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An adaptive observer design approach for a class of discrete-time nonlinear systems

机译：一类离散时间非线性系统的自适应观察者设计方法

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摘要

We consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete-time systems. This class contains systems that could be transformed into a quasi-LPV (linear parameter varying) polytopic model in the Takagi-Sugeno (T-S) form. Such systems could have unmeasured premise variables, a case usually overlooked in the observer design literature. We assert that, for such systems in discrete-time, the current literature lacks design strategies for joint state and parameter estimation. To this end, we adapt the existing literature on continuous-time linear systems for joint state and time-varying parameter estimation. We first develop the discrete-time version of this result for linear systems. A Lyapunov approach is used to illustrate stability, and bounds for the estimation error are obtained via the bounded real lemma. We use this result to achieve our objective for a design procedure for a class of nonlinear systems with constant parameters. This results in less conservative conditions and a simplified design procedure. A basic waste water treatment plant simulation example is discussed to illustrate the design procedure.
机译：我们考虑了一类非线性离散时间系统的各种联合估计和一些恒定参数的问题。该类包含可以在Takagi-Sugeno（T-S）形式中转换为Quasi-LPV（线性参数变化）多特素模型的系统。这种系统可以具有未测量的前提变量，通常在观察者设计文献中被忽视。我们断言，在离散时间的这种系统中，目前的文献缺乏联合状态和参数估计的设计策略。为此，我们在连续时间线性系统上适应现有文献，用于联合状态和时变参数估计。我们首先为线性系统开发此结果的离散时间版本。 Lyapunov方法用于说明稳定性，并且通过界限的真实引理获得估计误差的界限。我们使用此结果来实现具有恒定参数的一类非线性系统的设计过程的目标。这导致更保守的条件和简化的设计程序。讨论了基本废水处理设备仿真示例以说明设计过程。

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