Stochastic Model Predictive Control with Online Risk Allocation and Feedback Gain Selection

TL;DR

This paper introduces a convex approximation approach for stochastic model predictive control that enables efficient optimization of risk allocation and feedback policies using mixed-integer conic programming.

Contribution

It develops disjunctive convex chance constraints and candidate feedback law selection to transform intractable problems into solvable mixed-integer conic programs.

Findings

The method efficiently solves path-planning problems under uncertainty.

Convex approximations replace nonconvex Gaussian quantile functions.

The approach applies to general chance constraints with products of variables.

Abstract

Stochastic Model Predictive Control addresses uncertainties by incorporating chance constraints that provide probabilistic guarantees of constraint satisfaction. However, simultaneously optimizing over the risk allocation and the feedback policies leads to intractable nonconvex problems. This is due to (i) products of functions involving the feedback law and risk allocation in the deterministic counterpart of the chance constraints, and (ii) the presence of the nonconvex Gaussian quantile (probit) function. Existing methods rely on two-stage optimization, which is nonconvex. To address this, we derive disjunctive convex chance constraints and select the feedback law from a set of precomputed candidates. The inherited compositions of the probit function are replaced with power- and exponential-cone representable approximations. The main advantage is that the problem can be formulated as a mixed-integer conic optimization problem and efficiently solved with off-the-shelf software. Moreover, the proposed formulations apply to general chance constraints with products of exclusive disjunctive and Gaussian variables. The proposed approaches are validated with a path-planning application.