9,932 research outputs found
Balanced truncation model reduction of periodic systems
The balanced truncation approach to model reduction is considered for linear discrete-time periodic systems with time-varying dimensions. Stability of the reduced model is proved and a guaranteed additive bound is derived for the approximation error. These results represent generalizations of the corresponding ones for standard discrete-time systems. Two numerically reliable methods to compute reduced order models using the balanced truncation approach are considered. The square-root method and the potentially more accurate balancing-free square-root method belong to the family of methods with guaranteed enhanced computational accuracy. The key numerical computation in both methods is the determination of the Cholesky factors of the periodic Gramian matrices by solving nonnegative periodic Lyapunov equations with time-varying dimensions directly for the Cholesky factors of the solutions
An iterative scheme for finite horizon model reduction of continuous-time linear time-varying systems
In this paper, we obtain the functional derivatives of a finite horizon error
norm between a full-order and a reduced-order continuous-time linear
time-varying (LTV) system. Based on the functional derivatives, first-order
necessary conditions for optimality of the error norm are derived, and a
projection-based iterative scheme for model reduction is proposed. The
iterative scheme upon convergence produces reduced-order models satisfying the
optimality conditions. Finally, through a numerical example, we demonstrate the
better performance of the proposed model reduction scheme in comparison to the
finite horizon balanced truncation algorithm for continuous-time LTV systems
emgr - The Empirical Gramian Framework
System Gramian matrices are a well-known encoding for properties of
input-output systems such as controllability, observability or minimality.
These so-called system Gramians were developed in linear system theory for
applications such as model order reduction of control systems. Empirical
Gramian are an extension to the system Gramians for parametric and nonlinear
systems as well as a data-driven method of computation. The empirical Gramian
framework - emgr - implements the empirical Gramians in a uniform and
configurable manner, with applications such as Gramian-based (nonlinear) model
reduction, decentralized control, sensitivity analysis, parameter
identification and combined state and parameter reduction
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