【作者】 霍鑫；

【导师】 姚郁；

【作者基本信息】 哈尔滨工业大学 ， 控制科学与工程， 2011， 博士

【摘要】 在控制科学领域的工程实践和理论研究中,会遇到大量具有非光滑动态的系统。无论系统本身是非光滑的,还是由于施加了非光滑的控制,都属于非光滑控制系统的研究范畴,这方面的研究已经逐渐成为控制科学与系统科学的研究热点之一。在非光滑控制系统理论框架下对非光滑控制设计方法进行深入研究,对改进和完善非光滑控制系统理论具有重要意义。本文从研究系统轨迹同状态空间中单一或若干非光滑Lipschitz曲面的相对关系出发,讨论了由Filippov微分包含解描述的非光滑控制系统的分析与设计问题。分别针对切换控制、滑模变结构控制以及开关控制,进行了以下几方面的研究工作:首先,针对一类系统参数存在摄动的线性系统,提出了一种基于非光滑Lipschitz曲面的切换控制设计方法。依据相依锥判据的穿越条件和不相交条件,借鉴递推的思想构造了一系列的Lipschitz域,并分析了Lipschitz域内部系统轨迹关于平衡点的收敛性。在此基础上,以Lipschitz域的边界曲面作为控制设计的切换面,基于相依锥判据进一步给出了切换控制律,使得从状态空间中Lipschitz域外部和边界出发的系统轨迹能够在有限时间进入并保持在Lipschitz域的内部。其次,针对一类含有不确定性或外部扰动的非线性系统,提出了一种基于非光滑Lipschitz曲面的滑模变结构控制设计方法。利用相依锥判据作为控制设计时的滑模到达条件和滑模存在条件,分别给出了基于全局相依锥判据和非全局相依锥判据的滑模变结构控制设计方法。为进一步解决非光滑Lipschitz滑模面的构造问题,针对一类不确定线性系统,结合自稳定域的概念给出了一种非光滑Lipschitz滑模面的构造方法。然后,针对一类控制输入为开关量的线性系统,提出了一种基于非光滑Lipschitz曲面的开关控制设计方法。利用允许光滑切换面的不唯一性,通过多个光滑切换面的组合来构造新的非光滑Lipschitz切换面,给出了系统的平衡点集,并利用非光滑系统的LaSalle不变集原理证明了系统轨迹关于平衡点集的收敛性。本文提出的开关控制设计方法可以依据轨迹所在区域选取切换面,从而提高了控制设计的灵活性。最后,对某型大气层外动能拦截器末制导段的开关式导引律设计问题进行了研究。根据弹-目相对运动的特点,设计了一种分段线性Lipschitz开关曲线,并利用相依锥判据的穿越条件,分析了制导系统的稳定性。通过仿真,验证了本文方法的有效性,与现有基于光滑开关曲线的导引律设计方法进行比较,显示了本文提出的方法在减少发动机开关次数方面的优势。更多还原

【Abstract】 Nonsmooth systems arise in a large number of nature and physical science. In a control science point of view, there exist large numbers of dynamical systems with nonsmooth dynamics in the fields of engineering applications and theoretical studies. No matter the system is nonsmooth itself or is drived by a nonsmooth control input, the resulting system is called nonsmooth control system. The issues have received more and more attentions recently in control science and system science. It is important and theoretically meaningful to improve and develop nonsmooth control design methods in the framework of nonsmooth systems theory. Based on the relation between the trajectories of the closed-loop system and Lipschitz surfaces in the state space, the dissertation attempts to make a discussion on the analysis and synthesis of nonsmooth dynamical systems which can be described in the sense of Filippov differential inclusion, utilizing nonsmooth analysis and nonsmooth stability analysis as the mathematical tools. Several tops, such as switched control design, variable structure control design with sliding mode and on-off control design, are discussed as follows.Firstly, the switched control design problem with nonsmooth Lipschitz surfaces is investigated for a class of linear systems with parameter uncertainties. A series of Lipschitz domains with Lipschitz surfaces as their boundaries are constructed in a recursive way using the notion of self-stable region. The equilibrium is discussed, and the convergence of the trajectories to the equilibrium in the interior of the Lipschitz domain is studied utilizing contingent cone criteria. In addition, taking the boundaries of the Lipschitz domain as switching surfaces, a switched control design method is proposed to drive the trajectories entering the interior of the Lipschitz domain in finite time and maintaining in it, such that the global stability is achieved.Secondly, the sliding mode control design problem with nonsmooth Lipschitz surfaces is investigated for a class of nonlinear systems with uncertainties and perturbations. Contingent cone criteria are used as new approaching condition and existence condition of sliding mode. According to the new conditions, a sliding mode control design method based on the global contingent cone criteria and a sliding mode control design method based on the non-global contingent cone criteria, which is considered to reduce the conservative property, are proposed to drive the trajectories approaching the Lipschitz surface in finite time and sliding on it. In order to obtain the Lipschitz switching surface of the sliding mode control, a class of linear uncertain systems is considered, and a sliding mode control design method based on self-stable region is proposed. The stability of the new switching surface is analyzed and its properties are illustrated by comparing with some existing methods.Thirdly, the on-off control design problem with nonsmooth Lipschitz surfaces is investigated for a class of linear controllable systems with on-off control input. The new nonsmooth Lipschitz on-off switching surfaces are constructed by means of combination of finite alternative smooth subsurfaces. The equilibria set of the closed-loop system is discussed. The on-off control design method is proposed and the glaoblly asymptotic stability is analyzed utilizing LaSalle’s invariant principle of nonsmooth system. The switching surfaces can be designed with respect to the domains in the state space and the flexibility of the on-off control design can be improved.Finally, the on-off guidance law design problem with nonsmooth Lipschitz thresholds of divert thrusters for a certain type of exo-atmospheric interceptror is investigated. The Lipschitz threshold is constructed by means of combination of finite linear surfaces, considering the characteristics of the relative motion between the interceptror and the target. The stability of the guidance system is analyzed by utilizing contingent cone criteria. By comparing with some existing methods with smooth thresholds, the effectiveness and advantage of the proposed method are illustrated by some numerical simulations.更多还原