Sliding mode regulator as solution to optimal control problem for non-linear polynomial systems

This paper presents the optimal control problem for a non-linear polynomial system with respect to a Bolza–Meyer criterion with a non-quadratic non-integral term. The optimal solution is obtained as a sliding mode control, whereas the conventional polynomial-quadratic regulator does not lead to a ca...

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Bibliographic Details
Published in:Journal of the Franklin Institute 2010-08, Vol.347 (6), p.910-922
Main Authors: Basin, Michael, Calderon-Alvarez, Dario
Format: Article
Language:English
Subjects:
Identification
Optimal control
Sliding mode control
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Summary:This paper presents the optimal control problem for a non-linear polynomial system with respect to a Bolza–Meyer criterion with a non-quadratic non-integral term. The optimal solution is obtained as a sliding mode control, whereas the conventional polynomial-quadratic regulator does not lead to a causal solution and, therefore, fails. Performance of the obtained optimal controller is verified in the illustrative example against the conventional polynomial-quadratic regulator that is optimal for the quadratic Bolza–Meyer criterion. The simulation results confirm an advantage in favor of the designed sliding mode control.
ISSN:0016-0032
1879-2693
DOI:10.1016/j.jfranklin.2009.11.001