Closed-loop stabilization of nonlinear systems using Koopman Lyapunov-based model predictive control
| Autor: | Joseph Sang-Il Kwon, Abhinav Narasingam |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Lyapunov function
0209 industrial biotechnology Mathematics::Dynamical Systems Computer science Stability (learning theory) Bilinear interpolation 02 engineering and technology Eigenfunction Operator theory symbols.namesake Model predictive control Nonlinear system 020901 industrial engineering & automation 020401 chemical engineering Control theory Bounded function symbols 0204 chemical engineering Control-Lyapunov function |
| Zdroj: | CDC |
| DOI: | 10.1109/cdc42340.2020.9304259 |
| Popis: | This work considers the problem of stabilizing feedback control design for nonlinear systems. To achieve this, we integrate Koopman operator theory with Lyapunov-based model predictive control (LMPC). A bilinear representation of the nonlinear dynamics is determined using Koopman eigenfunctions. Then, a predictive controller is formulated in the space of Koopman eigenfunctions using an auxiliary Control Lyapunov Function (CLF) based bounded controller as a constraint which enables the characterization of stability of the Koopman bilinear system. Unlike previous studies, we show via an inverse mapping - realized by continuously differentiable functions - that the designed controller translates the stability of the Koopman bilinear system to the original closed-loop system. Remarkably, the feedback control design proposed in this work remains completely data-driven and does not require any explicit knowledge of the original system. Moreover, in contrast to standard LMPC, seeking a CLF for the bilinear system is computationally favorable compared to the original nonlinear system. The application of the proposed method is illustrated on a numerical example. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|