Stochastic Model Predictive Control with Online Risk Allocation and Feedback Gain Selection
This addresses a computational bottleneck in control systems for robotics or autonomous vehicles, but it is incremental as it builds on existing methods with approximations.
The paper tackles the intractable nonconvex problem in Stochastic Model Predictive Control by deriving disjunctive convex chance constraints and selecting feedback laws from precomputed candidates, enabling efficient solution as a mixed-integer conic optimization problem validated in a path-planning application.
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.