Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 54, Issue 4, Pages 881-886Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2008.2010970
Keywords
Approximating control; discrete-time systems; model predictive control; nonlinear systems; receding horizon control
Funding
- FAPESP [04/15672-5, 03/06736-7]
- CNPq [304429/2007-4, 304856/2007-0]
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This technical note addresses the approximation of the infinite horizon problem and the stability of the approximating controls generated by the receding horizon method. The setup takes into account systems and costs that may be nonlinear and discontinuous, with possibly state and control constraints, allowing for a wide range of problems. A detectability notion is introduced that matches standard regularity conditions such as existence of bounds for the cost, and does not require any continuity hypothesis. It is shown that the receding horizon controls associated with the finite horizon problems are approximating solutions for the infinite horizon problem, for a large enough horizon. Exponential stability of the controlled system and estimates for horizons ensuring stability and approximation of the infinite horizon problem are also studied.
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