This paper aims to provide a systematic approach to investigate the optimal feedback control systems governed by the fractional neutral evolution system with fixed delay in the sense of Caputo fractional derivatives i...This paper aims to provide a systematic approach to investigate the optimal feedback control systems governed by the fractional neutral evolution system with fixed delay in the sense of Caputo fractional derivatives in separable reflexive Banach spaces.Initially,we study the existence result of mild solutions for the system by applying fixed point theorem for a condensing map due to Martelli.The existence of feasible pairs is obtained by using the Filippov theorem and the Cesari property.Furthermore,the existence of optimal feedback control and time optimal control are studied for the corresponding control problem.Finally,an example is given to validate our findings.展开更多
In the present work adaptation in meshless framework is proposed.The grid adaptation or mesh adaptation is quite well developed area in case of conventional grid based solvers and is popularly known asAdaptivemesh ref...In the present work adaptation in meshless framework is proposed.The grid adaptation or mesh adaptation is quite well developed area in case of conventional grid based solvers and is popularly known asAdaptivemesh refinement(AMR).In such cases the adaptation is done by subdividing the cells or elements into finer cells or elements.In case ofmeshlessmethods there are no cells or elements but only a cloud of points.In this work we propose to achieve the meshless adaptation by locally refining the point density in the regions demanding higher resolution.This results into an adaptive enriched cloud of points.We call this method as Adaptive Cloud Refinement(ACR).Themeshless solvers need connectivity information,which is a set of neighboring nodes.It is crucial part of meshless solvers.Obviously because of refining point density,the connectivity of nodes in such regions gets modified and hence has to be updated.An efficient connectivity update must exploit the fact that the node distribution would be largely unaffected except the region of adaptation.Hence connectivity updating needs to be done locally,only in these regions.In this paper we also present an extremely fast algorithm to update connectivity over adapted cloud called as ACU(Automatic Connectivity Update).展开更多
文摘This paper aims to provide a systematic approach to investigate the optimal feedback control systems governed by the fractional neutral evolution system with fixed delay in the sense of Caputo fractional derivatives in separable reflexive Banach spaces.Initially,we study the existence result of mild solutions for the system by applying fixed point theorem for a condensing map due to Martelli.The existence of feasible pairs is obtained by using the Filippov theorem and the Cesari property.Furthermore,the existence of optimal feedback control and time optimal control are studied for the corresponding control problem.Finally,an example is given to validate our findings.
文摘In the present work adaptation in meshless framework is proposed.The grid adaptation or mesh adaptation is quite well developed area in case of conventional grid based solvers and is popularly known asAdaptivemesh refinement(AMR).In such cases the adaptation is done by subdividing the cells or elements into finer cells or elements.In case ofmeshlessmethods there are no cells or elements but only a cloud of points.In this work we propose to achieve the meshless adaptation by locally refining the point density in the regions demanding higher resolution.This results into an adaptive enriched cloud of points.We call this method as Adaptive Cloud Refinement(ACR).Themeshless solvers need connectivity information,which is a set of neighboring nodes.It is crucial part of meshless solvers.Obviously because of refining point density,the connectivity of nodes in such regions gets modified and hence has to be updated.An efficient connectivity update must exploit the fact that the node distribution would be largely unaffected except the region of adaptation.Hence connectivity updating needs to be done locally,only in these regions.In this paper we also present an extremely fast algorithm to update connectivity over adapted cloud called as ACU(Automatic Connectivity Update).
