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Robust continuous-time adaptive control by parameter projection

机译：通过参数投影进行鲁棒的连续时间自适应控制

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摘要

The problem of adaptive control of a continuous-time plant of arbitrary relative degree, in the presence of bounded disturbances as well as unmodeled dynamics, is addressed. The adaptation considered is the usual gradient update law with parameter projection, the latter being the only robustness enhancement modification employed. It is shown that if the unmodeled dynamics, which consists of multiplicative as well as additive system uncertainty, is small enough, then all the signals in the closed-loop system are bounded. This shows that extra modifications are not necessary for robustness with respect to bounded disturbances and small unmodeled dynamics. In the nominal case, where unmodeled dynamics and disturbances are absent, the asymptotic error in tracking a given reference signal is zero. Moreover, the performance of the adaptive controller is also robust.
机译：解决了在存在有界干扰以及未建模动力学的情况下对任意相对程度的连续时间工厂进行自适应控制的问题。所考虑的自适应是具有参数投影的常规梯度更新定律，后者是唯一采用的鲁棒性增强修改。结果表明，由乘法和加法系统不确定性组成的未建模动力学足够小，则闭环系统中的所有信号都是有界的。这表明对于有界干扰和较小的未建模动力学，鲁棒性不需要额外的修改。在标称情况下，如果没有未建模的动力学和干扰，则跟踪给定参考信号时的渐近误差为零。此外，自适应控制器的性能也很强大。

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