论文标题
数据驱动的稳定和稳健控制变量中具有错误的离散时间线性系统
Data-Driven Stabilizing and Robust Control of Discrete-Time Linear Systems with Error in Variables
论文作者
论文摘要
这项工作介绍了基于平方的（SOS）框架，以对离散时间线性系统进行数据驱动的稳定和鲁棒的控制任务，在这些系统中，全州观测值会因l- infinity限制的输入，测量和过程噪声（可变设置中的误差）损坏。通过解决由多项式非统治约束形成的可行性程序，提供了一致性集合中所有植物的状态反馈超惊实，二次稳定性或正稳定性的证书。在轻度的紧凑性和数据收集假设下，SOS收紧程度将融合以恢复真正的超级抗议或正稳定控制器，并引入了一些保守主义，以进行二次稳定性。通过在保持紧密度的同时，通过应用替代定理的应用，从一致性集说明中消除了未知的噪声变量，从而提高了此SOS方法的性能。扩展了此SOS可行性方法，可在H2控制成本下提供最佳的稳健控制器。一致性集说明可以扩展到包括数据和过程受L-侵点有限测量，过程和输入噪声的组合影响的情况。
This work presents a sum-of-squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input, measurement, and process noise (error in variable setting). Certificates of state-feedback superstability, quadratic stability or positive stability of all plants in a consistency set are provided by solving a feasibility program formed by polynomial nonnegativity constraints. Under mild compactness and data-collection assumptions, SOS tightenings in rising degree will converge to recover the true superstabilizing or positive stabilizing controller, with some conservatism introduced for quadratic stabilizability. The performance of this SOS method is improved through the application of a theorem of alternatives while retaining tightness, in which the unknown noise variables are eliminated from the consistency set description. This SOS feasibility method is extended to provide worst-case-optimal robust controllers under H2 control costs. The consistency set description may be broadened to include cases where the data and process are affected by a combination of L-infinity bounded measurement, process, and input noise.
