Abstract
This paper addresses the joint state estimation and control problems for unknown linear time-invariant systems subject to both process and measurement noise. The aim is to redesign the linear quadratic Gaussian (LQG) controller based solely on data. The LQG controller comprises a linear quadratic regulator (LQR) and a steady-state Kalman observer; while the data-based LQR design problem has been previously studied, constructing the Kalman gain and the LQG controller from noisy data presents a novel challenge. In this work, a data-based formulation for computing the steady-state Kalman gain is proposed based on semi-definite programming (SDP) using some noise-free input-state-output data. To compensate for the offline noise, a relaxed SDP is proposed, upon solving which, a robust observer gain is constructed. Additionally, a robust LQG controller is designed based on the observer gain and a data-based LQR gain. The proposed controller is proven to achieve robust global exponential stability (RGES) for the observer and input-to-state stability (ISS) for the resultant closed-loop systems under standard conditions. Finally, numerical tests are conducted to validate the proposed controllers' correctness and effectiveness.
Original language | English |
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Pages (from-to) | 1-13 |
Number of pages | 13 |
Journal | IEEE Transactions on Automatic Control |
DOIs | |
Publication status | Accepted/In press - 2024 |
Keywords
- Data-driven control
- Estimation
- Kalman filters
- Linear systems
- Noise
- Noise measurement
- Observers
- Trajectory
- linear quadratic gaussian
- noisy data
- semi-definite program
- state estimation