Model order reduction methods for linear time invariant systems are reviewed in this lecture. The basic ideas of the methods, such as the Padé approximation method, the rational interpolation method, the modal truncation method, the standard balanced truncation method, and the balancing related methods, are presented. The numerical algorithms of implementing the methods are discussed. For the b...

A model-reduction method for linear, parameter-varying systems based on parameter-varying balanced realizations is proposed for a body freedom flutter vehicle. A high-order linear, parameter-varying model with hundreds of states describes the coupling between the short period and first bendingmode with additional structural bending and torsion modes that couple with the rigid body dynamics. How...

We present a novel non-iterative and rigorously motivated approach for estimating hidden Markov models (HMMs) and factorial hidden Markov models (FHMMs) of high-dimensional signals. Our approach utilizes the asymptotic properties of a spectral, graph-based approach for dimensionality reduction and manifold learning, namely the diffusion framework. We exemplify our approach by applying it to the...

Partial dimension reduction is a general method to seek informative convex combinations of predictors of primary interest, which includes dimension reduction as its special case when the predictors in the remaining part are constants. In this paper, we propose a novel method to conduct partial dimension reduction estimation for predictors of primary interest without assuming that the remaining ...

We present a method for solving implicit (factored) Markov decision processes (MDPs) with very large state spaces. We introduce a property of state space partitions which we call-homogeneity. Intuitively, an-homogeneous partition groups together states that behave approximately the same under all or some subset of policies. Borrowing from recent work on model minimization in computer-aided soft...

We consider the problem of reducing a model in a way that preserves a partition of the system states. This is motivated, for instance, in situations where state variables are associated with the topology of a networked system. In earlier work we proposed an LMI method based on block-structured generalized controllability and observability gramians; to make such strategy feasible, coprime factor...

The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined methods for deriving interpolatory reduced models directly from input/output measurements; and extensions for the reduction of parametrized systems. This ch...

This paper introduces an interpolation framework for the weighted-H2 model reduction problem. We obtain a new representation of the weighted-H2 norm of SISO systems that provides new interpolatory first order necessary conditions for an optimal reduced-order model. The H2 norm representation also provides an error expression that motivates a new weighted-H2 model reduction algorithm. Several nu...

Modeling is an essential part of the analysis and the design of dynamic systems. Contemporary computer algorithms can produce very detailed models for complex systems with little time and effort. However, over complicated models may not be efficient. Therefore, reducing a model to a more manageable size has become an attractive research topic. A very useful type of reduced models is obtained by...