear systems with time-invariant uncertainties, instead of time-varying parametric uncertainties. However, when the control direction is unknown, the plant has of mixed parametric uncertainties and non-uniform trajectories, the above mentioned adaptive algorithm can not deal with these problems. Now, Nussbaum gain technique is an effective method to solve the problem of unknown control directions; iterative learning control is a kind of control methodology effectively dealing with repeated control problems, after some iterations, perfect tracking can be achieved over a finite time interval, but the present method has some defects, such as global Lipchitz continuity of nonlinear functions, uniform trajectory (independent of iteration) etc. Thus, how to incorporate Backstepping technique, Nussbaum gain technique and iterative learning control into solve problems of unknown control direction and non-uniform tracking trajectory is a subject worthwhile to research.
Motivated by the above discussion, the main results of this paper are summarized as follows:
Firstly, an output feedback stabilized control algorithm is proposed for a class of nonlinear time-delay systems with parametric uncertainties and multiple unknown control directions. Nussbaum function is used to deal with unknown control coefficients and Backstepping technique is used to design an adaptive control law. By constructing a Lyapunov-Krasvoskii functional, it is proved that the system is stable and its states are asymptotically convergent to zero, guaranteeing all signals bounded. Secondly, a hybrid adaptive iterative learning control method is proposed for a class of hybrid parametric nonlinear time-delay systems with unknown control direction.
Nussbaum function is used to deal with unknown control; the approach consisted of a differential-deference type updating law can deal with non-uniform trajectory tracking problem. By constructing a Lyapunov-Krasvoskii functional, it is proved that the system is stable and its states are asymptotically convergent to zero, guaranteeing all signals bounded over a finite interval. Thirdly, an adaptive iterative learning control algorithm is proposed for a class of high-order hybrid parametric nonlinear systems with unknown control gain, which are repeatable on a finite time interval. By using modified Backstepping technique, parameters reconstructed technique and piecewise integration mechanism. The algorithm is consisted of a differential-deference type updating law and a learning control law, which can deal with the tracking problem with iterative changing desired trajectory. By constructing a Lyapunov-like functional, one can guarantee the tracking error converging to zero in terms of mean-square on the finite interval and guarantee all signals bounded in a finite time interval. Lastly, the simulation researches are done to every method, which illustrate the effectiveness and feasibility of the proposed algorithms.
由以上研究思想,本文工作主要包括以下几个方面:
第一,针对一类具有参数不确定性和多个控制方向未知的非线性时滞系统,提出了一种基于观测器的输出反馈稳定化设计方案。利用Nussbaum增益技术处理未知控制系数,利用Backstepping技术设计自适应控制器。通过构造一个Lyapunov-Krasovskii泛函,证明了闭环系统的稳定性,实现了系统状态渐近收敛于零,且保证了所有信号有界;第二,针对一类控制方向未知的一阶混合参数化非线性时滞系统,提出一种自适应迭代学习控制方案。利用Nussbaum增益技术处理未知控制系数;设计微分-差分型参数自适应律以及迭代学习控制律,解决非一致目标跟踪问题。通过构造一个Lyapunov-Krasovskii泛函,证明了跟踪误差的平方在一个有限时间区间上的积分收敛于零,同时保证所有信号均在有限时间区间内有界;第三,针对一类控制增益未知的在有限时间区间上可重复运行的高阶混合参数化非线性系统,利用改进Backstepping技术,将参数重组技巧和分段积分机制相结合,提出一种由参数微分-差分型自适应律和学习控制律组成的混合自适应迭代学习控制算法,处理非一致目标轨迹跟踪问题。通过构造一个Lyapunov-like泛函使得跟踪误差的平方在一个有限时间区间上的积分收敛于零,同时保证所有信号均在有限时间区间内有界;第四,对文中所提的算法都做了计算机仿真研究,进一步验证了算法的可行性和有效性。
In last two decades, the control theory of nonlinear systems becomes one of hot topics in the fields of automatic control. The adaptive control based on Backstepping technique as a method of nonlinear control theory ensures the stability and asymptotic tracking convergence of unmatched nonlinear systems with time-invariant uncertainties, instead of time-varying parametric uncertainties. However, when the control direction is unknown, the plant has of mixed parametric uncertainties and non-uniform trajectories, the above mentioned adaptive algorithm can not deal with these problems. Now, Nussbaum gain technique is an effective method to solve the problem of unknown control directions; iterative learning control is a kind of control methodology effectively dealing with repeated control problems, after some iterations, perfect tracking can be achieved over a finite time interval, but the present method has some defects, such as global Lipchitz continuity of nonlinear functions, uniform trajectory (independent of iteration) etc. Thus, how to incorporate Backstepping technique, Nussbaum gain technique and iterative learning control into solve problems of unknown control direction and non-uniform tracking trajectory is a subject worthwhile to research.
Motivated by the above discussion, the main results of this paper are summarized as follows:
Firstly, an output feedback stabilized control algorithm is proposed for a class of nonlinear time-delay systems with parametric uncertainties and multiple unknown control directions. Nussbaum function is used to deal with unknown control coefficients and Backstepping technique is used to design an adaptive control law. By constructing a Lyapunov-Krasvoskii functional, it is proved that the system is stable and its states are asymptotically convergent to zero, guaranteeing all signals bounded. Secondly, a hybrid adaptive iterative learning control method is proposed for a class of hybrid parametric nonlinear time-delay systems with unknown control direction.
Nussbaum function is used to deal with unknown control; the approach consisted of a differential-deference type updating law can deal with non-uniform trajectory tracking problem. By constructing a Lyapunov-Krasvoskii functional, it is proved that the system is stable and its states are asymptotically convergent to zero, guaranteeing all signals bounded over a finite interval. Thirdly, an adaptive iterative learning control algorithm is proposed for a class of high-order hybrid parametric nonlinear systems with unknown control gain, which are repeatable on a finite time interval. By using modified Backstepping technique, parameters reconstructed technique and piecewise integration mechanism. The algorithm is consisted of a differential-deference type updating law and a learning control law, which can deal with the tracking problem with iterative changing desired trajectory. By constructing a Lyapunov-like functional, one can guarantee the tracking error converging to zero in terms of mean-square on the finite interval and guarantee all signals bounded in a finite time interval. Lastly, the simulation researches are done to every method, which illustrate the effectiveness and feasibility of the proposed algorithms.
引文
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