Input Disturbance Rejection in Channel Signal-to-Noise Ratio Constrained Feedback Control
Rojas, A.J. and Middleton, R.H. and Freudenberg, J.S. and Braslavsky, J.H. (2008) Input Disturbance Rejection in Channel Signal-to-Noise Ratio Constrained Feedback Control. American Control Conference, 2008, Proceedings. ISBN 978-1-4244-2078-0 . pp. 3100-3105. ISSN 0743-1619
Communication channels impose a number of obstacles to feedback control. One recent line of work considers the problem of feedback stabilisation subject to a constraint on the channel signal-to-noise ratio (SNR). It has been shown for continuous-time systems that the optimal control problem of achieving the infimal SNR can be formulated as a linear quadratic Gaussian (LQG) control problem with weights chosen as in the loop transfer recovery (LTR) technique. The present paper extends this formulation to: discretetime systems; communications over channels with memory; and input disturbance rejection. By using this formulation, we derive exact expressions for the linear time invariant (LTI) controller that achieves the infimal SNR under the effect of time-delay and additive coloured noise. We then quantify the infimal SNR required for both stabilisation and input disturbance rejection for a relative degree one, minimum phase plant and a memoryless Gaussian channel.
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