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The paper proposes a new method to determine a binary control signal for ananalog linear system such that the state, or some output, of the system followsa given target trajectory. The method can also be used for digital-to-analogconversion. The heart of the proposed method is a new binary-enforcing NUVprior (normal with unknown variance). The resulting computations, for eachplanning period, amount to iterating forward-backward Gaussian message passingrecursions (similar to Kalman smoothing), with a complexity (per iteration)that is linear in the planning horizon. In consequence, the proposed method isnot limited to a short planning horizon.

Binary Control and Digital-to-Analog Conversion Using Composite NUV Priors and Iterative Gaussian Message Passing