## 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 |

ISBN (Electronic) | 9780791846209 |

DOIs | |

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 |
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Volume | 3 |

### Other

Other | ASME 2014 Dynamic Systems and Control Conference, DSCC 2014 |
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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