基于Riccati反馈连续更新的广义线性化的指数稳定性与镇定
Exponential Stability and Stabilization of Extended Linearizations via Continuous Updates of Riccati Based Feedback
摘要：
近年来，许多关于非线性系统镇定的研究工作都是针对小扰动局部镇定不稳定定态解的情况。在这项工作中，我们明确解决的目标是从一个良好的发展状态，线性化为基础的本地方法将无法工作的驱动系统到一个非吸引力的稳态。考虑非线性系统的扩展线性化或状态相关系数表示，我们给出了解轨线稳定的充分条件。我们发现，如果系数矩阵在当前状态的一个足够大的邻域内是一致稳定的，那么状态最终会衰减。基于这些分析结果，我们提出了一个更新计划，旨在保持稳定性的Riccati为基础的反馈常数在一定时期内的状态演变。我们说明了所得到的算法的一般适用性的非线性自治系统的设定点稳定和它的数值效率在两个例子。
英文摘要：
Many recent works on stabilization of nonlinear systems target the case of locally stabilizing an unstable steady state solutions against small perturbation. In this work we explicitly address the goal of driving a system into a nonattractive steady state starting from a well developed state for which the linearization based local approaches will not work. Considering extended linearizations or state-dependent coefficient representations of nonlinear systems, we develop sufficient conditions for stability of solution trajectories. We find that if the coefficient matrix is uniformly stable in a sufficiently large neighborhood of the current state, then the state will eventually decay. Based on these analytical results we propose an update scheme that is designed to maintain the stabilization property of Riccati based feedback constant during a certain period of the state evolution. We illustrate the general applicability of the resulting algorithm for setpoint stabilization of nonlinear autonomous systems and its numerical efficiency in two examples.
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