Discrete‐time adaptive control algorithms can be executed directly in embedded code unlike their continuous‐time counterparts, which require discretization. However, their designs predicated on quadratic Lyapunov‐based frameworks are quite intricate due to the resulting complexity in the Lyapunov difference expressions. Therefore, a wide array of available continuous‐time results addressing transient performance issues using adaptive control algorithms cannot be applied or readily extended to the discrete‐time case. In this article, we present a new model reference adaptive control architecture for discrete‐time uncertain dynamical systems. Specifically, the proposed architecture consists of a command governor mechanism that adjusts the trajectory of a given command during the closed‐loop transient response. It is shown that this mechanism is effective in improving transient performance of discrete‐time model reference adaptive control architectures. Using a logarithmic Lyapunov function, we prove Lyapunov stability of the closed‐loop system as well as asymptotic convergence of the system error states involving the difference between the states of the uncertain dynamical system and the states of the reference model, as well as driving the command governor signal to zero.

中文翻译：

---

改善离散时间模型参考自适应控制体系结构的暂态性能

离散时间自适应控制算法可以直接在嵌入式代码中执行，这与需要离散化的连续时间对应算法不同。但是，由于基于Lyapunov差异表达式的复杂性，它们基于二次Lyapunov框架的设计非常复杂。因此，使用自适应控制算法解决瞬态性能问题的大量可用连续时间结果无法应用于或容易扩展到离散时间情况。在本文中，我们为离散时间不确定动力系统提出了一种新的模型参考自适应控制体系结构。具体而言，所提出的体系结构由命令调节器机制组成，该机制在闭环瞬态响应过程中调整给定命令的轨迹。结果表明，该机制可有效改善离散时间模型参考自适应控制体系结构的瞬态性能。使用对数Lyapunov函数，我们证明了闭环系统的Lyapunov稳定性以及系统误差状态的渐近收敛性，其中涉及不确定动力学系统的状态与参考模型的状态之间的差异，以及驱动了命令调速器信号为零。