A Semismooth Predictor Corrector Method for Real-Time Constrained Parametric Optimization with Applications in Model Predictive Control

TL;DR

This paper introduces a semismooth predictor-corrector method for efficiently solving real-time constrained parametric optimization problems, with applications demonstrated in nonlinear model predictive control.

Contribution

The paper develops a novel SSPC method that handles active set changes naturally and provides theoretical guarantees for solution trajectory tracking in real-time optimization.

Findings

Effective handling of active set changes

Theoretical bounds on tracking error

Successful application to nonlinear model predictive control

Abstract

Real-time optimization problems are ubiquitous in control and estimation, and are typically parameterized by incoming measurement data and/or operator commands. This paper proposes solving parameterized constrained nonlinear programs using a semismooth predictor-corrector (SSPC) method. Nonlinear complementarity functions are used to reformulate the first order necessary conditions of the optimization problem into a parameterized non-smooth root-finding problem. Starting from an approximate solution, a semismooth Euler-Newton algorithm is proposed for tracking the trajectory of the primal-dual solution as the parameter varies over time. Active set changes are naturally handled by the SSPC method, which only requires the solution of linear systems of equations. The paper establishes conditions under which the solution trajectories of the root-finding problem are well behaved and provides sufficient conditions for ensuring boundedness of the tracking error. Numerical case studies featuring the application of the SSPC method to nonlinear model predictive control are reported and demonstrate the advantages of the proposed method.