To circumvent the potentially poor transient response induced by nonlinear uncertain dynamics in the adaptive control system, this article proposes a new model reference adaptive control design scheme to improve its transient control response. We first construct a compensator to online extract the undesired dynamics in the online learning, which is incorporated into the reference model and control simultaneously. Then, an error feedback term is incorporated into the reference model to speed up the convergence of both the compensator and tracking error. Moreover, a new leakage term containing the estimation error is constructed and then added in the adaptive law to guarantee the convergence of both the estimation error and tracking error. To further reveal the mechanisms behind these proposed methods, a new methodology to analyze the transient error bounds based on L₂‐norm and Cauchy‐Schwartz inequality is also developed. Based on the analysis results, we find that the proposed methods can effectively reduce the bound of the tracking error and thus achieve an improved transient control performance without violating the system stability even with high‐gain adaptation. In addition, the frequency‐domain analysis is resorted to show the comparative responses of different adaptive laws, which indicate that the proposed adaptive law can maintain the stability margin even with a high‐gain learning rate. A numerical example is given to demonstrate improved control responses of these proposed schemes.

中文翻译：

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鲁棒的模型参考自适应控制，可增强瞬态性能

为了避免非线性不确定性动力学在自适应控制系统中引起的潜在不良瞬态响应，本文提出了一种新的模型参考自适应控制设计方案，以改善其瞬态控制响应。我们首先构造一个补偿器，以在线提取在线学习中不需要的动力，然后将其合并到参考模型中并同时进行控制。然后，将误差反馈项合并到参考模型中，以加快补偿器和跟踪误差的收敛速度。此外，构造一个包含估计误差的新泄漏项，然后将其添加到自适应定律中，以确保估计误差和跟踪误差的收敛。为了进一步揭示这些建议方法背后的机制，也发展了₂范数和Cauchy-Schwartz不等式。基于分析结果，我们发现所提出的方法可以有效地减小跟踪误差的范围，从而即使在高增益自适应的情况下也可以在不损害系统稳定性的情况下实现改进的瞬态控制性能。此外，通过频域分析来显示不同自适应律的比较响应，这表明所提出的自适应律即使在学习率较高的情况下也可以保持稳定性裕度。给出了一个数值示例来说明这些提议方案的改进控制响应。