Optimal Design of Stochastic Distributed Order Linear SISO Systems Using Hybrid Spectral Method
| Autor: | Ezra Kwok, Pham Luu Trung Duong, Moonyong Lee |
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| Rok vydání: | 2015 |
| Předmět: |
Optimal design
Mathematical optimization Polynomial chaos Article Subject lcsh:Mathematics General Mathematics Numerical analysis Monte Carlo method General Engineering lcsh:QA1-939 Optimal control Stability (probability) Moment (mathematics) lcsh:TA1-2040 lcsh:Engineering (General). Civil engineering (General) Spectral method Mathematics |
| Zdroj: | MATHEMATICAL PROBLEMS IN ENGINEERING Mathematical Problems in Engineering, Vol 2015 (2015) |
| ISSN: | 1563-5147 1024-123X |
| DOI: | 10.1155/2015/989542 |
| Popis: | The distributed order concept, which is a parallel connection of fractional order integrals and derivatives taken to the infinitesimal limit in delta order, has been the main focus in many engineering areas recently. On the other hand, there are few numerical methods available for analyzing distributed order systems, particularly under stochastic forcing. This paper proposes a novel numerical scheme for analyzing the behavior of a distributed order linear single input single output control system under random forcing. The method is based on the operational matrix technique to handle stochastic distributed order systems. The existing Monte Carlo, polynomial chaos, and frequency methods were first adapted to the stochastic distributed order system for comparison. Numerical examples were used to illustrate the accuracy and computational efficiency of the proposed method for the analysis of stochastic distributed order systems. The stability of the systems under stochastic perturbations can also be inferred easily from the moment of random output obtained using the proposed method. Based on the hybrid spectral framework, the optimal design was elaborated on by minimizing the suitably defined constrained-optimization problem. |
| Databáze: | OpenAIRE |
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