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

M. Cody Priess, Jongeun Choi, Clark Radcliffe

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 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 languageEnglish
Title of host publicationIndustrial 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
PublisherAmerican Society of Mechanical Engineers
Volume3
ISBN (Electronic)9780791846209
DOIs
Publication statusPublished - 2014 Jan 1
EventASME 2014 Dynamic Systems and Control Conference, DSCC 2014 - San Antonio, United States
Duration: 2014 Oct 222014 Oct 24

Other

OtherASME 2014 Dynamic Systems and Control Conference, DSCC 2014
CountryUnited States
CitySan Antonio
Period14/10/2214/10/24

Fingerprint

Biological systems
Inverse problems
Systems analysis
Linear matrix inequalities
Feedback
Controllers

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering

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 (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. Vol. 3 American Society of Mechanical Engineers, 2014.
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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.",
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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. 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. Vol. 3 American Society of Mechanical Engineers, 2014.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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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. Vol. 3. American Society of Mechanical Engineers. 2014 https://doi.org/10.1115/DSCC2014-6100