Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different ...Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.展开更多
The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms....The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms.When the control region is convex, a pointwise second-order necessary condition for stochastic singular optimal controls in the classical sense is established; while when the control region is allowed to be nonconvex, we obtain a pointwise second-order necessary condition for stochastic singular optimal controls in the sense of Pontryagin-type maximum principle. It is found that, quite different from the first-order necessary conditions,the correction part of the solution to the second-order adjoint equation appears in the pointwise second-order necessary conditions whenever the diffusion term depends on the control variable, even if the control region is convex.展开更多
In this paper,an optimal switch-time control problem is solved for a class of impulsive switched autonomous systems.The considered systems jump at the switching times,and the sequence of active subsystems is pre-speci...In this paper,an optimal switch-time control problem is solved for a class of impulsive switched autonomous systems.The considered systems jump at the switching times,and the sequence of active subsystems is pre-specified.The control variables consist of the impulse times and a set of scalars which determine the jump amplitudes.Moreover,the subsystems do not require a refractory period,which can bring more generality.Using the calculus of variation,the partial derivatives of the cost with respect to the control variables are derived,based on which the optimality conditions are given.Meanwhile,the obtained formulas can be used in some gradient descent algorithms to locate the optimal control variables.Finally,the viability of the proposed method is illustrated through two numerical examples.展开更多
The issue of dropping the random force f(i) and the arbitrariness of choosing the basic variable in the variational approach to turbulence closure problem, pointed out recently by the Russian scientists Bazdenkov and ...The issue of dropping the random force f(i) and the arbitrariness of choosing the basic variable in the variational approach to turbulence closure problem, pointed out recently by the Russian scientists Bazdenkov and Kukharkin, are discussed. According to the mean-square estimation method, the random force f(i) should be dropped in the error expression of the LFP (Langevin-Fokker-Planck) model. However, f(i) is not neglected, its effect has been taken into account by the variational approach. In order to optimize the perturbation solution of the Liouville equation, the LFP model requires that the basic variable is as near to Gaussian as possible. Hence, the velocity, instead of the vorticity, should be chosen as the basic variable in the three-dimensional turbulence. Although the LFP model and the zero-order Gaussian term of PDF (probability density function) imply whiteness assumption (zero correlation time of f(i)), the higher-order non-Gaussian terms of PDF correspond to the nonwhiteness of turbulence dynamics, the variational approach does calculate the nonwhiteness effect properly.展开更多
The trade-off between users’ fairness and network throughput may be unacceptable in a multi-rate 802.11 WLAN environment. In this paper, we will design a new intuitive simplified mathematical model called simplified ...The trade-off between users’ fairness and network throughput may be unacceptable in a multi-rate 802.11 WLAN environment. In this paper, we will design a new intuitive simplified mathematical model called simplified coefficient of variation (SCV) to closely reflect our topic. Through controlling the power of Access Points, SCV can optimize and improve the performance. Since our topic is a NP-hard problem, we use Ant Colony Algorithm to solve our model in a practical scenario. The simulation shows excellent results indicating that our model is efficient and superior to an existing method. Also we use software SAS to further reveal the relationships among the three indicators to illustrate the essence of our approach and an existing algorithm.展开更多
This paper considers dynamical systems under feedback with control actions limited toswitching.The authors wish to understand the closed-loop systems as approximating multi-scale problemsin which the implementation of...This paper considers dynamical systems under feedback with control actions limited toswitching.The authors wish to understand the closed-loop systems as approximating multi-scale problemsin which the implementation of switching merely acts on a fast scale.Such hybrid dynamicalsystems are extensively studied in the literature,but not much so far for feedback with partial stateobservation.This becomes in particular relevant when the dynamical systems are governed by partialdifferential equations.The authors introduce an augmented BV setting which permits recognition ofcertain fast scale effects and give a corresponding well-posedness result for observations with such minimalregularity.As an application for this setting,the authors show existence of solutions for systemsof semilinear hyperbolic equations under such feedback with pointwise observations.展开更多
基金supported by CNPq and CAPES(Brazilian research funding agencies)Portuguese funds through the Center for Research and Development in Mathematics and Applications(CIDMA)the Portuguese Foundation for Science and Technology(FCT),within project UID/MAT/04106/2013
文摘Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.
