28 problems

Consider the scalar positive linear-system setting above, with the certainty-equivalence (CE) policy and its certified disturbance-to-state $\ell_1$-gain bound. CE optimality conje…

Single-agent robust mean field control limit conjecture. In the limit $N\to+\infty$, the problem should become a robust control problem involving a single agent, with a cost depend…

Policy-iteration convergence conjecture. The method converges for sufficiently large $\beta$.

Let $\Pi$ be the set of admissible stationary strategies, let $\pi^*\in\Pi$ be an equilibrium strategy, and let $\pi^i\otimes_1\pi^*$ denote the strategy that uses $\pi^i$ in the i…

Let $V(t,x)$ denote the value function of the robust investment-consumption problem, and let $Y(t)$ be an auxiliary process. Suppose that $G$ is a function continuously differentia…

Let $\mathcal{C}_n$ be the space of full-order dynamic policies for $\mathcal{H}_\infty$ control. A policy $\mathsf{K}\in\mathcal{C}_n$ is Clarke stationary when…

Let $\mathcal{C}_n$ be the space of full-order dynamic policies, and let $\mathcal{C}_{\mathrm{nd}}$ be the subset of non-degenerate policies, namely those admitting a certificate…

The DRSC method uses an ambiguity set, namely a set of plausible models or distributions used for robust control. Conjecture on the slow shrinkage of the DRSC ambiguity set. The re…

Let $p^\zeta(s;t)$ and $p^x(s;t)$ denote the adjoint processes introduced in the control-dependent ambiguity-aversion formulation, with the model specialized by taking $\mu_2$, $b$…

Let $M\in\mathbb{Z}^{+}$ and let … Suppose that the switched system under consideration is robust feedback stabilizable. Non-conservatism conjecture. There exists an…

Let $\alpha \in (0,\infty)$ parameterize the controller and let $\mathcal{S}_K$ denote the corresponding closed-loop system, with $\varepsilon(\alpha)$ the associated epsilon param…

A monotone static nonlinearity is a static nonlinearity satisfying the monotonicity condition; a Zames–Falb multiplier is a multiplier of the type used to certify robust stability…

Polynomial-time computation conjecture. There exists a polynomial-time algorithm to compute $\nu$ within arbitrary precision.

Balancing-algorithm conjecture. Algorithm always converges. Moreover, the number of iterations required to reach a given tolerance is $O(\log(n))$ for fixed $\epsilon$, and…

Diagonal-maximality conjecture.

Exactness conjecture. $\overline{\nu}$ is exact for some class of norm-bounded disturbances.

Convex upper-bound conjecture. For positive systems, there exists a convex upper bound for a robustness measure against such uncertainties.

Local Lipschitz continuity conjecture. The function $\mathbf{u}^*(\mathbf{x})$ remains locally Lipschitz continuous in $\mathbf{x}$.

Consider a one-step data-driven MPC scheme using the terminal ingredients from Berberich et al. One-step robustness conjecture. Robustness of this scheme can be proven, using the i…

Bilateral-actuation conjecture. Bilateral control with actuators available at both boundaries might lead to smaller prediction errors and, consequently, better robustness margins b…

Robustness conjecture. The feedback optimization approach should work as well in the presence of uncertainties in the input-output map sensitivities.

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…