Related papers: Control in finite and infinite dimension
We develop a functional-analytic characterization of output tracking controllability for finite-dimensional linear systems. By formulating tracking as the surjectivity of the control-to-output map on suitable trajectory spaces, we show that…
The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of "weak Dirichlet process" in this context. Such a process $\X$,…
This paper addresses the design of finite-dimensional feedback control laws for linear discrete-time fractional-order systems with additive state disturbance. A set of sufficient conditions are provided to guarantee convergence of the state…
Our goal is to highlight some deep connections between numerical splitting methods and control theory. We consider evolution equations of the form $\dot{x} = f_0(x) + f_1(x)$, where $f_0$ encodes non-reversible dynamics, motivating schemes…
The solution of the global controllability problem is obtained for a class of the triangular systems of O.D.E. that are not feedback linearizable. The introduced class is a generalization of the classes of triangular systems investigated…
Control problems frequently arise in scientific and industrial applications, where the objective is to steer a dynamical system from an initial state to a desired target state. Recent advances in deep learning and automatic differentiation…
This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls…
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
In this article, we investigate the problem of simultaneously steering an uncountable family of finite dimensional time-varying linear systems. We call this class of control problems Ensemble Control, a notion coming from the study of spin…
This paper discusses the approximate controllability of a fractional differential control problem driven by a nonlinear hemivariational inequality in a Hilbert space. First, we prove the existence of a mild solution for a fractional control…
This work deals with optimal control problems as a strategy to drive bifurcating solution of nonlinear parametrized partial differential equations towards a desired branch. Indeed, for these governing equations, multiple solution…
This paper studies the linear-quadratic (LQ) optimal control problem of a class of systems governed by the first-order hyperbolic partial differential equations (PDEs) with final state constraints. The main contribution is to present the…
A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…
In the framework of bilinear control of the Schr\"odinger equation with bounded control operators, it has been proved that the reachable set has a dense complemement in ${\cal S}\cap {\cal H}^{2}$. Hence, in this setting, exact quantum…
The Linear Quadratic Regulator (LQR), which is arguably the most classical problem in control theory, was recently related to kernel methods in (Aubin-Frankowski, SICON, 2021) for finite dimensional systems. We show that this result extends…
In the recent paper `Well-posedness and regularity for a generalized fractional Cahn-Hilliard system' (arXiv:1804.11290) by the same authors, general well-posedness results have been established for a a class of evolutionary systems of two…
The deployment of learning-based models in safety-critical control systems demands mathematical guarantees that standard regression architectures cannot provide. This paper presents an integrated framework that bridges Neural Ordinary…
Correlated with the trend of increasing degrees of freedom in robotic systems is a similar trend of rising interest in Spatio-Temporal systems described by Partial Differential Equations (PDEs) among the robotics and control communities.…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr\"odinger equation with coherent control. The open system's dynamics is governed by the…