The problem of adaptive control design for multivariable linear time-invariant plants with unknown control direction is considered. A solution is proposed based on the SDU factorization of the high frequency gain matrix (HFG) and the monitoring function approach. The adaptation scheme is the binary model reference adaptive control (BMRAC) which utilizes parameter projection and sufficiently high adaptation gains. The signs of the leading principal minors of the HFG define the control directions, and the lack of knowledge of which is a major challenge in the multivariable framework. The role of the monitoring function is to monitor the output error transient and then provide the necessary changes of the adaptation gain signs to guarantee a stable adaptive control. In addition to proving the signal boundedness of the resulting closed-loop system, the output tracking error is shown to be asymptotically as well as exponentially practically stable, i.e., exponentially stable with respect to a small residual compact set of size inversely proportional to the BMRAC adaptation gain. The latter implies good transient properties of the output tracking error in contrast to conventional adaptive laws which only guarantee asymptotic stability but can lead to extremely slow error convergence. The extension of the proposed approach to matched disturbances is also briefly discussed following the classical paradigm of disturbance estimators. Numerical results with a visual servoing application illustrate the efficiency of the proposed method.

考虑控制方向未知的多变量线性时不变植物的自适应控制设计问题。提出了一种基于高频增益矩阵（HFG）的SDU分解和监视功能方法的解决方案。自适应方案是二进制模型参考自适应控制（BMRAC），它利用参数投影和足够高的自适应增益。HFG的主要主要未成年人的标志定义了控制方向，而对其知识的缺乏是多变量框架中的主要挑战。监视功能的作用是监视输出误差瞬态，然后提供自适应增益符号的必要变化，以确保稳定的自适应控制。除了证明最终闭环系统的信号有界外，输出跟踪误差被显示为渐近渐近稳定，即相对于与BMRAC自适应增益成反比的较小的剩余紧凑集合，呈指数稳定。与传统的自适应律相比，后者意味着输出跟踪误差具有良好的瞬态特性，而传统的自适应律只能保证渐近稳定性，但会导致误差收敛极慢。遵循扰动估计器的经典范例，还简要讨论了所提出方法对匹配扰动的扩展。视觉伺服应用的数值结果说明了该方法的有效性。相对于与BMRAC自适应增益成反比的较小的剩余紧凑集合，其指数稳定。与传统的自适应定律相比，后者意味着输出跟踪误差具有良好的瞬态特性，而传统的自适应定律仅保证渐近稳定性，但会导致误差收敛极慢。遵循扰动估计器的经典范例，还简要讨论了所提出方法对匹配扰动的扩展。视觉伺服应用的数值结果说明了该方法的有效性。相对于与BMRAC自适应增益成反比的较小的剩余紧凑集合，其指数稳定。与传统的自适应定律相比，后者意味着输出跟踪误差具有良好的瞬态特性，而传统的自适应定律仅保证渐近稳定性，但会导致极慢的误差收敛。遵循扰动估计器的经典范例，还简要讨论了所提出方法对匹配扰动的扩展。视觉伺服应用的数值结果说明了该方法的有效性。遵循扰动估计器的经典范例，还简要讨论了所提出方法对匹配扰动的扩展。视觉伺服应用的数值结果说明了该方法的有效性。遵循扰动估计器的经典范例，还简要讨论了所提出方法对匹配扰动的扩展。视觉伺服应用的数值结果说明了该方法的有效性。