The inverse problem of continuous-time linear quadratic gaussian control with application to biological systems analysis

M. Cody Priess; Jongeun Choi; Clark Radcliffe

doi:10.1115/DSCC2014-6100

The inverse problem of continuous-time linear quadratic gaussian control with application to biological systems analysis

M. Cody Priess, Jongeun Choi, Clark Radcliffe

Department of Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Citations (Scopus)

Abstract

In this paper, we demonstrate two methods for solving the inverse problem of continuous-time LQG control. This problem can be defined as: given a known LTI system with feedback controller K and Kalman gain L, can we find the weighting matrices Q,R (for state and input, respectively) and estimated noise intensities W, V (for process and measurement noise, respectively) such that the LQG control synthesis problem using these weights generates K and L? We formulate a regularized version of this problem as a minimization problem subject to a set of Linear Matrix Inequalities (LMIs). If feasible, a unique exact solution to the inverse LQR problem exists. If the LMIs are infeasible, we show a gradient descent algorithm that will find Q,R,W, and V to minimize the error in the recovered gain matrices K and L. We demonstrate these techniques through several numerical examples and formulate a human postural control case study to which we intend to apply our proposed techniques.

Original language	English
Title of host publication	Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy
Publisher	American Society of Mechanical Engineers
ISBN (Electronic)	9780791846209
DOIs	https://doi.org/10.1115/DSCC2014-6100
Publication status	Published - 2014
Event	ASME 2014 Dynamic Systems and Control Conference, DSCC 2014 - San Antonio, United States Duration: 2014 Oct 22 → 2014 Oct 24

Publication series

Name	ASME 2014 Dynamic Systems and Control Conference, DSCC 2014
Volume	3

Other

Other	ASME 2014 Dynamic Systems and Control Conference, DSCC 2014
Country/Territory	United States
City	San Antonio
Period	14/10/22 → 14/10/24

Bibliographical note

Publisher Copyright:
© 2014 by ASME.

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Mechanical Engineering
Industrial and Manufacturing Engineering

Access to Document

10.1115/DSCC2014-6100

Cite this

Priess, M. C., Choi, J., & Radcliffe, C. (2014). The inverse problem of continuous-time linear quadratic gaussian control with application to biological systems analysis. In Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy (ASME 2014 Dynamic Systems and Control Conference, DSCC 2014; Vol. 3). American Society of Mechanical Engineers. https://doi.org/10.1115/DSCC2014-6100

Priess, M. Cody ; Choi, Jongeun ; Radcliffe, Clark. / The inverse problem of continuous-time linear quadratic gaussian control with application to biological systems analysis. Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy. American Society of Mechanical Engineers, 2014. (ASME 2014 Dynamic Systems and Control Conference, DSCC 2014).

@inproceedings{52ab9ced212e4e529c636a1bed3c7933,

title = "The inverse problem of continuous-time linear quadratic gaussian control with application to biological systems analysis",

abstract = "In this paper, we demonstrate two methods for solving the inverse problem of continuous-time LQG control. This problem can be defined as: given a known LTI system with feedback controller K and Kalman gain L, can we find the weighting matrices Q,R (for state and input, respectively) and estimated noise intensities W, V (for process and measurement noise, respectively) such that the LQG control synthesis problem using these weights generates K and L? We formulate a regularized version of this problem as a minimization problem subject to a set of Linear Matrix Inequalities (LMIs). If feasible, a unique exact solution to the inverse LQR problem exists. If the LMIs are infeasible, we show a gradient descent algorithm that will find Q,R,W, and V to minimize the error in the recovered gain matrices K and L. We demonstrate these techniques through several numerical examples and formulate a human postural control case study to which we intend to apply our proposed techniques.",

author = "Priess, {M. Cody} and Jongeun Choi and Clark Radcliffe",

note = "Publisher Copyright: {\textcopyright} 2014 by ASME.; ASME 2014 Dynamic Systems and Control Conference, DSCC 2014 ; Conference date: 22-10-2014 Through 24-10-2014",

