SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3584-3607, December 2023.
Abstract. We complete the first step toward the resolution of several decades-old challenges in disturbance-robust adaptive control. For a scalar system with an unknown parameter for which no a priori bound is given, with a disturbance that is of unlimited magnitude and possibly persistent (not square integrable), and without a persistence of excitation necessarily verified by the state, we consider the problems of (practical) gain assignment relative to the disturbance. We provide a solution to these heretofore unsolved feedback design problems with the aid of infinite-dimensional nonlinear feedback employing distributed delay of the state and input itself. Specifically, in addition to (0) the global boundedness of the infinite-dimensional state of the closed-loop system when the disturbance is present, we establish (1) practical input-to-output stability with assignable asymptotic gain from the disturbance to the plant state; (2) assignable exponential convergence rate; and (3) assignable radius of the residual set. The accompanying identifier in our adaptive controller guarantees (4) boundedness of the parameter estimate even when disturbances are present; (5) an ultimate estimation error which is proportional to the magnitude of the disturbance with assignable gain when there exists sufficient excitation of the state; and (6) exact parameter estimation in finite time when the disturbance is absent and there is sufficient excitation. Among our results, one reveals a trade-off between “learning capacity” and “disturbance robustness”: the less sensitive the identifier is to the disturbance, the less likely it is to learn the parameter.

中文翻译：

---

延迟状态和输入非线性反馈无参数约束的扰动状态自适应镇定

SIAM 控制与优化杂志，第 61 卷，第 6 期，第 3584-3607 页，2023 年 12 月。
摘要。我们完成了解决干扰鲁棒自适应控制几十年来挑战的第一步。对于参数未知且未给出先验界限的标量系统，其扰动幅度无限且可能持续（不可平方可积），并且没有必要由状态验证的持续激励，我们考虑以下问题相对于干扰的（实际）增益分配。我们借助利用状态和输入本身的分布式延迟的无限维非线性反馈，为这些迄今为止未解决的反馈设计问题提供了解决方案。具体来说，除了 (0) 存在扰动时闭环系统无限维状态的全局有界性之外，我们还建立了 (1) 实际的输入到输出稳定性，其中可从扰动到植物状态；(2)可指定的指数收敛速度；(3)残差集的可分配半径。我们的自适应控制器中的随附标识符保证（4）即使存在干扰，参数估计的有界性；(5) 当存在足够的状态激励时，最终估计误差与具有可分配增益的扰动的大小成正比；(6)在无扰动且激励充足的情况下，在有限时间内进行精确的参数估计。在我们的结果中，揭示了“学习能力”和“干扰鲁棒性”之间的权衡：标识符对干扰越不敏感，学习参数的可能性就越小。