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On Model-Free Adaptive Control and Its Stability Analysis

机译：无模型自适应控制及其稳定性分析

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摘要

In this paper, the main issues of model-based control methods are first reviewed, followed by the motivations and the state of the art of the model-free adaptive control (MFAC). MFAC is a novel data-driven control method for a class of unknown nonaffine nonlinear discrete-time systems since neither explicit physical model nor Lyapunov stability theory or key technical lemma is used in the controller design and theoretical analysis except only for the input/output (I/O) measurement data. The basis of MFAC is the dynamic linearization data modeling method at each operating point of the closed-loop system. The established dynamic linearization data model is a virtual equivalent data relationship in the I/O sense to the original nonlinear plant by means of a novel concept called pseudo-partial derivative (PPD) or pseudo-gradient (PG) vector. Based on this virtual equivalent dynamic linearization data model and the time-varying PPD or PG estimation algorithm designed merely using the I/O measurements of a controlled plant, the MFAC system is constructed. The main contribution of this paper is that the theoretical analysis of the bounded-input bounded-output stability, the monotonic convergence of the tracking error dynamics, and the internal stability of the full form dynamic linearization based MFAC scheme are rigorously presented by the contraction mapping principle; the well known PID control and the traditional adaptive control for linear time-invariant systems are explicitly shown as the special cases of this MFAC. The simulation results verify the effectiveness of the proposed approach.
机译：在本文中，首先回顾了基于模型的控制方法的主要问题，然后讨论了无模型自适应控制（MFAC）的动机和最新技术。 MFAC是一种用于一类未知非仿射非线性离散时间系统的新颖的数据驱动控制方法，因为除了控制器的设计和理论分析外，除了输入/输出（ I / O）测量数据。 MFAC的基础是闭环系统每个工作点的动态线性化数据建模方法。建立的动态线性化数据模型是通过称为伪偏导数（PPD）或伪梯度（PG）向量的新颖概念在I / O意义上与原始非线性设备之间的虚拟等效数据关系。基于该虚拟等效动态线性化数据模型和仅使用受控工厂的I / O测量设计的时变PPD或PG估计算法，就构建了MFAC系统。本文的主要贡献是通过压缩映射严格地给出了有界输入有界输出稳定性，跟踪误差动力学的单调收敛以及基于完整动态线性化的MFAC方案的内部稳定性的理论分析。原理; MFAC的特例明确显示了线性不变时系统的众所周知的PID控制和传统的自适应控制。仿真结果验证了该方法的有效性。

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