This paper revisits a classical adaptive control problem: adaptive state tracking control of a state-space plant model, and solves the open discrete-time state tracking model reference adaptive control problem. Adaptive state tracking control schemes for continuous-time systems have been reported in the literature, using a Lyapunov-algorithm based design and analysis procedure. Such a procedure has not been successfully applied to the discrete-time adaptive state tracking control problem which has remained open. In this paper, new adaptive state tracking control schemes are developed for discrete-time systems, using gradient algorithms for updating the controller parameters. Both direct and indirect adaptive designs are derived, which have the desired parameter adaptation properties and closed-loop system stability and state tracking properties. Such a new gradient-algorithm based framework is also applicable to the continuous-time adaptive state tracking control problem to develop new solutions, as compared with the traditional Lyapunov-algorithm based solutions.

中文翻译：

---

使用梯度算法的离散时间自适应状态跟踪控制方案


本文重新审视了经典的自适应控制问题：状态空间对象模型的自适应状态跟踪控制，并解决了开放离散时间状态跟踪模型参考自适应控制问题。文献中已经报道了连续时间系统的自适应状态跟踪控制方案，使用基于李雅普诺夫算法的设计和分析程序。这种过程尚未成功应用于离散时间自适应状态跟踪控制问题，该问题仍然悬而未决。在本文中，针对离散时间系统开发了新的自适应状态跟踪控制方案，使用梯度算法来更新控制器参数。推导了直接和间接自适应设计，它们具有所需的参数自适应特性以及闭环系统稳定性和状态跟踪特性。与传统的基于李亚普诺夫算法的解决方案相比，这种新的基于梯度算法的框架也适用于连续时间自适应状态跟踪控制问题，以开发新的解决方案。