In particular, when o=0, this yields the definition of a Lyapunov function Finding, for a given supply rate, a valid storage function(or at least proving that one exists)is a major challenge in constructive analysis of nonlinear systems. The most com-

This lecture presents results describing the relation between existence of Lyapunov or storage functions and stability of dynamical systems 6.1 Stability of an equilibria

Using control authority to transform nonlinear models into linear ones is one of the most commonly used ideas of practical nonlinear control design. Generally, the trick helps one to recognize \simple\nonlinear feedback design tasks

12.1 Systems with controllable linearizations A relatively straightforward case of local controllability analysis is defined by systems with controllable linearizations 12.1.1 Controllability of linearized system Let To: 0, THR, uo: 0, T]H Rm be a

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.243j(Fall 2003): DYNAMICS OF NONLINEAR SYSTEMS

Lecture 1: Input/Output and State-Space Models This lecture presents some basic definitions and simple examples on nonlinear dynam

提出了一种基于多变量相重构的混沌时间序列预测方法.该预测方法从非线性动力学系统中获取与待预测时间序列相关的信息组成多变量时间序列,首先进行多变量相空间重构,然后利用局域多元线性回归模型在相空间中进行预测,最后从预测出的高维相点中分离出时间序列的预测值.由于考虑了动力学系统中多个变量之间相互耦合的关系,从而增加了重构相空间的系统信息量,使得相空间的相点轨迹更加逼近原系统的动力学行为.与采用单变量进行预测的方法相比,基于多变量相重构的预测方法无论是单步预测还是多步预测,都能有效地提高预测精度,且具有嵌入维数的选择对预测精度影响较小的优点.通过对Lorenz混沌信号进行预测,实验结果验证了方法的有效性

针对复杂集总干扰下六旋翼飞行器轨迹跟踪控制问题,给出了混合积分反步法控制与线性自抗扰控制的控制算法. 首先,通过牛顿-欧拉方程建立六旋翼飞行器的非线性动力学模型,并剖析系统输入输出的数学关系. 其次,根据六旋翼飞行器动力学模型的特点,将其分为位置与姿态两个控制环. 位置环采用积分反步法控制理论设计控制器,通过引入积分项来提高系统的抗干扰能力,消除轨迹跟踪的静态误差;姿态环采用线性自抗扰控制技术设计控制器,通过线性扩张观测器估计和补偿集总干扰影响,提高系统的鲁棒性. 最后,通过2组仿真算例和1组飞行试验验证了本文所提飞行控制算法的有效性. 研究结果表明:该控制算法对集总干扰有较好的抑制作用,能够使六旋翼飞行器既快又稳地跟踪上参考轨迹,具有一定的工程应用价值

Lyapunov analysis, which uses monotonicity of a given function of system state along trajectories of a given dynamical system, is a major tool of nonlinear system analysis It is possible, however, to use monotonicity of volumes of subsets of the state space to predict certain properties of system behavior. This lecture gives an introduction to suc methods

where f:R\×Rn×R→ R\ and g:R\×R\×R→ R are continuous functions. Assume that f, g are continuously differentiable with respect to their first two arguments in a neigborhood of the trajectory co(t), yo(t), and that the derivative