This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a ce...This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a certain optimal feedback control problem, each of which corresponds with one type of four-block problem. We also obtain a new formula for the optimal performance and prove the existence of an optimal controller.展开更多
In this paper, we deal with the unrestricted block relocation problem. We present a new integerprogramming formulation for solving the problem. The initial formulation is improved by tighteningconstraints and a pre-pr...In this paper, we deal with the unrestricted block relocation problem. We present a new integerprogramming formulation for solving the problem. The initial formulation is improved by tighteningconstraints and a pre-processing step to fix several variables. We design a exact iterativescheme algorithm based on a fast heuristic for the integer programming formulation (ISA-FH).Computational results show the effectiveness of the improved formulation and algorithm.展开更多
This paper addresses the blocking problem against a satellite attempting a geostationary or geosynchronous transfer.Calculation and optimization methods based on reachable domain and Lambert interception are designed ...This paper addresses the blocking problem against a satellite attempting a geostationary or geosynchronous transfer.Calculation and optimization methods based on reachable domain and Lambert interception are designed for the case of in-plane and nonplanar transfer orbits.Numerical validations against Hohmann transfer orbits were conducted to substantiate the proposed methods.Results indicate that,when blocking in-plane geostationary transfers,the blocker’s optimal stand-by orbit is the circular geostationary orbit.The mission-capable rates of in-plane elliptical blocking orbits,if properly arranged,resemble those of circular blocking orbits.When blocking nonplanar geosynchronous transfers,if only one blocker is involved,the optimal blocking orbit is circular.However,when multiple satellites collaborate on the same nonplanar blockade,the optimal blocking orbit is similar to a quasi-zenith orbit while the required capabilities for each blocker can be considerably reduced.Results indicate that geostationary or geosynchronous blocking can be achieved without occupying the precious geostationary orbit.Subsequently,the paper analyzes the impacts of non-Hohmann transfer orbits,inclined geostationary transfers,nonimpulsive maneuvers,and reaction times.The analysis pertaining to specific scenarios illustrates the interpretation and the definition used for orbital blockades;the engineering value of the computed results is revealed,providing insights for future research on orbital games.展开更多
文摘This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a certain optimal feedback control problem, each of which corresponds with one type of four-block problem. We also obtain a new formula for the optimal performance and prove the existence of an optimal controller.
基金National Natural Science Foundation of China(62073069)Liao Ning Revitalization Talents Program(XLYC2002041).
文摘In this paper, we deal with the unrestricted block relocation problem. We present a new integerprogramming formulation for solving the problem. The initial formulation is improved by tighteningconstraints and a pre-processing step to fix several variables. We design a exact iterativescheme algorithm based on a fast heuristic for the integer programming formulation (ISA-FH).Computational results show the effectiveness of the improved formulation and algorithm.
文摘This paper addresses the blocking problem against a satellite attempting a geostationary or geosynchronous transfer.Calculation and optimization methods based on reachable domain and Lambert interception are designed for the case of in-plane and nonplanar transfer orbits.Numerical validations against Hohmann transfer orbits were conducted to substantiate the proposed methods.Results indicate that,when blocking in-plane geostationary transfers,the blocker’s optimal stand-by orbit is the circular geostationary orbit.The mission-capable rates of in-plane elliptical blocking orbits,if properly arranged,resemble those of circular blocking orbits.When blocking nonplanar geosynchronous transfers,if only one blocker is involved,the optimal blocking orbit is circular.However,when multiple satellites collaborate on the same nonplanar blockade,the optimal blocking orbit is similar to a quasi-zenith orbit while the required capabilities for each blocker can be considerably reduced.Results indicate that geostationary or geosynchronous blocking can be achieved without occupying the precious geostationary orbit.Subsequently,the paper analyzes the impacts of non-Hohmann transfer orbits,inclined geostationary transfers,nonimpulsive maneuvers,and reaction times.The analysis pertaining to specific scenarios illustrates the interpretation and the definition used for orbital blockades;the engineering value of the computed results is revealed,providing insights for future research on orbital games.
