English
Related papers

Related papers: Derived control theorems for reductive groups

200 papers

We prove a Noether-Deuring theorem for the derived category of bounded complexes of modules over a Noetherian algebra.

Representation Theory · Mathematics 2012-01-16 Alexander Zimmermann

We consider controlled differential equations and give new estimates for higher order Euler schemes. Our proofs are inspired by recent work of A. M. Davie who considers first and second order schemes. In order to implement the general case…

Classical Analysis and ODEs · Mathematics 2007-05-23 Peter Friz , Nicolas Victoir

We describe in the paper the graded centers of the derived categories of the derived discrete algebras. In particular, we prove that if $A$ is a derived discrete algebra, then the reduced part of the graded center of the derived category of…

Representation Theory · Mathematics 2009-06-09 Grzegorz Bobinski

In this article, we completely describe the control sets of one-input linear control systems on solvable, nonnilpotent 3D Lie groups. We show that, if the restriction of the associate derivation to the nilradical is nontrivial, the Lie…

Optimization and Control · Mathematics 2023-10-04 Adriano Da Silva , Lino Grama , Alejandro Otero Robles

We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic…

Probability · Mathematics 2014-11-17 I. Bailleul , J. Diehl

In this paper, we study the graph of homothety classes of stable free lattices in a two-dimensional representation over a local UFD. This generalizes a classical result of the case where the base ring is a discrete valuation ring due to…

Number Theory · Mathematics 2023-01-27 Dong Yan

We consider controllability for divergence-free systems that have a conserved quantity and satisfy a H\"ormander condition. It is shown that such systems are controllable, provided that the conserved quantity is a proper function. The proof…

Mathematical Physics · Physics 2008-02-27 Martin Hairer

The analysis of industrial processes, modelled as descriptor systems, is often computationally hard due to the presence of both algebraic couplings and difference equations of high order. In this paper, we introduce a control refinement…

Systems and Control · Computer Science 2017-04-07 Fei Chen , Sofie Haesaert , Alessandro Abate , Siep Weiland

This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems,…

Optimization and Control · Mathematics 2015-10-15 Mouhamadou Dath , Philippe Jouan

Motivated by mechanical systems with symmetries, we focus on optimal control problems possessing symmetries. Following recent works, which generalized the classical concept of static turnpike to manifold turnpike, we extend the exponential…

Optimization and Control · Mathematics 2024-06-25 Kathrin Flaßkamp , Sofya Maslovskaya , Sina Ober-Blöbaum , Boris Wembe

In studying the structure of derived categories of module categories of group algebras or their blocks, it is fundamental to classify support $\tau$-tilting modules. Koshio and Kozakai showed that the structure of support $\tau$-tilting…

Representation Theory · Mathematics 2023-11-29 Naoya Hiramae

Approximate controllability of the Euler equations is investigated by means of a finite set of actuators. It is proven that approximate controllability holds if we can find a saturating subset of actuators. The notion of saturating set is…

Optimization and Control · Mathematics 2025-04-17 Sérgio S. Rodrigues

This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…

Systems and Control · Computer Science 2018-11-16 Siddharth H. Nair , Ravi N. Banavar

The set of strata of a reductive group can be viewed as an enlargement of the set of unipotent classes. In this paper the notion of distinguished unipotent class is extended to this larger set. The strata of a Weyl group are introduced and…

Representation Theory · Mathematics 2022-01-19 G. Lusztig

Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies controllability by taking in consideration the eigenvalues of an associated derivation D. When the state…

Optimization and Control · Mathematics 2016-01-05 Adriano Da Silva

For a right-invariant system on a compact Lie group G, I present two methods to design a control to drive the state from the identity to any element of the group. The first method, under appropriate assumptions, achieves exact control to…

Quantum Physics · Physics 2015-05-13 Domenico D'Alessandro

We propose an extension of the theory of control sets to the case of inputs satisfying a dwell-time constraint. Although the class of such inputs is not closed under concatenation, we propose a suitably modified definition of control sets…

Optimization and Control · Mathematics 2019-02-12 Francesco Boarotto , Mario Sigalotti

In this paper, we extend the popular integral control technique to systems evolving on Lie groups. More explicitly, we provide an alternative definition of "integral action" for proportional(-derivative)-controlled systems whose…

Systems and Control · Computer Science 2015-02-06 Zhifei Zhang , Alain Sarlette , Zhihao Ling

We develop an epsilon-controlled algebraic L-theory, extending our earlier work on epsilon-controlled algebraic K-theory. The controlled L-theory is very close to being a generalized homology theory; we study analogues of the homology exact…

Geometric Topology · Mathematics 2009-03-19 Andrew Ranicki , Masayuki Yamasaki

In contrast with unstructured models, structured discrete population models have been able to fit and predict chaotic experimental data. However, most of the chaos control techniques in the literature have been designed and analyzed in a…

Dynamical Systems · Mathematics 2019-02-21 Elena Braverman , Daniel Franco