非线性控制和观测器设计中的成形状态和时间相关收敛速率
Shaping state and time-dependent convergence rates in non-linear control and observer design
摘要：
本文推导了非线性、时变和反馈线性化系统的简单控制器设计，以达到指定的状态和时间相关的复收敛速度。这种方法可以被看作是一种通用的增益调度技术，具有全局指数稳定性保证。典型的应用包括具有强马赫或时间相关特征值的飞机的跨音速控制，或倒立摆的状态相关复特征值布置。作为一个推广的LTI Luenberger观测器的双观测器的设计技术推导出了广泛的非线性和时变系统，到目前为止，直接的观测器技术是不知道的。所得到的观察员设计说明非线性化工厂，范德波尔振荡器，离散对数映射序列预测和灯塔导航问题。这些结果[23]允许人们在全局上塑造理想地适合于非线性或时变系统的状态和时间相关的收敛行为。该技术也可以用来提供分析鲁棒性保证建模的不确定性。推导基于非线性收缩理论[18]，这是一种比较新的动态系统分析工具，其结果将被回顾和扩展。
英文摘要：
This paper derives for non-linear, time-varying and feedback linearizable systems simple controller designs to achieve specified state-and timedependent complex convergence rates. This approach can be regarded as a general gain-scheduling technique with global exponential stability guarantee. Typical applications include the transonic control of an aircraft with strongly Mach or time-dependent eigenvalues or the state-dependent complex eigenvalue placement of the inverted pendulum. As a generalization of the LTI Luenberger observer a dual observer design technique is derived for a broad set of non-linear and time-varying systems, where so far straightforward observer techniques were not known. The resulting observer design is illustrated for non-linear chemical plants, the Van-der-Pol oscillator, the discrete logarithmic map series prediction and the lighthouse navigation problem. These results [23] allow one to shape globally the state- and time-dependent convergence behaviour ideally suited to the non-linear or time-varying system. The technique can also be used to provide analytic robustness guarantees against modelling uncertainties. The derivations are based on non-linear contraction theory [18], a comparatively recent dynamic system analysis tool whose results will be reviewed and extended.
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