Mathematics > Optimization and Control
[Submitted on 4 Dec 2018]
Title:A Semismooth Predictor Corrector Method for Real-Time Constrained Parametric Optimization with Applications in Model Predictive Control
View PDFAbstract: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.
Submission history
From: Dominic Liao-McPherson [view email][v1] Tue, 4 Dec 2018 19:15:14 UTC (168 KB)
Current browse context:
math.OC
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.