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

TL;DR

This paper introduces a novel iterative Gaussian message passing approach using composite NUV priors for binary control and digital-to-analog conversion, enabling efficient long-horizon planning in linear systems.

Contribution

It presents a new binary-enforcing NUV prior and an iterative Gaussian message passing algorithm that scales linearly with the planning horizon.

Findings

Efficient binary control for linear systems with long planning horizons.

Applicable to digital-to-analog conversion tasks.

Computational complexity is linear in the planning horizon.

Abstract

The paper proposes a new method to determine a binary control signal for an analog linear system such that the state, or some output, of the system follows a given target trajectory. The method can also be used for digital-to-analog conversion. The heart of the proposed method is a new binary-enforcing NUV prior (normal with unknown variance). The resulting computations, for each planning period, amount to iterating forward-backward Gaussian message passing recursions (similar to Kalman smoothing), with a complexity (per iteration) that is linear in the planning horizon. In consequence, the proposed method is not limited to a short planning horizon.