2020/05/19 by Abhinav Narasingam, Narasingam, Abhinav, Joseph Sang‐Il Kwon +2
Computer Science · Decision Sciences · Engineering · Mathematics · Physics and Astronomy · #Advanced Control Systems Optimization #Artificial intelligence #Benchmark (surveying) #Computer science #Control (management) #Control Systems and Identification #Control theory (sociology) #Control-Lyapunov function #Controller (irrigation) #FOS: Electrical engineering #Lyapunov function #Lyapunov redesign #Mathematics #Model Reduction and Neural Networks #Model predictive control #Nonlinear system #Probabilistic and Robust Engineering Design #State space #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2005.09741
published in arXiv (Cornell University) (Cornell University) · 11 pages, corrected typos, removed commented out lines
openalex publication_date 2020/05/19 · arxiv created 2020/05/24 · arxiv updated 2020/05/26 · openalex created_date 2022/07/26 · openalex updated_date 2026/08/05
In this work, a predictive control framework is presented for feedback\nstabilization of nonlinear systems. To achieve this, we integrate Koopman\noperator theory with Lyapunov-based model predictive control (LMPC). The main\nidea is to transform nonlinear dynamics from state-space to function space\nusing Koopman eigenfunctions - for control affine systems this results in a\nbilinear model in the (lifted) function space. Then, a predictive controller is\nformulated in Koopman eigenfunction coordinates which uses an auxiliary Control\nLyapunov Function (CLF) based bounded controller as a constraint to ensure\nstability of the Koopman system in the function space. Provided there exists a\ncontinuously differentiable inverse mapping between the original state-space\nand (lifted) function space, we show that the designed controller is capable of\ntranslating the feedback stabilizability of the Koopman bilinear system to the\noriginal nonlinear system. Remarkably, the feedback control design proposed in\nthis work remains completely data-driven and does not require any explicit\nknowledge of the original system. Furthermore, due to the bilinear structure of\nthe Koopman model, seeking a CLF is no longer a bottleneck for LMPC. Benchmark\nnumerical examples demonstrate the utility of the proposed feedback control\ndesign.\n