基金supported by the National Basic Research Program of China(973 Program)(Grant No.2011CB808002)National Natural Science Foundation of China(Grant Nos.11221101+4 种基金1123100711401404 and 11471231)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT1273)the Changjiang Scholars Program from the Chinese Education Ministrythe Spanish Science and Innovation Ministry(Grant No.MTM2011-29306)
文摘The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms.When the control region is convex, a pointwise second-order necessary condition for stochastic singular optimal controls in the classical sense is established; while when the control region is allowed to be nonconvex, we obtain a pointwise second-order necessary condition for stochastic singular optimal controls in the sense of Pontryagin-type maximum principle. It is found that, quite different from the first-order necessary conditions,the correction part of the solution to the second-order adjoint equation appears in the pointwise second-order necessary conditions whenever the diffusion term depends on the control variable, even if the control region is convex.
基金supported by the National Natural Science Foundation of China under[Grant 61803238 and Grant 61873151].
文摘In this paper,an optimal switch-time control problem is solved for a class of impulsive switched autonomous systems.The considered systems jump at the switching times,and the sequence of active subsystems is pre-specified.The control variables consist of the impulse times and a set of scalars which determine the jump amplitudes.Moreover,the subsystems do not require a refractory period,which can bring more generality.Using the calculus of variation,the partial derivatives of the cost with respect to the control variables are derived,based on which the optimality conditions are given.Meanwhile,the obtained formulas can be used in some gradient descent algorithms to locate the optimal control variables.Finally,the viability of the proposed method is illustrated through two numerical examples.
基金The work is supported by the National Basic Research Program "Non-linear Sciences the National Natural Science Foundation of China
文摘The issue of dropping the random force f(i) and the arbitrariness of choosing the basic variable in the variational approach to turbulence closure problem, pointed out recently by the Russian scientists Bazdenkov and Kukharkin, are discussed. According to the mean-square estimation method, the random force f(i) should be dropped in the error expression of the LFP (Langevin-Fokker-Planck) model. However, f(i) is not neglected, its effect has been taken into account by the variational approach. In order to optimize the perturbation solution of the Liouville equation, the LFP model requires that the basic variable is as near to Gaussian as possible. Hence, the velocity, instead of the vorticity, should be chosen as the basic variable in the three-dimensional turbulence. Although the LFP model and the zero-order Gaussian term of PDF (probability density function) imply whiteness assumption (zero correlation time of f(i)), the higher-order non-Gaussian terms of PDF correspond to the nonwhiteness of turbulence dynamics, the variational approach does calculate the nonwhiteness effect properly.
文摘The trade-off between users’ fairness and network throughput may be unacceptable in a multi-rate 802.11 WLAN environment. In this paper, we will design a new intuitive simplified mathematical model called simplified coefficient of variation (SCV) to closely reflect our topic. Through controlling the power of Access Points, SCV can optimize and improve the performance. Since our topic is a NP-hard problem, we use Ant Colony Algorithm to solve our model in a practical scenario. The simulation shows excellent results indicating that our model is efficient and superior to an existing method. Also we use software SAS to further reveal the relationships among the three indicators to illustrate the essence of our approach and an existing algorithm.
基金support of the Elite Network of Bavaria under the grant #K-NW-2004-143
文摘This paper considers dynamical systems under feedback with control actions limited toswitching.The authors wish to understand the closed-loop systems as approximating multi-scale problemsin which the implementation of switching merely acts on a fast scale.Such hybrid dynamicalsystems are extensively studied in the literature,but not much so far for feedback with partial stateobservation.This becomes in particular relevant when the dynamical systems are governed by partialdifferential equations.The authors introduce an augmented BV setting which permits recognition ofcertain fast scale effects and give a corresponding well-posedness result for observations with such minimalregularity.As an application for this setting,the authors show existence of solutions for systemsof semilinear hyperbolic equations under such feedback with pointwise observations.
