# Calculate Sensitivity Function Using Parallel Algorithm

## Abstract

**Problem statement:** To calculate sensitivity functions for a large dimension control system using one processor, it takes huge time to find the unknowns vectors for a linear system, which represents the mathematical model of the physical control system. This study is an attempt to solve the same problem in parallel to reduce the time factor needed and increase the efficiency. **Approach:** Calculate in parallel sensitivity function using n-1 processors where n is a number of linear equations which can be represented as TX = W, where T is a matrix of size n_{1}×n_{2}, X = T^{-1} W, is a vector of unknowns and ∂X/∂h =T^{-1} ((∂T/∂h)-(∂W/∂h)) is a sensitivity function with respect to variation of system components h. The parallel algorithm divided the mathematical input model into two partitions and uses only (n-1) processors to find the vector of unknowns for original system x = (x_{1},x_{2},...,x_{n})^{T} and in parallel using (n-1) processors to find the vector of unknowns for similar system (x') t = d^{t}T^{−1} = (x_{1}',x_{2}',...x_{n}')^{T} by using Net-Processors, where d is a constant vector. Finally, sensitivity function (with respect to variation of component ∂X/∂h_{i} = (x_{i}×x_{i}') can be calculated in parallel by multiplication unknowns X_{i}×X_{i}', where i = 0,1,...n-1. **Results:** The running time t was reduced to O(t/n-1) and, The Performance of parallel algorithm was increased by 40-55%. **Conclusion:** Used parallel algorithm reduced the time to calculate sensitivity function for a large dimension control system and the performance was increased.

**Journal of Computer Science**

**DOI:**https://doi.org/10.3844/jcssp.2008.928.933

**Submitted On:**22 December 2008

**Published On:**30 November 2008

**How to Cite:** Rjoub, H. A. (2008). Calculate Sensitivity Function Using Parallel Algorithm. *Journal of Computer Science*, *4*(11), 928-933. https://doi.org/10.3844/jcssp.2008.928.933

**Copyright:** © 2008 H. A. Rjoub. This is an open access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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### Keywords

- Sensitivity Function
- parallel
- linear equations
- variation
- running time
- mathematical model