Hence, this upper bound equals the optimal value of the maximization problem inΣ, and (20) reduces to the minimization problem in (14)

It is straightforward to verify that, for each p∈[1,∞], the covariance matrixΣ ⋆ attains the upper bound in (21), is feasible for the original maximization problem inΣsince it can be shown to satisfy∥Σ ⋆ −bΣ∥p =r 2 andΣ ⋆ ∈S n + · 2015

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Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets

math.OC · 2025-12-11 · conditional · novelty 7.0

Distributionally robust regret-optimal control for finite-horizon linear-quadratic systems under moment-based ambiguity sets admits an equivalent tractable convex reformulation interpretable as a regularized nominal problem.

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Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets math.OC · 2025-12-11 · conditional · none · ref 2
Distributionally robust regret-optimal control for finite-horizon linear-quadratic systems under moment-based ambiguity sets admits an equivalent tractable convex reformulation interpretable as a regularized nominal problem.

Hence, this upper bound equals the optimal value of the maximization problem inΣ, and (20) reduces to the minimization problem in (14)

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