Hands-Off Covariance Steering: Inducing Feedback Sparsity via Iteratively Reweighted ${\ell }_{1,p}$ Regularization

Abstract

We consider the problem of optimally steering the state covariance matrix of a discrete-time linear stochastic system to a desired terminal covariance matrix, while inducing the control input to be zero over many time intervals. We propose to induce sparsity in the feedback gain matrices by using a sum-of-norms version of the iteratively reweighted ${\ell }_1$-norm minimization. We show that the lossless convexification property holds even with the regularization term. Numerical simulations show that the proposed method produces a Pareto front of transient cost and sparsity that is not achievable by a simple ${\ell }_1$-norm minimization and closely approximates the ${\ell }_0$-norm minimization obtained from brute-force search.

Accepted to CDC 2025