Related papers: Limit-case admissibility for positive infinite-dim…
We consider the infinite dimensional linear programming (inf-LP) approach for solving stochastic control problems. The inf-LP corresponding to problems with uncountable state and input spaces is in general computationally intractable. By…
This paper deals with the stabilization of a class of linear infinite-dimensional systems with unbounded control operators and subject to a boundary disturbance. We assume that there exists a linear feedback law that makes the origin of the…
Given a dynamical system with constrained outputs, the maximal admissible set (MAS) is defined as the set of all initial conditions such that the output constraints are satisfied for all time. It has been previously shown that for…
Given a finite-dimensional time continuous control system and $\varepsilon>0$, we address the question of the existence of controls that maintain the corresponding state trajectories in the $\varepsilon$-neighborhood of any prescribed path…
This paper has been withdrawn. This paper focuses on the admissibility condition for fractional-order singular system with order $\alpha \in (0,1)$. The definitions of regularity, impulse-free and admissibility are given first, then a…
This paper is devoted to the controllability of a general linear hyperbolic system in one space dimension using boundary controls on one side. Under precise and generic assumptions on the boundary conditions on the other side, we previously…
In this paper we present a new bootstrap procedure for elliptic systems with two unknown functions. Combining with the $L^p$-$L^q$-estimates, it yields the optimal $L^\infty$-regularity conditions for the three well-known types of weak…
Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies the properties of the maximal sets of approximate controllability.
We characterize the well-posedness of a class of infinite-dimensional port-Hamiltonian systems with boundary control and observation. This class includes in particular the Euler-Bernoulli beam equations and more generally 1D linear…
Exploiting tools from algebraic geometry, the problem of finiteness of determination of accessibility/strong accessibility is investigated for polynomial systems and also for analytic systems that are immersible into polynomial systems. The…
This is a brief introduction to control theory in finite-dimensional spaces. The material is partly based on my lectures for the Master 1 program in Math\'ematiques et applications at Sorbonne University, delivered over the past few years.…
In Ho, Russell, and Weiss, a Carleson measure criterion for admissibility of one-dimensional input elements with respect to diagonal semigroups is given. We extend their results from the Hilbert space situation $X=\ell_2$ and…
This paper analyzes the structure of the set of positive solutions of a class of one-dimensional superlinear indefinite bvp's. It is a paradigm of how mathematical analysis aids the numerical study of a problem, whereas simultaneously its…
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…
We study the interpolation and extrapolation properties of strictly singular operators between different $L_p$ spaces. To this end, the structure of strictly singular non-compact operators between $L_p-L_q$ spaces is analyzed. Among other…
This paper presents a novel feasible-set reshaping technique to optimization-based control with ensured constraint qualification. In our problem setting, the feasible set of admissible control inputs depends on the real-time state of the…
Operators such as Carleson operator are known to be bounded on $L^p$ for all $1<p<\infty$, but not from $L^1$ to weak-$L^1$ and from $H^p$ to $L^p$ for each $0<p\leq 1$, the object of this article is to give a estimate for all $0<p<\infty$.…
A compact space X is I-favorable if, and only if X can be representing as a limit of $\sigma$-complete inverse system of compact metrizable spaces with skeletal bonding maps.
In this paper we consider $L_p$-approximation, $p \in \{2,\infty\}$, of periodic functions from weighted Korobov spaces. In particular, we discuss tractability properties of such problems, which means that we aim to relate the dependence of…
We generalize the Maximum Principle for free end point optimal control problems involving sweeping systems derived in [9] to cover the case where the end point is constrained to take values in a certain set. As in [9], an ingenious smooth…