Derivative-Based Koopman Operators for Real-Time Control of Robotic Systems

@article{Mamakoukas2021DerivativeBasedKO,
  title={Derivative-Based Koopman Operators for Real-Time Control of Robotic Systems},
  author={Giorgos Mamakoukas and Maria L. Casta{\~n}o and Xiaobo Tan and Todd D. Murphey},
  journal={IEEE Transactions on Robotics},
  year={2021},
  volume={37},
  pages={2173-2192}
}
This article presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using higher order derivatives of general nonlinear dynamics that need not be known, we construct a Koopman-operator-based linear representation and utilize Taylor series accuracy analysis to derive an error bound. The resulting error formula is used to choose the order of… 
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References

SHOWING 1-10 OF 95 REFERENCES
Local Koopman Operators for Data-Driven Control of Robotic Systems
TLDR
The authors exploit the Koopman operator to develop a systematic, data-driven approach for constructing a linear representation in terms of higher order derivatives of the underlying nonlinear dynamics, which enables fast control synthesis of nonlinear systems.
Model-Based Control Using Koopman Operators
TLDR
It is illustrated how the Koopman operator can be used to obtain a linearizable data-driven model for an unknown dynamical process that is useful for model-based control synthesis.
Learning Data-Driven Stable Koopman Operators
TLDR
A formula for the global error of general Koopman representations is derived and imposing stability constraints on the data-driven model is motivated to improve the approximation of nonlinear systems over a longer horizon.
Koopman operator-based model reduction for switched-system control of PDEs
Model predictive control based on linear programming - the explicit solution
TLDR
The availability of the explicit structure of the MPC controller provides an insight into the type of control action in different regions of the state space, and highlights possible conditions of degeneracies of the LP, such as multiple optima.
Data-Driven Nonlinear Stabilization Using Koopman Operator
TLDR
The proposed approach is data-driven and relies on the use of time-series data generated from the control dynamical system for the lifting of a nonlinear system in the Koopman eigenfunction coordinates to construct a finite-dimensional bilinear representation of a control-affine nonlinear Dynamical system.
Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Control
TLDR
This work describes this Koopman-based system identification method and its application to model predictive controller design, which yields an explicit control-oriented linear model rather than just a "black-box" input-output mapping.
Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
Sequential Action Control: Closed-Form Optimal Control for Nonlinear and Nonsmooth Systems
TLDR
A new model-based algorithm that computes predictive optimal controls online and in a closed loop for traditionally challenging nonlinear systems and can avoid local minima and outperform nonlinear optimal controllers and recent case-specific methods in terms of tracking performance and at speeds that are orders of magnitude faster than traditionally achievable ones.
A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic systems
  • E. Todorov, Weiwei Li
  • Mathematics
    Proceedings of the 2005, American Control Conference, 2005.
  • 2005
We present an iterative linear-quadratic-Gaussian method for locally-optimal feedback control of nonlinear stochastic systems subject to control constraints. Previously, similar methods have been…
...
1
2
3
4
5
...