【作者】 叶华文；

【导师】 戴冠中； 王红；

【作者基本信息】 西北工业大学 ， 控制理论与控制工程， 2001， 博士

【摘要】 最近一段时期，基于耗散系统原理的非线性系统鲁棒镇定和镇定设计取得了许多重要成果，但仍然有待深入。本论文一方面给出相关理论结果的补充和改进，另一方面，运用已有的和新发展的理论结果给出复杂系统的鲁棒镇定和镇定设计。具体地说，本论文的研究内容如下： 1．无源性原理是耗散性原理的重要组成部分，我们探讨了该原理在鲁棒镇定和镇定设计中的应用。运用仿射无源系统的Kalman-Yacubovitch-Popov引理，饱和镇定非仿射非线性系统；运用联级无源系统的稳定原理鲁棒镇定几类不确定系统；运用零状态可探测概念，给出了镇定从驱动系统相对较弱的充分条件。 2．输入到状态稳定原理是耗散系统原理的新近发展，我们对其进行理论补充并探讨新结论的应用。给出了输入到状态稳定的一个新刻画，该结论可以为工程中输入到状态镇定设计提供理论依据；总结了一个简单实用的非线性小增益原理，与此结合，使输入到状态稳定原理成为镇定设计的一种更为有效的分析工具。 3．探讨无源性原理在输入到状态镇定中的应用。借助零状态可探测概念，减弱了通常文献中所需的前提条件，在此基础上研究了一类输入饱和线性系统的输入到状态镇定。 4．探讨控制李雅普诺夫函数在鲁棒镇定和镇定设计中的关键性作用。基于控制李雅普诺夫函数的Sontag-Type控制，是仿射系统鲁棒镇定研究中一种非常重要的控制律，通过研究我们发现，该控制律实质上是一种变结构控制；基于这一认识，也考虑到控制李雅普诺夫函数难于构造，我们抽象出弱控制李雅普诺夫函数概念，并证明了基于弱控制李雅普诺夫函数的Sontag-Type控制的镇定作用和优化特性；借鉴控制李雅普诺夫函数的抽象方式以及Sontag-Type控制的特殊结构，探讨了一类受扰系统的耗散化控制；探讨了齐性度理论与控制李雅普诺夫函数相结合的镇定设计问题。 5．探讨弱李雅普诺夫函数在镇定设计中的作用。刻画一类存在半正定弱李雅普诺夫函数的全局渐近稳定系统，并用所得结果改进了李雅普诺夫递推设计的一个重要理论依据；如何由弱李雅普诺夫函数重构控制李雅普诺夫函数，是一个十分重要的问题，因为成功的重构意味着可以进行深入的鲁棒分 产 摘要 析与设计，针对仿射系统我们给出了可以重构的充分条件，并用典型例子说 明了构造过程.6.在有限场(p全1)增益稳定基础上发展起来的非线性枷控制研究方兴未艾， 我们作出了一点理论方面的探讨，给出了一个不同于微分对策的估计最佳 控制和最糟扰动的不等式方法.更多还原

【Abstract】 For recent years, although a great many important results have been achieved in the field of robust stabilization and stabilization design of nonlinear systems based on dissipative system theory, many researches remain to be done. In this dissertation, on the one hand, we reinforce or improve some theoretic results, on the other hand, by using theorems existed or developed in this dissertation, we pursue the researches on robust stabilization and stabilization design in diverse complex nonlinear systems. The contributions of this dissertation consist of the following:1.Passivity theory is an important component of dissipative system theory, we investigate its applications to robust stabilization and stabilization design. Non-affine nonlinear systems via bounded controls and Kalman-Yakubovitch -Popov lemma of affine passive systems are stabilized. Several kinds of nonlinear systems with uncertainty by using stability theory of cascaded passive systems are stabilized robustly. The relative weaker sufficient conditions of stabilizing a class of driven-driving systems by using the concept of zero-state-detectability are put forward.2.1nput-to-state stable theory is a new area of dissipative system theory, we propose some theoretic results and investigate their applications. A new characterization of input-to-state stability which is beneficial to input-to-state stabilization design is presented. A nonlinear small-gain theory with which input-to-state stable theory becomes a more effective analysis tool of stabilization design is put forward.3.We investigate the function of passivity theory in input-to-state stabilization. The usual precondition guaranteeing input-to-state stabilization by exploiting the concept of zero-state-detectability is weakened, and a class of linear systems subject to saturation by using the results above is input-to-state stabilized. 4.The decisive function of control Lyapunov functions in robust stabilization and stabilization design is studied. Since Sontag-Type control based on controlLyapunov function is an important control law in robust stabilization of affine systems, we point out that is a kind of variable structural control in essence. Due to this recognition and the fact that control Lyapunov functions are difficult to be constructed, we propose the concept of weak control Lyapunov function and then prove the stabilizing property and the robustness of Sontag-Type control. Using the way of proposing the control Lyapunov function and the special structure of Sontag-Type control, we investigate the dissipassivation control of a kind of perturbed nonlinear systems. The applications of homogeneity theory to stabilization design based on control Lyapunov functions are studied and some new results are obtained.5.The function of weak Lyapunov functions in stabilization design is studied. We characterize a kind of globally asymptotically stable systems which have only semi-definite positive weak Lyapunov function. Based on this characterization, we improve the theoretic result which is the foundation of Lyapunov backstepping design. The problem that how to construct a control Lyapunov function from a weak Lyapunov function is a significant one, because the successful reconstruction implies that robust analysis and design can be probed in depth. For affine nonlinear systems, we present a sufficient reconstruction condition and interpretate the constructing procedure by typical examples.6.Nonlinear H-infinite control based on Lp(p l) gain stability is being extensively investigated recently. We present a theoretic result, i.e., put forward an inequality approach, which is different from the usual differential game method, to estimate the best control and the worst disturbance.更多还原