Balanced Truncation Based on Generalized Multiscale Finite Element Method for the Parameter-Dependent Elliptic Problem

In this paper,we combine the generalized multiscale finite element method(GMsFEM)with the balanced truncation(BT)method to address a parameterdependent elliptic problem.Basically,in progress of a model reduction we try to obtain accurate solutions with less computational resources.It is realized via a spectral decomposition from the dominant eigenvalues,that is used for an enrichment of multiscale basis functions in the GMsFEM.The multiscale bases computations are localized to specified coarse neighborhoods,and follow an offline-online process in which eigenvalue problems are used to capture the underlying system behaviors.In the BT on reduced scales,we present a local-global strategy where it requires the observability and controllability of solutions to a set of Lyapunov equations.As the Lyapunov equations need expensive computations,the efficiency of our combined approach is shown to be readily flexible with respect to the online space and an reduced dimension.Numerical experiments are provided to validate the robustness of our approach for the parameter-dependent elliptic model.

Reduced-order design of Robust H_∞ Controller for an Inertial Stabilized Aerial Platform

The uncertainty disturbance is one of the main disturbances that seriously influences the stabilization precision of an aerial inertially stabilized platform(ISP)system.In this paper,to improve the stabilization precision of the ISP under disturbance uncertainty,a robust H∞controller is designed in this paper.Then,the reduction order is carried out for high-order controllers generated by the robust H∞loop shaping control method.The application of the minimum implementation and balanced truncation algorithm in controller reduction is discussed.First,the principle of reduced order of minimum implementation and balanced truncation are analyzed.Then,the method is used to reduce the order of the high-order robust H∞loop shaping controller.Finally,the method is analyzed and verified by the simulations and experiments.The results show that by the reduced-order method of minimum implementation and balanced truncation,the stabilization precision of the robust H∞loop shaping controller is increased by about 10%.