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arXiv 2308.02484eess.SYcs.SY
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使用梯度算法的离散时间自适应状态跟踪控制方案

Discrete-Time Adaptive State Tracking Control Schemes Using Gradient Algorithms

Gang Tao

AI总结:

本文解决了离散时间系统自适应状态跟踪的开放问题,提出基于梯度算法更新控制器参数的直接与间接自适应控制方案,并将该新框架扩展至连续时间系统与Lyapunov方法对比。

摘要:

本文对一类经典的自适应控制问题进行了全面研究:即在连续时间下状态空间被控对象模型 $\dot{x}(t) = A x(t) + B u(t)$,或在离散时间下 $x(t+1) = A x(t) + B u(t)$ 的自适应控制,以实现对所选稳定参考模型系统(连续时间下 $\dot{x}_m(t) = A_m x_m(t) + B_m r(t)$,或离散时间下 $x_m(t+1) = A_m x_m(t) + B_m r(t)$)的状态跟踪。文献中已报道了针对连续时间系统的自适应状态跟踪控制方案,其使用了基于 Lyapunov 的设计与分析方法,但该方法未能成功应用于离散时间系统,因此离散时间自适应状态跟踪问题一直悬而未决。本文针对离散时间系统开发了新的自适应状态跟踪控制方案,使用梯度方法来设计用于更新控制器参数的自适应律。文中提出了直接和间接自适应设计,两者均具有标准且理想的自适应律特性。这种基于新梯度算法的框架也被开发用于连续时间系统的自适应状态跟踪控制,并与基于 Lyapunov 方法的框架进行了比较。

英文摘要:

This paper conducts a comprehensive study of a classical adaptive control problem: adaptive control of a state-space plant model: $\dot{x}(t) = A x(t) + B u(t)$ in continuous time, or $x(t+1) = A x(t) + B u(t)$ in discrete time, for state tracking of a chosen stable reference model system: $\dot{x}_m(t) = A_m x_m(t) + B_m r(t)$ in continuous time, or $x_m(t+1) = A_m x_m(t) + B_m r(t)$ in discrete time. Adaptive state tracking control schemes for continuous-time systems have been reported in the literature, using a Lyapunov design and analysis method which has not been successfully applied to discrete-time systems, so that the discrete-time adaptive state tracking problem has remained to be open. In this paper, new adaptive state tracking control schemes are developed for discrete-time systems, using a gradient method for the design of adaptive laws for updating the controller parameters. Both direct and indirect adaptive designs are presented, which have the standard and desired adaptive law properties. Such a new gradient algorithm based framework is also developed for adaptive state tracking control of continuous-time systems, as compared with the Lyapunov method based framework.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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