### 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 |
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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 |

Volume | 3 |

ISBN (Electronic) | 9780791846209 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

Event | ASME 2014 Dynamic Systems and Control Conference, DSCC 2014 - San Antonio, United States Duration: 2014 Oct 22 → 2014 Oct 24 |

### Other

Other | ASME 2014 Dynamic Systems and Control Conference, DSCC 2014 |
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Country | United States |

City | San Antonio |

Period | 14/10/22 → 14/10/24 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Mechanical Engineering
- Industrial and Manufacturing Engineering

### Cite this

*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

}

*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.

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 - 2014/1/1

Y1 - 2014/1/1

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

VL - 3

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

ER -