Generation of stable oscillations in uncertain nonlinear systems with matched and unmatched uncertainties

ABSTRACT

In this paper, a robust limit cycle control technique is proposed for generation of stable oscillations in a class of uncertain nonlinear systems with both matched and unmatched uncertainties. For this purpose, first, the modified Lyapunov function is introduced which is appropriate for stability analysis of invariant sets (instead of equilibrium points). The structure of the proposed Lyapunov function is related to the shape of the desirable limit cycle. Next, in order to design the robust limit cycle control input, the backstepping and Lyapunov redesign methods are employed, simultaneously. The The classical Lyapunov redesign controller is discontinuous and robust with respect to matched uncertainties. To overcome unmatched uncertainties, a modified version of the Lyapunov redesign controller is suggested in each step of backstepping which results in a continuous robust control law. Furthermore, the convergence of the phase trajectories of the uncertain closed-loop system to the target limit cycle is proved using the extended Lyapunov stability theorem. Finally, computer simulations are performed to show the applicability of the given approach. In this regard, two uncertain nonlinear practical systems are considered and robust stable oscillations are generated in these systems via the proposed controller. Simulation results confirm the effectiveness of the proposed technique.     

Stability analysis of distributed-order nonlinear dynamic systems

The problem of asymptotic stability analysis of equilibrium points in nonlinear distributed-order dynamic systems with non-negative weight functions is considered in this paper. The Lyapunov direct method is extended to be used for this stability analysis. To this end, at first, a discretisation scheme with convergence property is introduced for distributed-order dynamic systems. Then, on the basis of this tool, Lyapunov theorems are proved for asymptotic stability analysis of equilibrium points in distributed-order systems. As the order weight function assumed for the distributed-order systems is general enough, the results are applicable to a wide range of nonlinear distributed-order systems such as fractional-order systems with multiple fractional derivatives. To verify the applicability of the obtained results, these results are applied for the stability analysis of a distributed-order diffusion system and control of a fractional-order Lorenz system with multiple fractional derivatives.     

Lipschitz非线性系统观测器设计新方法

考虑了非线性项满足Lipschitz条件的非线性系统观测器设计问题, 利用Lyapunov方法给出了新的判断观测误差稳定性的条件, 并由所给的条件通过求解线性矩阵不等式来设计观测器. 通过算例与其它方法进行的比较, 说明了所提方法的有效性.     

基于输出严格无源的切换非线性系统的H∞ 分析

针对切换非线性系统,考虑了基于输出严格无源性的 ∞问题.利用每个子系统的输出严格无源性(这里并不要求每个子系统都在整个时间域上满足输出严格无源性,只要求子系统在其激活时间段内满足输出严格无源性),同时借助切换系统理论中的多 Lyapunov 函数方法,用输出严格无源性中的存储函数作为备选的多 Lyapunov 函数,设计了依赖存储函数的最小切换规则,研究了一类切换非线性系统的 ∞问题,给出了存在 ∞性能指标的充分条件.此外,这种基于输出严格无源性的方法也可用于分析切换级联系统的 ∞问题.最后,通过仿真算例验证了这种基于输出严格无源性的方法的有效性.     

非线性定常系统及其定常Lyapunov函数的多项式等价类

非线性定常系统及其定常Ｌｙａｐｕｎｏｖ函数的多项式等价类苗原李春文杜继宏（清华大学自动化系北京１０００８４）关键词稳定性,非线性多项式系统,李亚普诺夫函数．收稿日期１９９５－０５－１６１引言李亚普诺夫第二方法作为处理系统稳定性问题的最主要的方法之一已...     

双足步行机器人能量成型控制

为了使双足被动行走机器人的行走步态符合仿生规律,且当路面坡度变化后,迅速进入新的稳定步态行走,提出了角度不变能量成型控制策略.研究了欠驱动双足机器人能量匹配条件和能量成型控制器的求解;由于动能相对于旋转变换不具有对称性,通过在能量成型控制中附加一个辅助控制量,实现角度不变控制.仿真结果表明,该算方法可实现仿生控制,既能扩大吸引域,又改善系统的鲁棒性.     

Trajectory tracking problem: causal solutions for non-linear time-delay systems

The trajectory tracking problem is considered for a general class of non-linear time-delay systems. The existence of causal static state feedback solutions is investigated within an algebraic approach. Two classes of causal static compensators are considered that either involve delayed dynamics or not. Sufficient conditions are derived which are weaker than the ones existing in the current literature. These results are innovative for both linear and non-linear time-delay systems. The most advanced results do not imply a maximal loss of observability in opposition to more standard solutions.     

不可压缩流中二元机翼运动的Hopf分岔

机翼的颤振是一种典型的自激振动,它是由气动力、弹性力和惯性力的相互作用引起的一种气动弹性现象.本文研究了具有结构非线性刚度恢复力的机翼颤振的Hopf分岔问题.首先,利用连续时间的Hopf分岔显式临界准则分析了机翼颤振Hopf分岔的存在性,推导了第一李雅普诺夫系数的通项公式,为判定机翼Hopf分岔的稳定性提供了依据.其次,分析了机翼颤振退化的余维二Hopf分岔的存在性条件,得到了满足条件的双参数分岔区域.然后,推导了第二李雅普诺夫系数的通项公式并结合中心流形降阶原理和同构变换进一步分析了余维二Hopf分岔的稳定性以及其局部开折问题.最后,通过推导第三李雅普诺夫系数分析了余维三Hopf分岔中心的稳定性.     

Stochastic nonlinear stabilization — II: Inverse optimality

After considering the stabilization of a specific class of stochastic nonlinear systems in a companion paper, in this second part, we address the classical question of when is a stabilizing (in probability) controller optimal and show that for every system with a stochastic control Lyapunov function it is possible to construct a controller which is optimal with respect to a meaningful cost functional. Then we return to the problem from Part I and design an optimal backstepping controller whose cost functional includes penalty on control effort and which has an infinite gain margin.