Tensor-based performance assessment of switched control systems with time-varying disturbance dynamics

This paper concerns with performance assessment of switched control systems with time-varying disturbances dynamics. The covariance tensor-based data processing methods is proposed for solving the performance assessment problem for this class of dynamical systems. The time invariant minimum variance control for one type of process dynamics is no longer minimum variance control for another type of process, and being in the some one process the minimum variance control for one type of disturbance dynamics is no longer minimum variance control for another type of disturbance. An explicit solution to a minimum variance control under some one disturbance that can optimize entire performance of switched control systems with bounded disturbances dynamics is derived in this paper and is used as a benchmark to assess controller performance of switched systems under time invariant feedback controller. It is shown that this performance indices can be derived from routine operating data through covariance tensor-based data analysis and tensor decomposition technique. The proposed methods are illustrated through a simulated example of constructing data via using three-order and four-order tensor geometric structure, which demonstrates the benefits of applying tensor-based performance assessment approach.