Koopman based data-driven predictive control
arXiv:2102.05122
Abstract
Sparked by the Willems' fundamental lemma, a class of data-driven control methods has been developed for LTI systems. At the same time, the Koopman operator theory attempts to cast a nonlinear control problem into a standard linear one albeit infinite-dimensional. Motivated by these two ideas, a data-driven control scheme for nonlinear systems is proposed in this work. The proposed scheme is compatible with most differential regressors enabling offline learning. In particular, the model uncertainty is considered, enabling a novel data-driven simulation framework based on Wasserstein distance. Numerical experiments are performed with Bayesian neural networks to show the effectiveness of both the proposed control and simulation scheme.
References in corpus (11)
- Deep learning for universal linear embeddings of nonlinear dynamics
- Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
- On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator
- Safe Reinforcement Learning Using Robust MPC
- Koopman operator-based model reduction for switched-system control of PDEs
- Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces
- Maximum Likelihood Estimation in Data-Driven Modeling and Control
- Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition
- Data-based stabilization of unknown bilinear systems with guaranteed basin of attraction
- Data-driven stabilization of nonlinear polynomial systems with noisy data
- Nonlinear Data-Enabled Prediction and Control
Cited by in corpus (5)
- Robust Tube-based Model Predictive Control with Koopman Operators--Extended Version
- Linear tracking MPC for nonlinear systems Part II: The data-driven case
- An overview of systems-theoretic guarantees in data-driven model predictive control
- On a Stochastic Fundamental Lemma and Its Use for Data-Driven Optimal Control
- Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics