相关论文: A Baire Category Approach to the Bang-Bang Propert…

Lyapunov's theorem is a classical result in convex analysis, concerning the convexity of the range of nonatomic measures. Given a family of integrable vector functions on a compact set, this theorem allows to prove the equivalence between…

We study the uniform computational content of different versions of the Baire Category Theorem in the Weihrauch lattice. The Baire Category Theorem can be seen as a pigeonhole principle that states that a complete (i.e., "large") metric…

By reformulating the classical proof as a Baire Category argument, we show that Besicovitch's Theorem in Cantor space is provable in $ACA_0$, and additionally that the witnessing subset is computable from one jump of the original set. We…

Category-measure duality concerns applications of Baire-category methods that have measure-theoretic analogues. The set-theoretic axiom needed in connection with the Baire category theorem is the Axiom of Dependent Choice DC rather than the…

We prove a model theoretic Baire category theorem for $\tilde\tau_{low}^f$-sets in a countable simple theory in which the extension property is first-order and show some of its applications. We also prove a trichotomy for minimal types in…

We investigate the bang-bang property for fairly general classes of $L^\infty-L^1$ constrained bilinear optimal control problems in two cases: that of the one-dimensional torus, in which case we consider parabolic equations, and that of…

A topological space $X$ is Baire if the Baire Category Theorem holds for $X$, i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems in the theory of functional spaces is the…

We consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the other defined by the control variables constrained by simple…

The Baire category theorem states that every complete pseudometric space is a Baire space. There are some results in metric spaces which have their analogue in uniform spaces, however this is not one of them. Nonetheless, since the Baire…

Stability and safety are two important aspects in safety-critical control of dynamical systems. It has been a well established fact in control theory that stability properties can be characterized by Lyapunov functions. Reachability…

This paper presents converse theorems for safety in terms of barrier functions for unconstrained continuous-time systems modeled as differential inclusions. Via a counterexample, we show the lack of existence of autonomous and continuous…

We prove that the Baire Category Theorem is equivalent to the following: Let G be a topological groupoid such that the unit space is a complete metric space, and there is a countable cover of G by neighbourhood bisections. If G is…

In this paper we investigate a class of swing options with firm constraints in view of the modeling of supply agreements. We show, for a fully general payoff process, that the premium, solution to a stochastic control problem, is concave…

The main result can be given a short and elementary proof which has been incorporated into Lemma 3.2 of arXiv:1206.5775

This paper establishes the equivalence between robust safety and the existence of a barrier function certificate for differential inclusions. More precisely, for a robustly-safe differential inclusion, a barrier function is constructed as…

We prove that for a stratifiable scattered space $X$ of finite scattered height, the function space $C_k(X)$ endowed with the compact-open topology is Baire if and only if $X$ has the Moving Off Property of Gruenhage and Ma. As a byproduct…

A large collection of financial contracts offering guaranteed minimum benefits are often posed as control problems, in which at any point in the solution domain, a control is able to take any one of an uncountable number of values from the…

A topological space $X$ is Baire if the Baire Category Theorem holds for $X$, i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems for the space $B_1(X)$ of all Baire-one…

We have defined almost separable space. We show that like separability, almost separability is $c$ productive and converse also true under some restrictions. We establish a Baire Category theorem like result in Hausdorff, Pseudocompacts…

We investigate bang-bang control problems and the possibility to apply Newton's method to solve such kind of problems numerically. To this end, we show that the signum function is Fr\'echet differentiable between appropriate function…