Inexact Adjoint-based SQP Algorithm for Real-Time Stochastic Nonlinear MPC

This paper presents a real-time algorithm for stochastic nonlinear model predictive control (NMPC). The optimal control problem (OCP) involves a linearization based covariance matrix propagation to formulate the probabilistic chance constraints. Our proposed solution approach uses a tailored Jacobian approximation in combination with an adjoint-based sequential quadratic programming (SQP) method. The resulting algorithm allows the numerical elimination of the covariance matrices from the SQP subproblem, while ensuring Newton-type local convergence properties and preserving the block-sparse problem structure. It allows a considerable reduction of the computational complexity and preserves the positive definiteness of the covariance matrices at each iteration, unlike an exact Jacobian-based implementation. The real-time feasibility and closed-loop control performance of the proposed algorithm are illustrated on a case study of an autonomous driving application subject to external disturbances. Copyright (C) 2020 The Authors.