论文标题
自适应最佳$ \ ell_ \ infty $诱导的最小阶段SISO植物的稳定稳定在有限的干扰和副本因子扰动下
Adaptive optimal $\ell_\infty$-induced robust stabilization of minimum phase SISO plant under bounded disturbance and coprime factor perturbations
论文作者
论文摘要
本文解决了在$ \ ell_1 $设置中稳健控制理论框架中，离散时间最小相植物在$ \ ell_1 $设置中的最佳稳定稳定问题的问题。植物标称模型具有稳定零的转移功能的系数是未知的，并且属于系数空间中已知的有界多面体。植物的副因子扰动和外部干扰的上限的增长也未知。所考虑的问题是设计自适应控制器，该控制器以规定的准确性最小化了输出的最坏情况渐近上限。该问题的解决方案是基于未知参数的设置会员估计，并将控制标准视为识别标准。在额外的非限制性假设下，通过非线性编程通过估计参数的非线性转换来减少最佳估计的在线计算的难题。尽管未知参数具有未知能力，但拟议的自适应控制器以规定的准确性保证了自适应系统输出的最佳渐近上限，作为具有已知参数的植物的最佳控制器。除了自适应控制的最佳性外，提出的解决方案还提供了当前估计值和先验假设的在线验证/验证。
This paper addresses the problem of optimal robust stabilization of a discrete-time minimum-phase plant in the framework of robust control theory in the $\ell_1$ setup and under poor a priori information. Coefficients of the transfer function of the plant nominal model with stable zeros are unknown and belong to a known bounded polyhedron in the space of coefficients. The gains of coprime factor perturbations of the plant and the upper bound of external disturbance are also unknown. The problem under consideration is to design adaptive controller that minimizes, with the prescribed accuracy, the worst-case asymptotic upper bound of the output. Solution of the problem is based on set-membership estimation of unknown parameters and treating the control criterion as the identification criterion. A hard nonconvex problem of on-line computation of optimal estimates is reduced, under additional nonrestrictive assumption, to a linear-fractional programming via a nonlinear transformation of estimated parameters. Despite the non-identifiability of the unknown parameters, the proposed adaptive controller guarantees, with the prescribed accuracy, the same optimal asymptotic upper bound of the output of adaptive system as the optimal controller for the plant with known parameters. In addition to the optimality of adaptive control, the proposed solution provides on-line verification/validation of current estimates and a priori assumptions.
