From Covariance Control to Covariance Steering: The First 40 Years

Abstract

Uncertainty propagation and mitigation is at the core of all robotic and control systems. The standard approach so far has followed the spirit of control of a system “with uncertainties,” as opposed to the direct control “of uncertainties” affecting the system itself. Covariance control, developed by Bob Skelton and his colleagues in the early 80’s was introduced as a principled approach to handle uncertainty with guarantees in the asymptotic case. The finite-time case has only recently been addressed under the name covariance steering. Borrowing ideas from the classical Optimal Mass Transport (OMT) and the Schrödinger Bridge problems, covariance steering provides a new tool to control stochastic systems with strict performance guarantees that go beyond classical controllability results, which hold only for deterministic systems. In this talk, we will review some recent results on covariance and distribution control for stochastic systems subject to probabilistic (chance) constraints, robust and data-driven distributional control, and will demonstrate the application of the theory to solve problems on control, robotics, and generative AI applications.