Model-Predictive Control with New NUV Priors

Normals with unknown variance (NUV) can represent many useful priors including $L_p$ norms and other sparsifying priors, and they blend well with linear-Gaussian models and Gaussian message passing algorithms. In this paper, we elaborate on recently proposed discretizing NUV priors, and we propose new NUV representations of half-space constraints and box constraints. We then demonstrate the use of such NUV representations with exemplary applications in model predictive control, with a variety of constraints on the input, the output, or the internal stateof the controlled system. In such applications, the computations boil down to iterations of Kalman-type forward-backward recursions, with a complexity (per iteration) that is linear in the planning horizon. In consequence, this approach can handle long planning horizons, which distinguishes it from the prior art. For nonconvex constraints, this approach has no claim to optimality, but it is empirically very effective.

Half-Space and Box Constraints as NUV Priors: First Results

Normals with unknown variance (NUV) can represent many useful priors and blend well with Gaussian models and message passing algorithms. NUV representations of sparsifying priors have long been known, and NUV representations of binary (and M-level) priors have been proposed very recently. In this document, we propose NUV representations of half-space constraints and box constraints, which allows to add such constraints to any linear Gaussian model with any of the previously known NUV priors without affecting the computational tractability.

A Binarizing NUV Prior and its Use for M-Level Control and Digital-to-Analog Conversion

Priors with a NUV representation (normal with unknown variance) have mostly been used for sparsity. In this paper, a novel NUV prior is proposed that effectively binarizes. While such a prior may have many uses, in this paper, we explore its use for discrete-level control (with M $\geq$ 2 levels) including, in particular, a practical scheme for digital-to-analog conversion. 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 and can therefore outperform "optimal" methods. A preference for sparse level switches can easily be incorporated.

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

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.