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IMA Journal of Mathematical Control and Information 1997 14(4):319-332; doi:10.1093/imamci/14.4.319
© 1997 by Institute of Mathematics and its Applications
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Optimal guaranteed-cost control of discrete-time nonlinear uncertain systems

ANDREY V. SAVKIN and IAN R. PETERSEN

Department of Electrical and Electronic Engineering and Cooperative Research Center for Sensor Signal and Information Processing, University of Melbourne Parkville, Victoria 3052, Australia
Department of Electrical Engineering, Australian Defence Force Academy Campbell, 2600, Australia

The paper presents a result on state-feedback optimal guaranteed-cost control for a class of nonlinear uncertain discrete-time systems. The problem of optimal guaranteed-cost control being considered is defined over a finite time interval. The uncertainty class considered in the paper involves structured uncertainties which are required to satisfy a certain ‘averaged-sum quadratic constraint’. This uncertainty class combines aspects of norm-bounded and stochastic uncertainty descriptions. The solution to the optimal guaranteed-cost control problem is obtained by solving a parametrized dynamic-programming equation.


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