Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data

We illustrate procedures to identify a state-space representation of a lossless- or dissipative system from a given noise-free trajectory; important special cases are passive- and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; state-space equations are then computed solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order mode

Dissipativity preserving model reduction by retention of trajectories of minimal dissipation

We present a method for model reduction based on ideas from the behavioral theory of dissipative systems, in which the reduced order model is required to reproduce a subset of the set of trajectories of minimal dissipation of the original system. The passivity-preserving model reduction method of Antoulas (Syst Control Lett 54:361-374, 2005) and Sorensen (Syst Control Lett 54:347-360, 2005) is shown to be a particular case of this more general class of model reduction procedures

Optimal time-domain moment matching with partial placement of poles and zeros

In this paper we consider a minimal, linear, time-invariant (LTI) system of order n, large. Our goal is to compute an approximation of order ν < n that simultaneously matches ν moments, has ℓ poles and k zeros fixed, with ℓ + k < ν, and achieves minimal H2 norm of the approximation error. For this, in the family of ν order parametrized models that match ν moments we impose ℓ+k linear constraints yielding a subfamily of models with ℓ poles and k zeros imposed. Then, in the subfamily of ν order models matching ν moments, with ℓ poles and k zeros imposed we propose an optimization problem that provides the model yielding the minimal H2-norm of the approximation error. We analyze the first-order optimality conditions of this optimization problem and compute explicitly the gradient of the objective function in terms of the controllability and the observability Gramians of the error system. We then propose a gradient method that finds the (optimal) stable model, with fixed ℓ poles and k zeros

A framework for synthesis of reduced order models

A framework for model reduction and synthesis is presented, which enables the re-use of reduced order models in circuit simulation. Especially when model reduction exploits structure preservation, we show that using the model as a current-driven element is possible, and allows for synthesis without controlled sources. Two synthesis techniques are considered: (1) by means of realizing the reduced transfer function into a netlist and (2) by unstamping the reduced system matrices into a circuit representation. The presented framework serves as a basis for reduction of large parasitic R/RC/RCL network

Identification of Port-Hamiltonian Systems from Frequency Response Data

In this paper, we study the identification problem of a passive system from tangential interpolation data. We present a simple construction approach based on the Mayo-Antoulas generalized realization theory that automatically yields a port-Hamiltonian realization for every strictly passive system with simple spectral zeros. Furthermore, we discuss the construction of a frequency-limited port-Hamiltonian realization. We illustrate the proposed method by means of several examples

Matrix nearness-based guaranteed passive system approximation

In this paper we present a new approach towards global passive approximation in order to find a passive real-rational transfer function G(s) that is an arbitrarily close approximation of the passive transfer function nearest to a non-passive square transfer function H (s). It is based on existing solutions to pertinent matrix nearness problems. It is shown that the key point in constructing the passive real-rational transfer function G(s), is to find a good rational approximation of the well-known ramp function over an interval defined by the minimum and maximum dissipation of H(s). The proposed algorithms rely on the stable-anti-stable decomposition of a given transfer function. Pertinent examples are given to show the scope and accuracy of the proposed algorithms

A Matlab toolbox for the regularization of descriptor systems arising from generalized realization procedures

In this report we introduce a Matlab toolbox for the regularization of descriptor systems. We apply it, in particular, for systems resulting from the generalized realization procedure of [16], which generates, via rational interpolation techniques, a linear descriptor system from interpolation data. The resulting system needs to be regularized to make it feasible for the use in simulation, optimization, and control. This process is called regularization.DFG, SFB 1029, Substantial efficiency increase in gas turbines through direct use of coupled unsteady combustion and flow dynamic