CDC2000 Model Reduction Methodologies

Model Reduction Methodologies
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Control Integrated Control and CPU Scheduling Linear Design Techniques Adaptive Disturbance / Noise Compensation Nonlinear Model Predictive Control Sensitivity Design, Analysis and Limitations Analysis of Linear Systems Linear Matrix Inequalities in Design Lyapunov's 2nd Method Robotics: Tracking Control Lagrangian and Hamiltonian Theory Variable Structure Control Machine Vision Signal Processing Methods in Control Applied Nonlinear Control Author Index A B C D E F G H I J K L M N O P Q R S T U V W X Y Z	A Comparative Study of 7 Algorithms for Model Reduction Authors: Serkan Gugercin, Athanasios C. Antoulas, Volume: 1, Page 2367 Paper number 1345 Abstract: In this note, we compare seven model reduction algorithms by applying them to four different dynamical systems. There are four SVD based methods, and three moment matching based methods. The results illustrate that overall, balanced reduction and approximate balanced reduction are the best when we consider whole frequency range. Moment matching methods always lead to higher error norms than SVD based methods due to their local nature; but they are numerically more efficient. Among them, the rational Krylov algorithm gives the best results. CD001345.PDF (From Author) TOP Model Reduction of Singular Systems Authors: Wanquan Liu, Victor Sreeram, Volume: 1, Page 2373 Paper number 1185 Abstract: In this paper, the model reduction problem for singular systems is investigated. Firstly, the previous model reduction algorithm reported in [9] is presented and proved to be wrong. Detail examination of the algorithm [9] will show that the difficulty of model reduction for singular systems is to retain its impulsive nature. Thus, based on this observation, we closely investigate the impulsive controllability and impulsive observability of singular systems and propose a new decomposition approach for singular systems. Then a new model reduction algorithm is designed based on a new decomposition via the machinery of Nehari's approximation algorithm. This new model reduction algorithm will retain impulsive nature of the original system. Finally, one example is presented to illustrate the effectiveness of the proposed model reduction algorithm. CD001185.PDF (From Author) TOP Balanced Truncation Model Reduction Of Periodic Systems Authors: Andras Varga, Volume: 1, Page 2379 Paper number 1122 Abstract: 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. CD001122.PDF (From Author) TOP On Stochastic Balancing Related Model Reduction Authors: Andras Varga, Volume: 1, Page 2385 Paper number 1123 Abstract: We propose a general method based on the balanced stochastic truncation (BST) approach for the model reduction of stable linear systems. The new method relies on a recent general inner-outer factorization result and extends the applicability of the BST method to systems with infinite zeros. A computational algorithm with enhanced accuracy for the new BST model reduction approach is presented. The capabilities and advantages of the new approach are illustrated on an example. CD001123.PDF (From Author) TOP