# American Institute of Mathematical Sciences

September  2015, 35(9): 4665-4681. doi: 10.3934/dcds.2015.35.4665

## Control of dynamical systems with discrete and uncertain observations

 1 Scientific Systems Company, Inc, 500 West Cummings Park, Suite 3000, Woburn, MA 01801, United States 2 Coordinated Science Laboratory and the Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States

Received  April 2014 Revised  October 2014 Published  April 2015

In this paper we provide a design methodology to compute control strategies for a primary dynamical system which is operating in a domain where other dynamical systems are present and the interactions between these systems and the primary one are of interest or are being pursued in some sense. The information from the other systems is available to the primary dynamical system only at discrete time instances and is assumed to be corrupted by noise. Having available only this limited and somewhat corrupted information which depends on the noise, the primary system has to make a decision based on the estimated behavior of other systems which may range from cooperative to noncooperative. This decision is reflected in a design of the most appropriate action, that is, control strategy of the primary system. The design is illustrated by considering some particular collision avoidance problem scenarios.
Citation: Aleksandar Zatezalo, Dušan M. Stipanović. Control of dynamical systems with discrete and uncertain observations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4665-4681. doi: 10.3934/dcds.2015.35.4665
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##### References:
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