论文标题
Lyapunov分析最小二乘基于直接自适应控制
Lyapunov Analysis of Least Squares Based Direct Adaptive Control
论文作者
论文摘要
自适应控制策略通常是基于梯度方法而设计的，以便在Lyapunov分析中简单起见。但是，从收敛速度和鲁棒性到测量噪声的各个方面，最小二乘（LS）的参数标识符（基于适当的设计参数）表现出比基于梯度的表现更好的瞬态性能。另一方面，由于难以将基于LS的自适应定律整合到直接方法之内，因此大多数基于LS的自适应控制程序都是通过间接自适应控制方法设计的，因为很难将基于Lyapunov的成本函数驱动到（零）为零。在本文中，提出了一个形式的建设性分析框架，以将基于递归LS的参数识别与直接自适应控制相结合。为此，为分析提出了类似Lyapunov的函数，以实现适应性定律，以确保参数的指数收敛。通过MATLAB/SIMULINK和CARSIM模拟研究了建议的程序在自适应巡航控制设计中的应用，从而验证了分析结果。
Adaptive control strategies usually are designed based on gradient methods for the sake of simplicity in Lyapunov analysis. However, least squares (LS)-based parameter identifiers, with proper selection of design parameters, exhibit better transient performance than the gradient-based ones, from the aspects of convergence speed and robustness to measurement noise. On the other hand, most of the LS-based adaptive control procedures are designed via the indirect adaptive control approaches, due to the difficulty in integrating an LS-based adaptive law within the direct approaches starting with a certain Lyapunov-like cost function to be driven to (a neighborhood of) zero. In this paper, a formal constructive analysis framework is proposed to integrate the recursive LS-based parameter identification with direct adaptive control. To this end, a Lyapunov-like function is proposed for the analysis to achieve adaptive laws, which guarantee the exponential convergence of the parameters. Application of the proposed procedure in adaptive cruise control design is studied through Matlab/Simulink and CarSim simulations, validating the analytical results.
