Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov＇s theorem for a fractional i...Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov＇s theorem for a fractional integro-differential inclusion involving Caputo＇s fractional derivative. This result allows us to obtain a continuous selection of the solution set of the problem considered.展开更多
We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions an...We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.展开更多
In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functio...In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases.展开更多
The large-range uncertainties of specific impulse,mass flow per second,aerodynamic coefficients and atmospheric density during rapid turning in solid launch vehicles(SLVs) ascending leads to the deviation of the actua...The large-range uncertainties of specific impulse,mass flow per second,aerodynamic coefficients and atmospheric density during rapid turning in solid launch vehicles(SLVs) ascending leads to the deviation of the actual trajectory from the reference one.One of the traditional trajectory tracking methods is to observe the uncertainties by Extended State Observer(ESO) and then modify the control commands.However,ESO cannot accurately estimate the uncertainties when the uncertainty ranges are large,which reduces the guidance accuracy.This paper introduces differential inclusion(DI) and designs a controller to solve the large-range parameter uncertainties problem.When above uncertainties have large ranges,it can be combined with the ascent dynamic equation and described as a DI system in the mathematical form of a set.If the DI system is stabilized,all the subsets are stabilized.Different from the traditional controllers,the parameters of the designed controller are calculated by the uncertain boundaries.Therefore,the controller can solve the problem of large-range parameter uncertainties of in ascending.Firstly,the ascent deviation system is obtained by linearization along the reference trajectory.The trajectory tracking system with engine parameters and aerodynamic uncertainties is described as an ascent DI system with respect to state deviation,which is called DI system.A DI adaptive saturation tracking controller(DIAST) is proposed to stabilize the DI system.Secondly,an improved barrier Lyapunov function(named time-varying tangent-log barrier Lyapunov function) is proposed to constrain the state deviations.Compared with traditional barrier Lyapunov function,it can dynamically adjust the boundary of deviation convergence,which improve the convergence rate and accuracy of altitude,velocity and LTIA deviation.In addition,the correction amplitudes of angle of attack(AOA) and angle of sideslip(AOS) need to be limited in order to guarantee that the overload constraint is not violated during actual flight.In this paper,a fixed time adaptive saturation compensation auxiliary system is designed to shorten the saturation time and accelerate the convergence rate,which eliminates the adverse effects caused by the saturation.Finally,it is proved that the state deviations are ultimately uniformly bounded under the action of DIAST controller.Simulation results show that the DI ascent tracking system is stabilized within the given uncertainty boundary values.The feasible bounds of uncertainty is broadened compared with Integrated Guidance and Control algorithm.Compared with Robust Gain-Scheduling Control method,the robustness to the engine parameters are greatly improved and the control variable is smoother.展开更多
In this paper,we consider nonconvex-valued functional differential inclusions with nonlinear semigroups in Banach spaces,the existence of the integral solutions is proved.
This paper studies the existence of solutions to a class of multivalued differential equations by using a surjectivity result for multivalued (S+) type mappings. The authors then apply their results to evolution hemiv...This paper studies the existence of solutions to a class of multivalued differential equations by using a surjectivity result for multivalued (S+) type mappings. The authors then apply their results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.展开更多
主观群体动力学模型(subjective group dynamics,SGD)探讨群际背景中个体的群体评价与群体成员评价的关系,针对群际偏见、分化评估和分化接纳意识(awareness of differential inclusion,ADI)三个核心变量间的关系及其影响因素,提出并验...主观群体动力学模型(subjective group dynamics,SGD)探讨群际背景中个体的群体评价与群体成员评价的关系,针对群际偏见、分化评估和分化接纳意识(awareness of differential inclusion,ADI)三个核心变量间的关系及其影响因素,提出并验证了一系列理论假设。SGD的理论基础包括社会认同理论、复杂性-极端性假设和态度极化模型、"白乌鸦效应"和个体对人知觉的发展。SGD模型的研究结果深化了群内偏好研究,支持了社会领域理论,并从群体机制角度为同伴拒斥研究提供了新思路,解释了群体同质性效应并修正了认知发展理论。该领域的发展需要从跨文化检验模型、完善模型结构、研究它与其他变量的关系等方面进行进一步探索。展开更多
基金supported by CNCS grant PN-II-ID-PCE-2011-3-0198
文摘Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov＇s theorem for a fractional integro-differential inclusion involving Caputo＇s fractional derivative. This result allows us to obtain a continuous selection of the solution set of the problem considered.
