Learning Stochastic Parametric Differentiable Predictive Control Policies

The problem of synthesizing stochastic explicit model predictive control policies is known to be quickly intractable even for systems of modest complexity when using classical control-theoretic methods. To address this challenge, we present a new scalable method called stochastic parametric differentiable predictive control (SP-DPC) for optimizing neural control policies governing stochastic linear systems subject to nonlinear chance constraints. SP-DPC is formulated as a deterministic approximation to the stochastic parametric constrained optimal control problem. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. We provide theoretical probabilistic guarantees for policies learned via the SP-DPC method on closed-loop stability and chance constraints satisfaction. We demonstrate the proposed policy optimization algorithm in numerical examples.