Convex Optimization for Finite-Horizon Robust Covariance Control of Linear Stochastic Systems

This work addresses the finite-horizon robust covariance control problem for discrete time, partially observable, linear systems affected by random zero mean noise and deterministic uncertain-but-bounded disturbances restricted to lie in what is called ellitopic uncertainty set (e.g., finite intersection of centered at origin ellipsoids/elliptic cylinders). Performance specifications are imposed on state-control trajectory via averaged convex quadratic inequalities, inequalities mean, chance constrained as well convex-monotone constraints matrix. For this we develop a computationally tractable procedure designing affine policies, sense that parameters policy guarantees aforementioned performance obtained solutions an explicit program. Our theoretical findings illustrated numerical example.