# Advantages of Bilinear Koopman Realizations for the Modeling and Control of Systems With Unknown Dynamics

@article{Bruder2020AdvantagesOB, title={Advantages of Bilinear Koopman Realizations for the Modeling and Control of Systems With Unknown Dynamics}, author={Daniel Bruder and Xun Fu and Ram Vasudevan}, journal={IEEE Robotics and Automation Letters}, year={2020}, volume={6}, pages={4369-4376} }

Nonlinear dynamical systems can be made easier to control by lifting them into the space of observable functions, where their evolution is described by the linear Koopman operator. This letter describes how the Koopman operator can be used to generate approximate linear, bilinear, and nonlinear model realizations from data, and argues in favor of bilinear realizations for characterizing systems with unknown dynamics. Necessary and sufficient conditions for a dynamical system to have a valid…

## 18 Citations

### Koopman Linearization for Data-Driven Batch State Estimation of Control-Affine Systems

- Computer ScienceIEEE Robotics and Automation Letters
- 2022

The Koopman State Estimator (KoopSE), a framework for model-free batch state estimation of control-affine systems that makes no linearization assumptions, requires no problem-specific feature selections, and has an inference computational cost that is independent of the number of training points is presented.

### Data-Efficient Model Learning for Control with Jacobian-Regularized Dynamic-Mode Decomposition

- Engineering
- 2022

Jacobian-Regularized Dynamic-Mode Decomposition (JDMD), a data-efficient algorithm for learning models for model-predictive control (MPC), demonstrates its ability to quickly learn bilinear Koopman dynamics representations across several realistic examples in simulation.

### System norm regularization methods for Koopman operator approximation

- Computer ScienceProceedings of the Royal Society A
- 2022

DMD and DMD with control are reformulated as convex optimization problems with linear matrix inequality constraints and asymptotic stability constraints and system norm regularizers are incorporated as methods to improve the numerical conditioning of the Koopman operator.

### Autonomous Driving using Linear Model Predictive Control with a Koopman Operator based Bilinear Vehicle Model

- MathematicsIFAC-PapersOnLine
- 2022

### Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectories

- Mathematics
- 2022

. Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state…

### Neural Koopman Control Barrier Functions for Safety-Critical Control of Unknown Nonlinear Systems

- Mathematics, Computer Science
- 2022

This work utilizes Koopman operator theory (KOT) to associate the (unknown) nonlinear system with a higher dimensional bilinear system and proposes a data- driven learning framework that uses a learner and a falsiﬁer to simultaneously learn a corresponding CBF.

### Data-Driven Control: Overview and Perspectives *

- Computer Science2022 American Control Conference (ACC)
- 2022

An overview and conceptual classification of the main approaches in data-driven process control is provided, and current limitations and future directions are identified.

### Finite Sample Identification of Bilinear Dynamical Systems

- Mathematics, Computer Science
- 2022

This work identifies how much data is needed to estimate the unknown bilinear system up to a desired accuracy with high probability and shows that numerical experiments are well-aligned with the theoretical results.

### Global, Unified Representation of Heterogenous Robot Dynamics Using Composition Operators

- MathematicsArXiv
- 2022

— The complexity of robot dynamics often pertains to the hybrid nature of dynamics, where governing dynamic equations consist of heterogenous equations that are switched depending on the state of the…

### GUARANTEED CONSTRAINT SATISFACTION IN KOOPMAN-BASED OPTIMAL CONTROL

- Computer Science
- 2022

The Koopman framework and an eDMD-based bilinear surrogate modeling approach for control systems are utilized and an error bound on predicted observables is shown to show that satisfaction of tightened constraints in the purely data-based surrogate model implies constraint satisfaction for the original system.

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