Related papers: Uniformly hyperbolic control theory
Hyperbolic spaces, which have the capacity to embed tree structures without distortion owing to their exponential volume growth, have recently been applied to machine learning to better capture the hierarchical nature of data. In this…
Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
This article is devoted to the investigation of the topological pressure of generic points for nonuniformly hyperbolic systems via Pesin theory. In particular, our result can be applied to the nonuniformly hyperbolic diffeomorphisms…
Differential balancing theory for nonlinear model reduction relies on differential controllability and observability functions. In this paper, we further investigate them from two different perspectives. First, we establish novel…
Model-based manipulation of deformable objects has traditionally dealt with objects while neglecting their dynamics, thus mostly focusing on very lightweight objects at steady state. At the same time, soft robotic research has made…
This paper addresses the problems of stabilization, robust control, and observer design for nonlinear systems. We build upon recently a proposed method based on contraction theory and convex optimization, extending the class of systems to…
This paper is the first part of a project devoted to studying the interconnection between controllability properties of a dynamical system and the large-time asymptotics of trajectories for the associated stochastic system. It is proved…
Robust control design is mainly devoted to guarantee closed-loop stability of a model-based control law in presence of parametric and structural uncertainties. The control law is usually a complex feedback law which is derived from a…
This short note is devoted to the representative dynamics, which realizes a link between the theory of controlled systems and representation theory. Dynamical inverse problem of representation theory for controlled systems is considered: to…
We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Under appropriate conditions, there is a…
This paper deals with controllability of dynamical networks. It is often unfeasible or unnecessary to fully control large-scale networks, which motivates the control of a prescribed subset of agents of the network. This specific form of…
Aim of this paper is to review some basic ideas and recent developments in the theory of strictly hyperbolic systems of conservation laws in one space dimension. The main focus will be on the uniqueness and stability of entropy weak…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
This paper focuses on a model for opinion dynamics, where the influence weights of agents evolve in time. We formulate a control problem of consensus type, in which the objective is to drive all agents to a final target point under suitable…
We investigate the expressive power of deep residual neural networks idealized as continuous dynamical systems through control theory. Specifically, we consider two properties that arise from supervised learning, namely universal…
Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…
We consider the basic features of complex dynamical and control systems. Special attention is paid to the problems of synthesis of dynamical models of complex systems, construction of efficient control models, and to the development of…
This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…
We prove an almost sure invariance principle that is valid for general classes of nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time systems and flows are covered by this result. In particular, the result…
We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…