A program for solving the L2 reduced-order model problem with fixed denominator degree

We present a trust-region approach for optimal H2 model reduction of multiple-input/multiple-output (MIMO) linear dynamical systems. The proposed approach generates a sequence of reduced order models producing monotone improving H2 error norms and is globally convergent to a reduced order model guaranteed to satisfy first-order optimality conditions with respect to H2 error criteria. Unlike existing H2 descent methods, the method does not require solving any Lyapunov equations and is both numerically stable and computationally tractable even for very large order systems. This method appears to be the first descent approach that uses Hessian information for optimal H2 model reduction of MIMO dynamical systems.

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“…A similar expression for SISO systems was initially introduced by Krajewski et al [11], and rediscovered later by Gugercin and Antoulas [6], [4]:…”

Section: H 2 Error Gradients and Hessiansmentioning

confidence: 97%

A trust region method for optimal H<inf>2</inf> model reduction

Beattie

Gugercin

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

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“…For SISO systems, Krajewski et al [66] developed and proved a similar expression, which was later rediscovered in [56,53,9].…”

Section: Descent Algorithms For H2 Model Reductionmentioning

confidence: 95%

“…The (simpler) problem of finding locally optimal H2 reduced models has been studied extensively. Optimality conditions have been formulated either in terms of Lyapunov and Sylvester equations [89,64,61,96,91,81,27] or in terms of rational (tangential) interpolation conditions [73,54,55,57,84,35,67,21,22,18,66,76]. [57] showed the equivalence between the Lyapunov/Sylvester equation conditions and the interpolation framework that we describe here.…”

Section: Interpolatory H2-optimality Conditionsmentioning

confidence: 99%

“…Convergence may be guaranteed a priori in some circumstances [46]; yet there are known cases where convergence may fail [57,46]. When convergence occurs, the resulting reduced model is guaranteed to be a local H2-minimizer since the local maxima of the H2 minimization problem are known to be repellent [66]. Overall in practice, IRKA has seen significant success in computing high fidelity (locally) optimal reduced models and has been successfully applied in large-scale settings to find H2-optimal reduced models for systems with hundreds of thousands of state variables; for example, see [65] for application in cellular neurophysiology, [30] for energy efficient building design in order to produce accurate compact models for the indoor-air environment, [57] for optimal cooling for steel profiles.…”

Section: Irka For Optimal H2 Approximationmentioning

confidence: 99%

See 1 more Smart Citation

Chapter 7: Model Reduction by Rational Interpolation

Beattie¹,

Gugercin²

2017

Model Reduction and Approximation

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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 chapter offers a survey of interpolatory model reduction methods starting from basic principles and ranging up through recent developments that include weighted model reduction and structure-preserving methods based on generalized coprime representations. Our discussion is supported by an assortment of numerical examples.Mathematics Subject Classification (2010). 41A05, 93A15, 93C05, 37M99.

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“…The methods suggested in the literature to find L 2 -optimal reduced-order models are difficult to implement [2,3] or depend crucially on the initial conditions, [4]. To avoid these difficulties, resort can be made to a slightly different approach that refers to the L 2 norm of the so-called equation error.…”

mentioning

confidence: 99%

On MIMO model reduction by the weighted equation–error approach

Krajewski

Viaro

2007

Numer Algor

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The paper deals with the problem of approximating a stable continuous-time multivariable system by minimizing the L 2 -norm of a weighted equation error. Necessary and sufficient conditions of optimality are derived, and the main properties of the optimal reduced-order models are presented. Based on these conditions and properties, two efficient procedures for generating approximants that retain different numbers of Markov parameters and time moments are suggested and applied to benchmark examples. The results show that both the transient and the steady-state behaviour of the original systems are reproduced satisfactorily.

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A program for solving the L2 reduced-order model problem with fixed denominator degree

Cited by 20 publications

References 19 publications

A trust region method for optimal H<inf>2</inf> model reduction

A trust region method for optimal H<inf>2</inf> model reduction

Chapter 7: Model Reduction by Rational Interpolation

On MIMO model reduction by the weighted equation–error approach

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