Related papers: Limit-case admissibility for positive infinite-dim…
For abstract linear systems in Hilbert spaces we revisit the problems of exact controllability and complete stabilizability (stabilizability with an arbitrary decay rate), the latter property is equivalent to exact null controllability. We…
Let $(\Omega,\Sigma,\mu)$ be a measure space and $1< p < +\infty$. In this paper we show that, under quite general conditions, the set $L_{p}(\Omega) - \bigcup\limits_{1 \leq q < p}L_{q}(\Omega)$ is maximal spaceable, that is, it contains…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
Maximum hands-off control is a control that has the minimum L0 norm among all feasible controls. It is known that the maximum hands-off (or L0-optimal) control problem is equivalent to the L1-optimal control under the assumption of…
We consider a class of nonlinear non-diagonal elliptic systems with $p$-growth and establish the $L^q$-integrability for all $q\in [p,p+2]$ of any weak solution provided the corresponding right hand side belongs to the corresponding…
Suppose L = {<, . . .} is any countable first order language in which < is interpreted as a linear order. Let T be any complete first order theory in the language L such that T has a kappa-like model where kappa is an inaccessible cardinal.…
In this paper, we study the concept of approximate controllability of retarded network systems of neutral type. On one hand, we reformulate such systems as free-delay boundary control systems on product spaces. On the other hand, we use the…
In this paper, we address the problem of computing the maximal admissible robust positive invariant (MARPI) set for discrete-time linear time-varying systems with parametric uncertainties and additive disturbances. The system state and…
We define embedding of an $n$-dimensional normed space into $L_{-p},\ 0<p<n$ by extending analytically with respect to $p$ the corresponding property of the classical $L_p$-spaces. The well-known connection between embeddings into $L_p$ and…
A class of infinite horizon optimal control problems involving mixed quasi-norms of $L^p$-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The…
In the paper, we consider integral operators with non-negative kernels satisfying conditions, which are less restrictive than conditions studied earlier. We establish criteria for the boundedness of these operators in Lebesgue spaces.
This paper is devoted to the controllability analysis of a class of linear control systems in a Hilbert space. It is proposed to use the minimum energy controls of a reduced lumped parameter system for solving the infinite dimensional…
An admissible observation operator is zero-class admissible if the norm of the output map tends to zero as the time tends to zero. Sufficient and necessary conditions for zero-class admissibility of observation operators are developed and a…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
We address an open problem in ensemble control: Whether there exist controllable linear ensemble systems over multi-dimensional parameterization spaces? We provide a negative result: Any real-analytic linear ensemble system is not…
We show that every unstable NIP theory admits a V-definable linear quasi-order, over a finite set of parameters. In particular, if the theory is omega-categorical, then it interprets an infinite linear order. This partially answers a…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, optimal points, and minimal points of these CILPs can be…
Positive systems describing networks with inherently non-negative states and inputs arise naturally in routing, logistics, and compartmental modelling. We consider problems modelled as positive linear systems in incidence form with linear…
In this paper, existence conditions and a design procedure of reduced-order switched positive observers for continuous- and discrete-time switched positive linear systems with uncertainty are established. In the analyzed class, arbitrary…