Related papers: A data-driven method for computing polyhedral inva…

Though black-box predictors are state-of-the-art for many complex tasks, they often fail to properly quantify predictive uncertainty and may provide inappropriate predictions for unfamiliar data. Instead, we can learn more reliable models…

This paper presents a new robust data-driven predictive control scheme for unknown linear time-invariant systems by using input-state-output or input-output data based on whether the state is measurable. To remove the need for the…

We study the problem of computing robust controllable sets for discrete-time linear systems with additive uncertainty. We propose a tractable and scalable approach to inner- and outer-approximate robust controllable sets using constrained…

In this paper we consider the problem of computing control invariant sets for linear controlled systems with constraints on the input and on the states. We focus in particular on the complexity of the computation of the N-step operator,…

We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least squares problem…

We propose a data-driven algorithm for numerical invariant synthesis and verification. The algorithm is based on the ICE-DT schema for learning decision trees from samples of positive and negative states and implications corresponding to…

We consider the problem of designing an invariant set using only a finite set of input-state data collected from an unknown polynomial system in continuous time. We consider noisy data, i.e., corrupted by an unknown-but-bounded disturbance.…

In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In…

In this article, we survey the primary research on polyhedral computing methods for constrained linear control systems. Our focus is on the modeling power of convex optimization, featured to design set-based robust and optimal controllers.…

This article is concerned with the approximation of unbounded convex sets by polyhedra. While there is an abundance of literature investigating this task for compact sets, results on the unbounded case are scarce. We first point out the…

We propose a novel data-driven stochastic model predictive control framework for uncertain linear systems with noisy output measurements. Our approach leverages multi-step predictors to efficiently propagate uncertainty, ensuring chance…

In this paper, we develop a method for computing controlled invariant sets using Semidefinite Programming. We apply our method to the controller design problem for switching affine systems with polytopic safe sets. The task is reduced to a…

In this paper, we provide a direct data-driven approach to synthesize safety controllers for unknown linear systems affected by unknown-but-bounded disturbances, in which identifying the unknown model is not required. First, we propose a…

We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear…

This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…

We develop methods for forming prediction sets in an online setting where the data generating distribution is allowed to vary over time in an unknown fashion. Our framework builds on ideas from conformal inference to provide a general…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

This article establishes the foundation for a new theory of invariant/integral manifolds for non-autonomous dynamical systems. Current rigorous support for dimensional reduction modelling of slow-fast systems is limited by the rare events…

We present a stochastic constrained output-feedback data-driven predictive control scheme for linear time-invariant systems subject to bounded additive disturbances. The approach uses data-driven predictors based on an extension of Willems'…

Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we present an approach based on conservative set-based enclosure of the dynamics that can handle…