scholarly journals Solution stability to parametric distributed optimal control problems with finite unilateral constraints

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nguyen Hai Son
Keyword(s):  
Sufficient Conditions ◽  
Necessary Optimality Conditions ◽  
Solution Stability ◽  
Unilateral Constraints ◽  
Solution Map ◽  
Distributed Optimal Control ◽  
First Order ◽  
Stability Of Solution ◽  
Distributed Optimal Control Problems ◽  
Objective Functional

<p style='text-indent:20px;'>This paper deals with stability of solution map to a parametric control problem governed by semilinear elliptic equations with finite unilateral constraints, where the objective functional is not convex. By using the first-order necessary optimality conditions, we derive some sufficient conditions under which the solution map is upper semicontinuous with respect to parameters.</p>

Sparse Optimal Control of the Schlögl and FitzHugh–Nagumo Systems

2013 ◽  
Vol 13 (4) ◽  
pp. 415-442 ◽  
Author(s):  
Eduardo Casas ◽  
Christopher Ryll ◽  
Fredi Tröltzsch
Keyword(s):  
Optimal Control ◽  
Necessary Optimality Conditions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Optimal Controls ◽  
Wave Fronts ◽  
First Order ◽  
Schlögl Model ◽  
Sparse Optimal Control ◽  
Objective Functional

Abstract. We investigate the problem of sparse optimal controls for the so-called Schlögl model and the FitzHugh–Nagumo system. In these reaction–diffusion equations, traveling wave fronts occur that can be controlled in different ways. The L1-norm of the distributed control is included in the objective functional so that optimal controls exhibit effects of sparsity. We prove the differentiability of the control-to-state mapping for both dynamical systems, show the well-posedness of the optimal control problems and derive first-order necessary optimality conditions. Based on them, the sparsity of optimal controls is shown. The theory is illustrated by various numerical examples, where wave fronts or spiral waves are controlled in a desired way.

scholarly journals Distributed optimal control problems for phase field systems with singular potential

2018 ◽  
Vol 26 (2) ◽  
pp. 71-85
Author(s):  
Pierluigi Colli ◽  
Gianni Gilardi ◽  
Gabriela Marinoschi ◽  
Elisabetta Rocca
Keyword(s):  
Control Problem ◽  
Phase Field ◽  
Singular Potential ◽  
Necessary Optimality Conditions ◽  
Logarithmic Potential ◽  
Diffuse Interface ◽  
Distributed Optimal Control ◽  
Distributed Optimal Control Problems ◽  
Field Systems ◽  
The Cost

Abstract In this paper we review some results obtained for a distributed con- trol problem regarding a class of phase field systems of Caginalp type with logarithmic potential. The aim of the control problem is forcing the location of the diffuse interface to be as close as possible to a pre- scribed set. However, due to some discontinuity in the cost functional, we have to regularize it and solve the related control problem for the approximation. We discuss the necessary optimality conditions.

scholarly journals Conceptual Analysis and Empirical Observations of Animal Minds

Philosophia ◽  
2021 ◽  
Author(s):  
Ricardo Parellada
Keyword(s):  
Conceptual Analysis ◽  
Animal Cognition ◽  
Sufficient Conditions ◽  
Second Order ◽  
Alarm Calls ◽  
Vervet Monkeys ◽  
Animal Minds ◽  
First Order

AbstractThe relation between conceptual analysis and empirical observations when ascribing or denying concepts and beliefs to non-human animals is not straightforward. In order to reflect on this relation, I focus on two theoretical proposals (Davidson’s and Allen’s) and one empirical case (vervet monkeys’ alarm calls), the three of which are permanently discussed and considered in the literature on animal cognition. First, I review briefly Davidson’s arguments for denying thought to non-linguistic animals. Second, I review Allen’s criteria for ascribing concepts to creatures capable of correcting their discriminatory powers by taking into account their previous errors. Allen affirms that this is an empirical proposal which offers good reasons, but not necessary or sufficient conditions, for concept attribution. Against Allen, I argue that his important proposal is not an empirical, but a conceptual one. Third, I resort to vervet monkeys to show that Allen’s criteria, and not Davidson’s, are very relevant for ascribing first-order and denying second-order beliefs to this species and thus make sense of the idea of animal cognition.

Resolution systems and their applications I

1980 ◽  
Vol 3 (2) ◽  
pp. 235-268
Author(s):  
Ewa Orłowska
Keyword(s):  
Theorem Proving ◽  
Sufficient Conditions ◽  
Predicate Calculus ◽  
Resolution Method ◽  
First Order ◽  
Deductive Systems ◽  
Resolution System ◽  
Resolution Principle ◽  
Necessary And Sufficient ◽  
Classical Predicate

