Model reduction for linear delay systems using a delay-independent balanced truncation approach

A model reduction approach for asymptotically stable linear delay-differential equations is presented in this paper. Specifically, a balancing approach is developed on the basis of energy functionals that provide (bounds on) a measure of energy related to observability and controllability, respectively. The reduced-order model derived in this way is again a delay-differential equation, such that the method is structure preserving. In addition, asymptotic stability is preserved and an a priori bound on the reduction error is derived, providing a measure of accuracy of the reduction. The results are illustrated by means of application on an example

Model order reduction for linear time delay systems:A delay-dependent approach based on energy functionals

This paper proposes a model order reduction technique for asymptotically stable linear time delay systems with point-wise delays. The presented delay-dependent approach, which can be regarded as an extension of existing balancing model order reduction techniques for linear delay-free systems, is based on energy functionals that characterize observability and controllability properties of the time delay system. The reduced model obtained by this approach is an asymptotically stable time delay system of the same type as the original model, meaning that the approach is both stability- and structure-preserving. It also provides an a priori bound on the reduction error, serving as a measure of the reduction accuracy. The effectiveness of the proposed method is illustrated by numerical simulations.</p

Model Order Reduction for (Stochastic-) Delay Equations With Error Bounds

We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic interpretation. Transferring error bounds based on Hankel operators to delay systems, we find error estimates for the difference between the dynamics of the full and reduced model. This analysis also yields new error bounds for bilinear systems and stochastic systems with multiplicative noise and non-zero initial states

An extended model order reduction technique for linear delay systems

\u3cp\u3eThis paper presents a model reduction technique for linear delay differential equations that, first, preserves the infinite-dimensional nature of the system, and, second, enables the preservation of additional properties such as physical interconnection structures or uncertainties. This structured/robust reduction of delay systems is achieved by allowing additional degrees of freedom in the characterization of (bounds on) controllability and observability energy functionals, leading to a so-called extended balancing procedure. In addition, the proposed technique preserves stability properties and provides an a priori error bound. The relevance of the method in controller reduction is discussed and illustrative numerical examples are presented.\u3c/p\u3

A physics-based approach to flow control using system identification

Control of amplifier flows poses a great challenge, since the influence of environmental noise sources and measurement contamination is a crucial component in the design of models and the subsequent performance of the controller. A modelbased approach that makes a priori assumptions on the noise characteristics often yields unsatisfactory results when the true noise environment is different from the assumed one. An alternative approach is proposed that consists of a data-based systemidentification technique for modelling the flow; it avoids the model-based shortcomings by directly incorporating noise influences into an auto-regressive (ARMAX) design. This technique is applied to flow over a backward-facing step, a typical example of a noise-amplifier flow. Physical insight into the specifics of the flow is used to interpret and tailor the various terms of the auto-regressive model. The designed compensator shows an impressive performance as well as a remarkable robustness to increased noise levels and to off-design operating conditions. Owing to its reliance on only timesequences of observable data, the proposed technique should be attractive in the design of control strategies directly from experimental data and should result in effective compensators that maintain performance in a realistic disturbance environment

Stability-preserving model order reduction for nonlinear time delay systems

Delay elements are needed to model physical, industrial and engineering systems as action and reaction always come with latency. In this paper, we present an algorithm to obtain the reduced-order models (ROMs) while preserving the stability of nonlinear time delay systems (TDSs), which are approximated first by the piecewise-linear TDSs. One contribution is the derivation of the input-output stability of piecewise-linear TDSs, for the first time. The other is the preservation of the input-output stability of the ROMs. The system matrices are obtained by the left projection matrix from the solution of linear matrix inequalities (LMIs) for the input-output stability test of the original piecewise-linear TDSs and the right projection matrix from matching the estimated moments. An application example then verifies the effectiveness of the proposed method.published_or_final_versio