Optimal projection methods for model order reduction of discrete-time systems

2018 ◽  
Vol 36 (4) ◽  
pp. 1105-1131 ◽  
Author(s):  
Salim Ibrir
Keyword(s):  
Discrete Time ◽  
Model Order Reduction ◽  
Numerical Algorithms ◽  
Order Reduction ◽  
Order System ◽  
Model Order ◽  
Reduced Order ◽  
Discrete Time Systems ◽  
Optimal Projection ◽  
Time Systems

AbstractNumerical algorithms are developed for model order reduction of discrete-time systems using both optimal projection and $H_2$-norm minimization. The state-space matrices of the reduced-order system are obtained via the solution of a convex optimization problem. Subsequently, the results are exploited for the design of non-linear reduced-order systems verifying the input-to-state stability property. Proofs of stability and error approximation bounds are provided along with numerical simulations to highlight the strengths and the validity of the theoretical results.

scholarly journals Development of an Improved Frequency Limited Model Order Reduction Technique and Error Bound for Discrete-Time Systems

2021 ◽  
Vol 30 (4) ◽  
pp. 729-738
Author(s):  
S. Batool ◽  
M. Imran ◽  
M. Imran ◽  
E. Elahi ◽  
A. Maqbool ◽  
...  
Keyword(s):  
Error Bound ◽  
Discrete Time ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Reduction Technique ◽  
Model Order ◽  
Discrete Time Systems ◽  
Time Systems

Iterative-learning procedures for nonlinear-model-order reduction in discrete time

2019 ◽  
Vol 37 (3) ◽  
pp. 953-986
Author(s):  
Salim Ibrir
Keyword(s):  
Nonlinear Model ◽  
Discrete Time ◽  
Model Order Reduction ◽  
Approximation Error ◽  
Order Reduction ◽  
Galerkin Projection ◽  
Dimensional System ◽  
Model Order ◽  
Reduced Order ◽  
Low Order

Abstract Efficient numerical procedures are developed for model-order reduction of a class of discrete-time nonlinear systems. Based on the solution of a set of linear-matrix inequalities, the Petrov–Galerkin projection concept is utilized to set up the structure of the reduced-order nonlinear model that preserves the input-to-state stability while ensuring an acceptable approximation error. The first numerical algorithm is based on the construction of a constant optimal projection matrix and a constant Lyapunov matrix to form the reduced-order dynamics. The second proposed algorithm aims to incorporate the output of the original system to correct the instantaneous value of the truncation matrix and maintain an acceptable approximation error even with low-order systems. An extension to uncertain systems is provided. The usefulness and the efficacy of the developed procedures are approved by the consideration of two numerical examples treating a nonlinear low-order system and a high-dimensional system, issued from the discretization of the damped heat-transfer partial-differential equation.

scholarly journals A NOVEL MIXED METHOD FOR THE MODEL ORDER REDUCTION OF LINEAR SYSTEMS USING PARTICLE SWARM OPTIMIZATION AND POLYNOMIAL METHOD

2013 ◽  
pp. 75-77
Author(s):  
M. SUDHEER KUMAR ◽  
N. NAGENDRA ◽  
T. MADHUBABU
Keyword(s):  
Mixed Method ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Original System ◽  
Pso Algorithm ◽  
Order System ◽  
Polynomial Method ◽  
Model Order ◽  
Reduced Order ◽  
Lower Order System

In this paper, a novel mixed method is used for reducing the higher order system to lower order system. The denominator polynomials are obtained by the PSO Algorithm and the numerator coefficients are derived by the polynomial method. This method is simple and computer oriented. If the original system is stable then reduced order system is also stable. The proposed method is illustrated with the help of typical numerical examples considered from the literature.

scholarly journals Dominant Pole Based Approximation for Discrete Time System

2019 ◽  
Vol 4 (1) ◽  
pp. 56-65 ◽  
Author(s):  
Richa ◽  
Awadhesh Kumar
Keyword(s):  
Discrete Time ◽  
Model Order Reduction ◽  
Large Scale ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Discrete Time System ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Dominant Pole

This paper presents an effective procedure for model order reduction of discrete time control system. The exact model derived from complex dynamic systems proves to be very complicated for analysis, control and design. This necessity brings about using a tool known as model order reduction technique or model simplification. A novel mixed method has been implemented in this paper for reducing the order of the large scale dynamic discrete system. Dominant pole based pole clustering method has been used to derive the coefficients of denominator polynomial while Padé approximation has been applied to obtain the coefficients of numerator polynomial of the reduced order model. The proposed method is quite simple and able to generate a stable reduced order model from high order stable discrete systems. The dominancy of poles has been decided by values of the ratio of residue to its pole. The pole is considered dominant which have larger ratio value. An illustrative example has been considered to show the various reduction steps. The result obtained confirms the effectiveness of the approach.

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