控制矩阵未知的MIMO系统的指数稳定自适应控制
Exponentially Stable Adaptive Control of MIMO Systems with Unknown Control Matrix
摘要：
本文研究线性时不变多输入多输出（MIMO）对象的直接模型参考自适应控制问题，不需要任何关于系统矩阵的先验知识。为了解决这一问题，提出了一种新的方法，该方法包括三个主要阶段。首先，使用著名的DREM过程，进行对象参数化，得到线性回归，其中对象矩阵和状态初始条件是未知参数。其次，这种回归被代入已知的方程的控制器参数的计算。第三，利用具有指数收敛速度的新调节律辨识控制器参数。据作者所知，这种方法是第一个同时提供以下特征的方法：1）它适用于一般的完全未知的MIMO系统（例如，没有关于状态或控制分配矩阵的任何信息，后者的符号等）; 2)在有限激励条件下，保证了参数和跟踪误差的指数收敛性：3）保证了控制律参数矩阵的过渡曲线的单调性。用一架小型客机的橡胶和副翼控制模型进行的实验结果证实了所有的理论结果。
英文摘要：
The scope of this research is a problem of the direct model reference adaptive control of linear time-invariant multi-input multi-output (MIMO) plants without any a priori knowledge about system matrices. To handle it, a new method is proposed, which includes three main stages. Firstly, using the well-known DREM procedure, the plant parametrization is made to obtain the linear regressions, in which the plant matrices and state initial conditions are the unknown parameters. Secondly, such regressions are substituted into the known equations for the controller parameters calculation. Thirdly, the controller parameters are identified using the novel adjustment law with exponential rate of convergence. To the best of the authors knowledge, such a method is the first one to provide the following features simultaneously: 1) it is applicable for the generic completely unknown MIMO systems (e.g. without any information about state or control allocation matrices, the sign of the latter, etc.); 2) it guarantees the exponential convergence of both the parameter and tracking errors under the mild requirement of the regressor finite excitation; 3) it ensures monotonicity of the transient curves of the control law parameters matrices. The results of the conducted experiments with the model of a rubber and ailerons control of a small passenger aircraft corroborate all the theoretical results.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