The central method employed today for theorem-proving is the resolution method introduced by J. A. Robinson in 1965 for the classical predicate calculus. Since then many improvements of the resolution method have been made. On the other hand, treatment of automated theorem-proving techniques for non-classical logics has been started, in connection with applications of these logics in computer science. In this paper a generalization of a notion of the resolution principle is introduced and discussed. A certain class of first order logics is considered and deductive systems of these logics with a resolution principle as an inference rule are investigated. The necessary and sufficient conditions for the so-called resolution completeness of such systems are given. A generalized Herbrand property for a logic is defined and its connections with the resolution-completeness are presented. A class of binary resolution systems is investigated and a kind of a normal form for derivations in such systems is given. On the ground of the methods developed the resolution system for the classical predicate calculus is described and the resolution systems for some non-classical logics are outlined. A method of program synthesis based on the resolution system for the classical predicate calculus is presented. A notion of a resolution-interpretability of a logic L in another logic L ′ is introduced. The method of resolution-interpretability consists in establishing a relation between formulas of the logic L and some sets of formulas of the logic L ′ with the intention of using the resolution system for L ′ to prove theorems of L. It is shown how the method of resolution-interpretability can be used to prove decidability of sets of unsatisfiable formulas of a given logic.

scholarly journals Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
K. C. Panda ◽  
R. N. Rath ◽  
S. K. Rath
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Oscillation And Nonoscillation

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.

System Properties of One-Dimensional Distributed Systems

1977 ◽  
Vol 99 (2) ◽  
pp. 85-90 ◽  
Author(s):  
L. S. Bonderson
Keyword(s):  
Distributed Systems ◽  
Sufficient Conditions ◽  
State Variables ◽  
One Dimensional ◽  
First Order ◽  
Lumped Element ◽  
Order Form ◽  
Power Product ◽  
System Properties ◽  
Necessary And Sufficient

The system properties of passivity, losslessness, and reciprocity are defined and their necessary and sufficient conditions are derived for a class of linear one-dimensional multipower distributed systems. The utilization of power product pairs as state variables and the representation of the dynamics in first-order form allows results completely analogous to those for lumped-element systems.

A concept of inner prederivative for set-valued mappings and its applications

2018 ◽  
Vol 24 (3) ◽  
pp. 1059-1074
Author(s):  
Michel H. Geoffroy ◽  
Yvesner Marcelin
Keyword(s):  
Optimality Conditions ◽  
Necessary Optimality Conditions ◽  
Welfare Economics ◽  
Inverse Mapping ◽  
First Order ◽  
Inverse Mapping Theorem ◽  
Homogeneous Set ◽  
Optimal Allocations ◽  
Variational Perturbations ◽  
Set Valued Mappings

We introduce a class of positively homogeneous set-valued mappings, called inner prederivatives, serving as first order approximants to set-valued mappings. We prove an inverse mapping theorem involving such prederivatives and study their stability with respect to variational perturbations. Then, taking advantage of their properties we establish necessary optimality conditions for the existence of several kind of minimizers in set-valued optimization. As an application of these last results, we consider the problem of finding optimal allocations in welfare economics. Finally, to emphasize the interest of our approach, we compare the notion of inner prederivative to the related concepts of set-valued differentiation commonly used in the literature.

scholarly journals El autoconocimiento de las creencias: una objeción al método de la transparencia

2019 ◽  
pp. 429
Author(s):  
Javier Vidal
Keyword(s):  
Practical Reasoning ◽  
Sufficient Conditions ◽  
Second Order ◽  
Mental Life ◽  
The Unconscious ◽  
First Order ◽  
Rational Deliberation ◽  
Self Knowledge

According to the method of transparency, genuine self-knowledge is the outcome of an inference from world to mind. A. Byrne (2018) has developed a theory in which the method of transparency consists in following an epistemic rule in order to form self-verifying second-order beliefs. In this paper, I argue that Byrne’s theory does not establish sufficient conditions for having self-knowledge of first-order beliefs. Examining a case of self-deception, I strive to show that following such a rule might not result in self-knowledge when one is involved in rational deliberation. In the case under consideration, one precisely comes to believe that one believes that p without coming to believe that p. The justification for one’s not forming the belief that p with its distinctive causal pattern in mental life and behaviour, is that one already had the unconscious belief that not-p, a belief that is not sensitive to the principles governing theoretical and practical reasoning.

scholarly journals The nonlocal solvability conditions for a system of two quasilinear equations of the first order with absolute terms

2019 ◽  
Vol 21 (3) ◽  
pp. 317-328
Author(s):  
Marina V. Dontsova
Keyword(s):  
Cauchy Problem ◽  
Finite Number ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Local Solution ◽  
Quasilinear Equations ◽  
Solvability Conditions ◽  
First Order ◽  
The Cauchy Problem ◽  
Global Estimates

The Cauchy problem for a system of two first-order quasilinear equations with absolute terms is considered. The study of this problem’s solvability in original coordinates is based on the method of an additional argument. The existence of the local solution of the problem with smoothness which is not lower than the smoothness of the initial conditions, is proved. Sufficient conditions of existence are determined for the nonlocal solution that is continued by a finite number of steps from the local solution. The proof of the nonlocal resolvability of the Cauchy problem relies on original global estimates.

Sign in / Sign up

Export Citation Format

Share Document