Approach to modeling and estimation for uncertain systems

Optimal modeling and optimal estimation are discussed for uncertain dynamic systems. Uncertainty of the system is assumed to be presented by multiple models, or a set of possible parameters, and their own probabilities. Optimal solutions are derived by minimizing cost functions of quadratic form. If the number of the multiple models is finite, the optimal nominal model and the optimal estimator can be realized by systems of finite order. In general, however, the order of these optimal solutions is much higher than that of each possible dynamic model. In order to make their implementation more practical, approximation by reduced-order models is necessary. These problems can be reduced to those of ordinary reduced-order modeling and reduced-order estimation, where some computation is necessary. Suboptimal reduced-order models and estimators that can be obtained with simple calculation are also investigated. Approaches developed recently, including the balanced realization model, the chained aggregation model, and the principal coordinate realization model are applied. These approaches are compared by using simple examples. In the examples, performance robustness obtained by the multiple model method is also illustrated.