11 problems

Let $\cX=\{x_j\}_{j=1}^d$ be a set of data points and, for each $x_j\in\cX$, let $\cX_j=\{x_j,u_{jl},x_{jl}^+\}_{l=1}^{d_j}$ be collected data triplets satisfying the stated assump…

Proportional error-bound conjecture. For other sampling strategies, such as ergodic sampling, similar arguments to those used for the proportional error bound should apply if the e…

The paper considers DeePC applied to a traffic system, with the Hankel matrix used as a model of the system's trajectories. DeePC applicability conjecture. DeePC could work well in…

Computability conjecture. Although Assumption can be shown to hold, it should be possible to compute $tilde{\sigma}_i$ and $\sigma_i^\prime$ based only on the available input-outpu…

Let a descriptor system be represented by a quasi-Weierstraß system with nilpotent matrix $N$ of index $s$ and a matrix $A_1$ of dimension $q$. Suppose that recent results allowing…

For simplicity, output constraints are omitted, so let $\mathbb{Y}=\mathbb{R}^p$. Extension conjecture. The presented robust data-driven model predictive control results should ext…

Consider the proposed data-driven MPC scheme with terminal ingredients, with noise and disturbances affecting the data and measurements. Modify Problem … and a regularization on…

Let the measured data used by the data-driven MPC scheme be affected by noise, and let the MPC problem be modified by including a slack variable in the Hankel-matrix constraint and…

Performance-extension conjecture. An extension of Theorem to include performance criteria for the closed loop should be straightforward, for example by robustly verifying the perfo…

General polytopic output-constraint conjecture. Similar data-driven MPC results should hold for general polytopic output constraints.

Distributionally robust interpretation conjecture. The one-norm regularization in the regularized DeePC problem is related to distributionally robust optimization problems, in whic…