27 problems

The stochastic setting considered here concerns model predictive control under uncertainty; the relevant turnpike property describes the tendency of optimal trajectories to remain…

A stochastic control system may be unstable in its deterministic form yet become stabilized by stochastic perturbations; this phenomenon is described as almost sure exponential sta…

Uniform-horizon conjecture. The function $\tau(\epsilon):\mathbb{R}\to\mathbb{N}$ is independent of $N$ and depends only on

Stability conjecture. A result resembling the stability result established for single-iteration MPC in the simplified setting should hold for the considered scenario.

Let $\Pi^\star$ be the optimal periodic orbit used in the economic model predictive control scheme, and let $\lambda$ be the rotated-stage-cost function. The paper previously estab…

Let ISCD-MPC denote the iterative state- and control-dependent model predictive control technique described in the paper. A chain of integrators is a system formed by integrators o…

The proposed approach concerns model predictive control with artificial setpoints for systems subject to partially unknown constraints; terminal ingredients are the terminal region…

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 $[E,A,B]$ be a singular differential-algebraic system and let $X$ and the constraint-room relation be as defined in the paper. Constraint-room conjecture. The relation … holds…

Let horizon-dependent bounds $(\gamma_k)$ be used in the linear program defining the suboptimality factor $\alpha_N$, and let $\hat{\alpha}_N$ denote the analytical bound introduce…

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…

The linearized dynamics are given by $x_{k+1}=A_{\tilde{x}}x_k+Bu_k+e_{\tilde{x}}$, and Assumption 2 requires the existence of $\underline{\sigma}>0$ such that…

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…

Let $N$ be the prediction horizon, let $N_{\overline{Y}}$ denote the horizon appearing in the stability guarantees, and let $\alpha_N$ be the suboptimality index. The setting may i…

The prediction horizon is denoted by $N$, and the $cmathcal{L}_2cgain$ measures the induced gain from estimation errors to the relevant output or error signal in the output-feedbac…

Consider a periodic optimal control problem satisfying Assumption 2, namely, there is a positive constant $c_{\kappa}$ such that, at every time step and for every constant paramete…

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

The stochastic motion-planning problem is parameterized by a noise parameter $\epsilon$, and the decoupling result refers to a tractable replanning algorithm using suitably designe…

Funnel-MPC feasibility conjecture. Feasibility of this Funnel-MPC scheme can be proved by using optimality of the predicted open-loop trajectories; in particular, feasibility along…

The localized region parameter $d$ determines the size of the region within which subsystems coordinate their actions, while $N$ denotes the number of systems and $T$ the predictio…

Consider model predictive control for the nonholonomic mobile robot, with the stage cost … The discussion concerns using the homogeneous approximation of the system at the origin i…

Model predictive control (MPC) is considered for optimal control problems, with approximation properties established for time-invariant and undiscounted problems. The target settin…

The problems considered involve noisy data, with $m=10\,000$ constraints and the number of variables $n$ ranging from 10 to 500. Let $M_Q$ denote the matrix whose ill-conditioning…