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2012 (Vol. 4, Issue: 13)
Article Information:

Lyapunov Equations Approach for Robust Nonlinear Optimal Control Problems

Zhenyu Han, Shurong Li and Shaowen Peng
Corresponding Author:  Zhenyu Han 

Key words:  Optimal control, lyapunov equations, robust optimization, uncertainty, , ,
Vol. 4 , (13): 2017-2023
Submitted Accepted Published
March 31, 2012 April 11, 2012 July 01, 2012

In this study, nonlinear constrained optimal control problems with uncertain parameters which can be addressed by a robust worst-case formulation are considered. The robust worst-case formulation leads to a bi-level min-max optimization problem. We propose a method to solve this min-max optimization problem based on Lyapunov differential equations. Employing first order derivatives of both the reference states and uncertainty parameters, the linear approximation of the dynamic system and inequality constraints can be obtained. After that, the Lyapunov differential equations can be formed based on the linear approximation and the upper bound for the worst case of the inequality state constraints accepted by the uncertain parameters can be obtained. Then the bi-level min-max optimization problem is transformed into a normal single-level optimization control problems which can be solved easily. To show the effectiveness of the proposed method, the simulation results of two robust constrained nonlinear optimal control problems are presented.

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  Cite this Reference:
Zhenyu Han, Shurong Li and Shaowen Peng, 2012. Lyapunov Equations Approach for Robust Nonlinear Optimal Control Problems.  Research Journal of Applied Sciences, Engineering and Technology, 4(13): 2017-2023.
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ISSN (Online):  2040-7467
ISSN (Print):   2040-7459
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