Computationally Efficient Chance Constrained Covariance Control with Output Feedback
Joshua Pilipovsky, Panagiotis Tsiotras
TL;DR
The paper addresses the problem of steering the state distribution of a stochastic linear system between Gaussian endpoints under chance constraints on state and input, using partial state measurements. It proposes an efficient solution by pairing a Kalman filter (to obtain the filtered state) with a DC reformulation of the chance constraints and solving via successive convexification, ultimately formulating the covariance steering as an SDP with a lossless relaxation. The approach yields a computationally scalable method for output-feedback covariance steering (OFCC-CS) and demonstrates significant speedups over batch methods on a double integrator example, while maintaining constraint satisfaction and a specified terminal distribution. This work advances practical, efficient planning under uncertainty for systems with measurement noise and probabilistic constraints, with potential extensions to data-driven and unknown-dynamics scenarios.
Abstract
This paper studies the problem of developing computationally efficient solutions for steering the distribution of the state of a stochastic, linear dynamical system between two boundary Gaussian distributions in the presence of chance-constraints on the state and control input. It is assumed that the state is only partially available through a measurement model corrupted with noise. The filtered state is reconstructed with a Kalman filter, the chance constraints are reformulated as difference of convex (DC) constraints, and the resulting covariance control problem is reformulated as a DC program, which is solved using successive convexification. The efficiency of the proposed method is illustrated on a double integrator example with varying time horizons, and is compared to other state-of-the-art chance constrained covariance control methods.