Generalizing Output-Feedback Covariance Steering to Incorporate Non-Orthogonal Estimation Errors

Abstract

This paper addresses the problem of steering a state distribution over a finite horizon in discrete time with output feedback. The incorporation of output feedback introduces additional challenges arising from the statistical coupling between the true state distribution and the corresponding filtered state distribution. In particular, this paper extends existing distribution steering formulations to scenarios in which estimation errors are not orthogonal to the state estimates. A general framework is developed to capture this non-orthogonality, and the resulting problem is formulated in a form solvable via sequential convex programming with rank constraints. The proposed approach generalizes existing methods and is validated through numerical examples and Monte Carlo simulations, including cases with non-orthogonal estimation errors that prior techniques cannot address.

Figures (4)

• Figure 3: Case 1 & 2: Trajectory of predicted true state distributions calculated using the proposed method.
• Figure 4: Validation of proposed method for Cases 1 & 2: Comparison of true state distributions at selected time indices ($k = 0, 5, 10, 15, 19$) calculated from existing method Pilipovsky-CS-Output-Feedback and a Monte Carlo simulation ($n_{\text{MC}} = 10{,}000$).
• Figure 5: Case 3 with underweighted Kalman gain: Comparison of true state distributions at selected time indices ($k = 0, 5, 10, 15, 19$) calculated from the proposed method and from the existing method Pilipovsky-CS-Output-Feedback. Solution consistency presented through a Monte Carlo simulation ($n_{\text{MC}} = 10{,}000$).
• Figure 6: Time history for spectral norm of feedback gain matrix $K_k$ calculated using the proposed method.

Theorems & Definitions (3)

• Remark 1
• Remark 2
• Remark 3