The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of ...The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem.Also,we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems.After that,we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem.Next,we have shown that both the saddle point conditions(Fritz-John and Kuhn-Tucker)are sufficient without any convexity requirements.Then with the convexity requirements,we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints.Here,all the results are derived with the help of interval order relations.Finally,we illustrate all the results with the help of a numerical example.展开更多
Many space missions require the execution of large-angle attitude slews during which stringent pointing constraints must be satisfied.For example,the pointing direction of a space telescope must be kept away from dire...Many space missions require the execution of large-angle attitude slews during which stringent pointing constraints must be satisfied.For example,the pointing direction of a space telescope must be kept away from directions to bright objects,maintaining a prescribed safety margin.In this paper we propose an open-loop attitude control algorithm which determines a rest-to-rest maneuver between prescribed attitudes while ensuring that any of an arbitrary number of body-fixed directions of light-sensitive instruments stays clear of any of an arbitrary number of space-fixed directions.The approach is based on an application of a version of Pontryagin’s Maximum Principle tailor-made for optimal control problems on Lie groups,and the pointing constraints are ensured by a judicious choice of the cost functional.The existence of up to three first integrals of the resulting system equations is established,depending on the number of light-sensitive and forbidden directions.These first integrals can be exploited in the numerical implementation of the attitude control algorithm,as is shown in the case of one light-sensitive and several forbidden directions.The results of the test cases presented confirm the applicability of the proposed algorithm.展开更多
基金Taif University Researchers Supporting Project number(TURSP-2020/20),Taif University,Taif,Saudi Arabia。
文摘The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem.Also,we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems.After that,we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem.Next,we have shown that both the saddle point conditions(Fritz-John and Kuhn-Tucker)are sufficient without any convexity requirements.Then with the convexity requirements,we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints.Here,all the results are derived with the help of interval order relations.Finally,we illustrate all the results with the help of a numerical example.
基金Partial support for this work by the Klaus Tschira Foundation is gratefully acknowledgedOpen access funding enabled and organized by Projekt DEAL.
文摘Many space missions require the execution of large-angle attitude slews during which stringent pointing constraints must be satisfied.For example,the pointing direction of a space telescope must be kept away from directions to bright objects,maintaining a prescribed safety margin.In this paper we propose an open-loop attitude control algorithm which determines a rest-to-rest maneuver between prescribed attitudes while ensuring that any of an arbitrary number of body-fixed directions of light-sensitive instruments stays clear of any of an arbitrary number of space-fixed directions.The approach is based on an application of a version of Pontryagin’s Maximum Principle tailor-made for optimal control problems on Lie groups,and the pointing constraints are ensured by a judicious choice of the cost functional.The existence of up to three first integrals of the resulting system equations is established,depending on the number of light-sensitive and forbidden directions.These first integrals can be exploited in the numerical implementation of the attitude control algorithm,as is shown in the case of one light-sensitive and several forbidden directions.The results of the test cases presented confirm the applicability of the proposed algorithm.
