Sparsity-Exploiting Anytime Algorithms for Model Predictive Control: A Relaxed Barrier Approach

• Published in: IEEE transactions on control systems technology Vol. 28; no. 2; pp. 425 - 435
• Main Authors: Feller, Christian, Ebenbauer, Christian
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Anytime algorithms; barrier functions; Closed loop systems; Cost function; Discrete time systems; Feedback control; Linear systems; Mathematical models; model predictive control; Numerical prediction; Numerical stability; Optimal control; Prediction algorithms; Predictive control; real-time optimization; Sparsity; Stability analysis
• ISSN: 1063-6536; 1558-0865
• DOI: 10.1109/TCST.2018.2880142

We present and analyze a novel class of stabilizing and numerically efficient model predictive control (MPC) algorithms for discrete-time linear systems subject to polytopic input and state constraints. The proposed approach combines the previously presented concept of relaxed barrier function-based MPC with suitable warm-starting and sparsity-exploiting factorization techniques and allows to rigorously prove important stability and constraint satisfaction properties of the resulting closed-loop system independently of the number of performed Newton iterations. The effectiveness of the proposed approach is demonstrated by means of a numerical benchmark example.