文摘We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.
基金supported by the Dong-A University research fund
文摘In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases.
基金supported by the National Natural Science Foundation of China (Grant Nos.61627810, 61790562 and 61403096)。
文摘The large-range uncertainties of specific impulse,mass flow per second,aerodynamic coefficients and atmospheric density during rapid turning in solid launch vehicles(SLVs) ascending leads to the deviation of the actual trajectory from the reference one.One of the traditional trajectory tracking methods is to observe the uncertainties by Extended State Observer(ESO) and then modify the control commands.However,ESO cannot accurately estimate the uncertainties when the uncertainty ranges are large,which reduces the guidance accuracy.This paper introduces differential inclusion(DI) and designs a controller to solve the large-range parameter uncertainties problem.When above uncertainties have large ranges,it can be combined with the ascent dynamic equation and described as a DI system in the mathematical form of a set.If the DI system is stabilized,all the subsets are stabilized.Different from the traditional controllers,the parameters of the designed controller are calculated by the uncertain boundaries.Therefore,the controller can solve the problem of large-range parameter uncertainties of in ascending.Firstly,the ascent deviation system is obtained by linearization along the reference trajectory.The trajectory tracking system with engine parameters and aerodynamic uncertainties is described as an ascent DI system with respect to state deviation,which is called DI system.A DI adaptive saturation tracking controller(DIAST) is proposed to stabilize the DI system.Secondly,an improved barrier Lyapunov function(named time-varying tangent-log barrier Lyapunov function) is proposed to constrain the state deviations.Compared with traditional barrier Lyapunov function,it can dynamically adjust the boundary of deviation convergence,which improve the convergence rate and accuracy of altitude,velocity and LTIA deviation.In addition,the correction amplitudes of angle of attack(AOA) and angle of sideslip(AOS) need to be limited in order to guarantee that the overload constraint is not violated during actual flight.In this paper,a fixed time adaptive saturation compensation auxiliary system is designed to shorten the saturation time and accelerate the convergence rate,which eliminates the adverse effects caused by the saturation.Finally,it is proved that the state deviations are ultimately uniformly bounded under the action of DIAST controller.Simulation results show that the DI ascent tracking system is stabilized within the given uncertainty boundary values.The feasible bounds of uncertainty is broadened compared with Integrated Guidance and Control algorithm.Compared with Robust Gain-Scheduling Control method,the robustness to the engine parameters are greatly improved and the control variable is smoother.
文摘In this paper,we consider nonconvex-valued functional differential inclusions with nonlinear semigroups in Banach spaces,the existence of the integral solutions is proved.
基金This research is supported by the National Natural Science Foundation of China(10171008)
文摘This paper studies the existence of solutions to a class of multivalued differential equations by using a surjectivity result for multivalued (S+) type mappings. The authors then apply their results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.
文摘主观群体动力学模型(subjective group dynamics,SGD)探讨群际背景中个体的群体评价与群体成员评价的关系,针对群际偏见、分化评估和分化接纳意识(awareness of differential inclusion,ADI)三个核心变量间的关系及其影响因素,提出并验证了一系列理论假设。SGD的理论基础包括社会认同理论、复杂性-极端性假设和态度极化模型、"白乌鸦效应"和个体对人知觉的发展。SGD模型的研究结果深化了群内偏好研究,支持了社会领域理论,并从群体机制角度为同伴拒斥研究提供了新思路,解释了群体同质性效应并修正了认知发展理论。该领域的发展需要从跨文化检验模型、完善模型结构、研究它与其他变量的关系等方面进行进一步探索。
