MPC Performances for Nonlinear Systems Using Several Linearization Models

Igarashi, Yusuke; Yamakita, Masaki; Ng, Jerry; Asada, H. Harry

doi:10.23919/acc45564.2020.9147306

Cited by 21 publications

(13 citation statements)

References 12 publications

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“…• Augmented state feedback can be used to better inform controllers [24]. • Linear observer design is enabled for augmented state feedback.…”

Section: B Dual-faceted Linearization (Dfl)mentioning

confidence: 99%

Learning of Causal Observable Functions for Koopman-DFL Lifting Linearization of Nonlinear Controlled Systems and Its Application to Excavation Automation

Selby,

Asada

2021

Preprint

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Effective and causal observable functions for loworder lifting linearization of nonlinear controlled systems are learned from data by using neural networks. While Koopman operator theory allows us to represent a nonlinear system as a linear system in an infinite-dimensional space of observables, exact linearization is guaranteed only for autonomous systems with no input, and finding effective observable functions for approximation with a low-order linear system remains an open question. Dual Faceted Linearization uses a set of effective observables for low-order lifting linearization, but the method requires knowledge of the physical structure of the nonlinear system. Here, a data-driven method is presented for generating a set of nonlinear observable functions that can accurately approximate a nonlinear control system to a low-order linear control system. A caveat in using data of measured variables as observables is that the measured variables may contain input to the system, which incurs a causality contradiction when lifting the system, i.e. taking derivatives of the observables. The current work presents a method for eliminating such anti-causal components of the observables and lifting the system using only causal observables. The method is applied to excavation automation, a complex nonlinear dynamical system, to obtain a low-order lifted linear model for control design.

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“…• Augmented state feedback can be used to better inform controllers [24]. • Linear observer design is enabled for augmented state feedback.…”

Section: B Dual-faceted Linearization (Dfl)mentioning

confidence: 99%

Learning of Causal Observable Functions for Koopman-DFL Lifting Linearization of Nonlinear Controlled Systems and Its Application to Excavation Automation

Selby,

Asada

2021

Preprint

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“…This methodology has been compared with more typical Koopman operator modeling and it was reported that choosing the observables based on DFL yielded performance comparable to a Koopman model utilizing a substantially larger vector of observables [21]. This makes DFL advantageous in applications where having a compact and interpretable model is necessary.…”

Section: Lifting Linearization Based On Dflmentioning

confidence: 99%

Dynamic Modeling of Bucket-Soil Interactions Using Koopman-DFL Lifting Linearization for Model Predictive Contouring Control of Autonomous Excavators

Sotiropoulos¹,

Asada²

2021

Preprint

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A lifting-linearization method based on the Koopman operator and Dual Faceted Linearization is applied to the control of a robotic excavator. In excavation, a bucket interacts with the surrounding soil in a highly nonlinear and complex manner. Here, we propose to represent the nonlinear bucket-soil dynamics with a set of linear state equations in a higher-dimensional space. The space of independent state variables is augmented by adding variables associated with nonlinear elements involved in the bucket-soil dynamics. These include nonlinear resistive forces and moment acting on the bucket from the soil, and the effective inertia of the bucket that varies as the soil is captured into the bucket. Variables associated with these nonlinear resistive and inertia elements are treated as additional state variables, and their time evolution is represented as another set of linear differential equations. The lifted linear dynamic model is then applied to Model Predictive Contouring Control, where a cost functional is minimized as a convex optimization problem thanks to the linear dynamics in the lifted space. The lifted linear model is tuned based on a data-driven method by using a soil dynamics simulator. Simulation experiments verify the effectiveness of the proposed lifting linearization compared to its counterpart.

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“…Due to the linear dynamics of the new coordinates, prediction hardships through numerical integration and non-convexity in optimization of "dynamics of states" have the potential to be alleviated (e.g. model predictive control [11,12]). Moreover, one can argue that the Koopman operator paradigm delivers a global instead of a point-wise system description as one iteration of the Koopman operator acting on an observable is equivalent to an iteration along all of the trajectories of the system and it is not to be confused with a local linearization around a working point.…”

Section: Introductionmentioning

confidence: 99%

Koopman Operator Dynamical Models: Learning, Analysis and Control

Bevanda,

Sosnowski,

Hirche

2021

Preprint

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The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional -necessitating finite approximations -for which there is no overarching framework. Although there are principled ways of learning such finite approximations, they are in many instances overlooked in favor of, often ill-posed and unstructured methods. Also, Koopman operator theory has long-standing connections to known system-theoretic and dynamical system notions that are not universally recognized. Given the former and latter realities, this work aims to bridge the gap between various concepts regarding both theory and tractable realizations. Firstly, we review data-driven representations (both unstructured and structured) for Koopman operator dynamical models, categorizing various existing methodologies and highlighting their differences. Furthermore, we provide concise insight into the paradigm's relation to system-theoretic notions and analyze the prospect of using the paradigm for modeling control systems. Additionally, we outline the current challenges and comment on future perspectives.

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MPC Performances for Nonlinear Systems Using Several Linearization Models

Cited by 21 publications

References 12 publications

Learning of Causal Observable Functions for Koopman-DFL Lifting Linearization of Nonlinear Controlled Systems and Its Application to Excavation Automation

Learning of Causal Observable Functions for Koopman-DFL Lifting Linearization of Nonlinear Controlled Systems and Its Application to Excavation Automation

Dynamic Modeling of Bucket-Soil Interactions Using Koopman-DFL Lifting Linearization for Model Predictive Contouring Control of Autonomous Excavators

Koopman Operator Dynamical Models: Learning, Analysis and Control

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