Control and dynamics of linear systems under finite quantised feedback

Authors:
Wing Shing Wong;Hui Cheng
Affiliations:
Department of Information Engineering, Chinese University of Hong Kong, Shatin, N.T., Hong Kong.;Department of Automation, Sun Yat-sen University, Guangzhou 510275, China
Venue:
International Journal of Systems, Control and Communications
Year:
2011

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Abstract

This paper addresses control problems and analyses dynamics for linear systems under finite quantised feedback. The optimal one-bit control laws are developed, which minimise either an asymptotic time-averaged expected cost function or an asymptotic expected cost function. The closed-loop system with one-bit controller is a piecewise linear transformation. In the paper, the dynamical behaviour of the closed-loop system is investigated via invariant measures. The invariant distribution can be obtained from the induced matrix when the closed-loop system is a Markov transformation. It is shown that there are infinitely many cases of Markov transformations.