A Hamiltonian approximation method for the reduction of controlled systems

This paper considers the problem of model reduction for controlled systems. The paper considers a dual/adjoint formulation of the general optimization problem to minimize a criterion function subject to plant dynamics and system constraints. By carrying out an approximation on the Lagrangian or Hamiltonian system that is inferred from the dual optimization problem, a reduced Hamiltonian system is obtained that approximates the optimally controlled dynamical system. The merits of the method are illustrated on an example of a controlled binary distillation process

Estimating disturbances and model uncertainty in model validation for robust control

Abstract—Deterministic approaches to model validation for robust control are investigated. In common deterministic model validation approaches, a trade-off between disturbances and model uncertainty is present, resulting in an ill-posed problem. In this paper, an approach to model validation is presented that attempts to remedy the ill-posedness. By employing accu-rate, non-parametric, deterministic disturbance models in con-junction with enforcing averaging properties of deterministic disturbances, a novel framework enabling model validation for robust control is obtained. The approach results in a realistically estimated model uncertainty and a disturbance model, and is illustrated in a simulation example. I

Tight Approximation Guarantees for Concave Coverage Problems

33 pages. v3 minor corrections and added FPT hardnessInternational audienceIn the maximum coverage problem, we are given subsets $T_1, \ldots, T_m$ of a universe $[n]$ along with an integer $k$ and the objective is to find a subset $S \subseteq [m]$ of size $k$ that maximizes $C(S) := \Big|\bigcup_{i \in S} T_i\Big|$. It is a classic result that the greedy algorithm for this problem achieves an optimal approximation ratio of $1-e^{-1}$. In this work we consider a generalization of this problem wherein an element $a$ can contribute by an amount that depends on the number of times it is covered. Given a concave, nondecreasing function $\varphi$, we define $C^{\varphi}(S) := \sum_{a \in [n]}w_a\varphi(|S|_a)$, where $|S|_a = |\{i \in S : a \in T_i\}|$. The standard maximum coverage problem corresponds to taking $\varphi(j) = \min\{j,1\}$. For any such $\varphi$, we provide an efficient algorithm that achieves an approximation ratio equal to the Poisson concavity ratio of $\varphi$, defined by $\alpha_{\varphi} := \min_{x \in \mathbb{N}^*} \frac{\mathbb{E}[\varphi(\text{Poi}(x))]}{\varphi(\mathbb{E}[\text{Poi}(x)])}$. Complementing this approximation guarantee, we establish a matching NP-hardness result when $\varphi$ grows in a sublinear way. As special cases, we improve the result of [Barman et al., IPCO, 2020] about maximum multi-coverage, that was based on the unique games conjecture, and we recover the result of [Dudycz et al., IJCAI, 2020] on multi-winner approval-based voting for geometrically dominant rules. Our result goes beyond these special cases and we illustrate it with applications to distributed resource allocation problems, welfare maximization problems and approval-based voting for general rules