year = "2014",

doi = "10.1115/DSCC2014-6100",

language = "English",

series = "ASME 2014 Dynamic Systems and Control Conference, DSCC 2014",

publisher = "American Society of Mechanical Engineers",

booktitle = "Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy",

}

Priess, MC, Choi, J & Radcliffe, C 2014, The inverse problem of continuous-time linear quadratic gaussian control with application to biological systems analysis. in Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy. ASME 2014 Dynamic Systems and Control Conference, DSCC 2014, vol. 3, American Society of Mechanical Engineers, ASME 2014 Dynamic Systems and Control Conference, DSCC 2014, San Antonio, United States, 14/10/22. https://doi.org/10.1115/DSCC2014-6100

The inverse problem of continuous-time linear quadratic gaussian control with application to biological systems analysis. / Priess, M. Cody; Choi, Jongeun; Radcliffe, Clark.
Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy. American Society of Mechanical Engineers, 2014. (ASME 2014 Dynamic Systems and Control Conference, DSCC 2014; Vol. 3).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - The inverse problem of continuous-time linear quadratic gaussian control with application to biological systems analysis

AU - Priess, M. Cody

AU - Choi, Jongeun

AU - Radcliffe, Clark

PY - 2014

Y1 - 2014

N2 - In this paper, we demonstrate two methods for solving the inverse problem of continuous-time LQG control. This problem can be defined as: given a known LTI system with feedback controller K and Kalman gain L, can we find the weighting matrices Q,R (for state and input, respectively) and estimated noise intensities W, V (for process and measurement noise, respectively) such that the LQG control synthesis problem using these weights generates K and L? We formulate a regularized version of this problem as a minimization problem subject to a set of Linear Matrix Inequalities (LMIs). If feasible, a unique exact solution to the inverse LQR problem exists. If the LMIs are infeasible, we show a gradient descent algorithm that will find Q,R,W, and V to minimize the error in the recovered gain matrices K and L. We demonstrate these techniques through several numerical examples and formulate a human postural control case study to which we intend to apply our proposed techniques.

AB - In this paper, we demonstrate two methods for solving the inverse problem of continuous-time LQG control. This problem can be defined as: given a known LTI system with feedback controller K and Kalman gain L, can we find the weighting matrices Q,R (for state and input, respectively) and estimated noise intensities W, V (for process and measurement noise, respectively) such that the LQG control synthesis problem using these weights generates K and L? We formulate a regularized version of this problem as a minimization problem subject to a set of Linear Matrix Inequalities (LMIs). If feasible, a unique exact solution to the inverse LQR problem exists. If the LMIs are infeasible, we show a gradient descent algorithm that will find Q,R,W, and V to minimize the error in the recovered gain matrices K and L. We demonstrate these techniques through several numerical examples and formulate a human postural control case study to which we intend to apply our proposed techniques.

UR - http://www.scopus.com/inward/record.url?scp=84929232007&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929232007&partnerID=8YFLogxK

U2 - 10.1115/DSCC2014-6100

DO - 10.1115/DSCC2014-6100

M3 - Conference contribution

AN - SCOPUS:84929232007

T3 - ASME 2014 Dynamic Systems and Control Conference, DSCC 2014

BT - Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy

PB - American Society of Mechanical Engineers

T2 - ASME 2014 Dynamic Systems and Control Conference, DSCC 2014

Y2 - 22 October 2014 through 24 October 2014

ER -

Priess MC, Choi J, Radcliffe C. The inverse problem of continuous-time linear quadratic gaussian control with application to biological systems analysis. In Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy. American Society of Mechanical Engineers. 2014. (ASME 2014 Dynamic Systems and Control Conference, DSCC 2014). doi: 10.1115/DSCC2014-6100

The inverse problem of continuous-time linear quadratic gaussian control with application to biological systems analysis

Abstract

Publication series

Other

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this