Mixed Norm ℋ2/ℋ∞ and Entropy Covariance Control: A Convex Optimization Approach

In this paper, we develop a covariance control problem to address a tradeoff between ℋ₂ performance and ℋ_∞ disturbance attenuation. In particular, we formulate a mixed-norm ℋ₂/ℋ_∞ and entropy covariance control problem that guarantees that the state covariance of an uncertain dynamical system driven by white noise is upper bounded in the sense of the cone of nonnegative definite matrices by a given threshold matrix via state feedback control. This is accomplished by combining covariance control theory and mixed norm ℋ₂/ℋ_∞ control theory. By using suitable transformations involving dynamic weighting on the complimentary sensitivity system transfer function, the formulation is applicable to robustness problems. The proposed formulation allows for solutions via semidefinite programming. Finally, an illustrative numerical example is provided to show the efficacy of the proposed approach.