Abstract
A class of linear dynamical control systems subject to uncertain but bounded disturbances is considered. The bounds imposed on the disturbances depend on the control magnitude and grow with the control. This situation occurs if the disturbances are due to the inaccuracy of the control implementation and often takes place in engineering applications such as transportation, aerospace, and robotic systems. Under certain assumptions, the minimax control problem is formulated and solved. Explicit expressions for the optimal control (both open-loop and feedback) are obtained that provide the minimax to the given performance index for arbitrary but bounded disturbances. Examples are given.
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L.S. Pontryagin V.G. Boltyanskii R.V. Gamkrelidze E.F. Mishchenko (1962) Mathematical Theory of Optimal Processes Wiley-Interscience New York, NY
F.L. Chernousko (2002) ArticleTitleMinimax Control for a Class of Systems under Disturbances Doklady Mathematics 65 310–313
F.L. Chernousko (2004) ArticleTitleOptimal Control for a Class of Systems Subjected to Disturbances Journal of Applied Mathematics and Mechanics 68 503–510 Occurrence Handle10.1016/j.jappmathmech.2004.07.003 Occurrence Handle2005i:49027
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1This work was supported by the Russian Foundation for Basic Research (Project 05-01-00647) and the Grant for Russian Scientific Schools (NSh 1627.2003.1).
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Chernousko, F.L. Minimax Control for a Class of Linear Systems Subject to Disturbances1. J Optim Theory Appl 127, 535–548 (2005). https://doi.org/10.1007/s10957-005-7501-1
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DOI: https://doi.org/10.1007/s10957-005-7501-1