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Designing SDRE-Based Controller for a Class of Nonlinear Singularly Perturbed Systems
Seyed Mostafa Ghadami, Roya Amjadifard, Hamid Khaloozadeh
Pages - 1 - 18     |    Revised - 15-11-2012     |    Published - 28-02-2013
Volume - 4   Issue - 1    |    Publication Date - June 2013  Table of Contents
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KEYWORDS
Singularly Perturbed Systems, State-Dependent Riccati Equation, Nonlinear Optimal Control, Finite-Horizon Optimization Problem, Single Link Flexible Joint Robot Manipulator
ABSTRACT
Designing a controller for nonlinear systems is difficult to be applied. Thus, it is usually based on a linearization around their equilibrium points. The state dependent Riccati equation control approach is an optimization method that has the simplicity of the classical linear quadratic control method. On the other hand, the singular perturbation theory is used for the decomposition of a high-order system into two lower-order systems. In this study, the finite-horizon optimization of a class of nonlinear singularly perturbed systems based on the singular perturbation theory and the state dependent Riccati equation technique together is addressed. In the proposed method, first, the Hamiltonian equations are described as a state-dependent Hamiltonian matrix, from which, the reduced-order subsystems are obtained. Then, these subsystems are converted into outerlayer, initial layer correction and final layer correction equations, from which, the separated state dependent Riccati equations are derived. The optimal control law is, then, obtained by computing the Riccati matrices.
CITED BY (2)  
1 Zhang, Y., Naidu, D. S., Cai, C., & Zou, Y. (2015). Composite control of a class of nonlinear singularly perturbed discrete-time systems via D-SDRE. International Journal of Systems Science, (ahead-of-print), 1-10.
2 Zhang, Y., Subbaram Naidu, D., Cai, C., & Zou, Y. (2014, August). Nonlinear Model Predictive Control for regulation of a class of Nonlinear Singularly Perturbed discrete-time systems. In Resilient Control Systems (ISRCS), 2014 7th International Symposium on (pp. 1-6). IEEE.
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Mr. Seyed Mostafa Ghadami
Department of Electrical Engineering,Science and Research Branch, Islamic Azad University, Tehran, Iran - Iran
m.gadami@yahoo.com
Dr. Roya Amjadifard
TarbiatMoallem University, Tehran, Iran - Iran
Associate Professor Hamid Khaloozadeh
K.N. Toosi University of Technology, Tehran, Iran - Iran