Model reduction with a finite horizon H-infinity criterion

An important problem in flight control and Eying qualities is the approxima tion of a complex high-order system by a low-order model. For a given reduc ed-order model, we define the correlation measure between the plant and the model outputs to be the minimum of the ratio of weighted signal energy to weighted error energy. We give a criterion for the evaluation of the correl ation measure in terms of minimization of a parameter occurring in a two-po int boundary-value problem, Once the correlation measure for a given reduce d-order model can be evaluated, a nonlinear programming algorithm can be us ed to select a model that maximizes the correlation between the plant and m odel outputs, The correlation index used can be regarded as an extension of the H-infinity performance criterion to the finite interval time-varying e ase. However, the usual H-infinity problem seeks an optimal controller, whe reas our problem Is to select the reduced-order model matrices that give th e best correlation index. We also give an expression for the variation of t he correlation due to parameter variations. The utilization of the theory i s demonstrated by means of some examples.