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The Inverse Problem of Continuous-Time Linear Quadratic Gaussian Control With Application to Biological Systems Analysis

[+] Author Affiliations
M. Cody Priess, Jongeun Choi, Clark Radcliffe

Michigan State University, East Lansing, MI

Paper No. DSCC2014-6100, pp. V003T42A004; 9 pages
doi:10.1115/DSCC2014-6100
From:
  • ASME 2014 Dynamic Systems and Control Conference
  • Volume 3: 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
  • San Antonio, Texas, USA, October 22–24, 2014
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-4620-9
  • Copyright © 2014 by ASME

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.

Copyright © 2014 by ASME

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