Constrained reentry trajectory optimization for hypersonic vehicles is a challenging job. In particular, this problem becomes more difficult when several objectives with preemptive priorities are expected for differen...Constrained reentry trajectory optimization for hypersonic vehicles is a challenging job. In particular, this problem becomes more difficult when several objectives with preemptive priorities are expected for different purposes. In this paper, a fuzzy satisfactory goal programming method is proposed to solve the multi-objective reentry trajectory optimization problem. Firstly, direct collocation approach is used to discretize the reentry trajectory optimal-control problem with nonlinear constraints into nonlinear multiobjective programming problem with preemptive priorities, where attack angles and bank angles at nodes and collocation nodes are selected as control variables. Secondly, the preemptive priorities are transformed into the relaxed order of satisfactory degrees according to the principle that the objective with higher priority has higher satisfactory degree. Then the fuzzy satisfactory goal programming model is proposed. The balance between optimization and priorities is realized by regulating parameter λ, such that the satisfactory reentry trajectory can be acquired. The simulation demonstrates that the proposed method is effective for the multi-objective reentry trajectory optimization of hypersonic vehicles.展开更多
This paper derives a new constraint qualification for nondifferential convex programming problem, by using the distance between the feasible set and the perturbed feasible sets. If the feasible sot is bounded, then th...This paper derives a new constraint qualification for nondifferential convex programming problem, by using the distance between the feasible set and the perturbed feasible sets. If the feasible sot is bounded, then this constraint qualification is weaker than Stater's constrains qualification.展开更多
基于回答集语义的逻辑程序(Answer Set Programming,ASP)是描述性问题求解的典范,广泛应用于规划、诊断、调度以及生物信息学等领域。为了增强ASP的表达能力,一些工作在ASP引入了数据库系统中的聚合函数约束,并提出了SPT,FLP等语义,抽...基于回答集语义的逻辑程序(Answer Set Programming,ASP)是描述性问题求解的典范,广泛应用于规划、诊断、调度以及生物信息学等领域。为了增强ASP的表达能力,一些工作在ASP引入了数据库系统中的聚合函数约束,并提出了SPT,FLP等语义,抽象约束剥离聚合函数约束的具体形式成为研究ASP语义等性质的重要工具,并得到了抽象约束逻辑程序的各种回答集语义之间的关系和复杂性问题等的相关结果。对此,进一步研究了仅含凸抽象约束原子抽象约束逻辑的性质,证明了仅含凸抽象约束原子的正规逻辑程序判定是否存在FLP回答集是Σ_(2)^(p)完全的,其审慎推理和大胆推理分别是Π_(2)^(p)完全的和Σ_(2)^(p)完全的。这些复杂性结果进一步理清了各类逻辑程序间的表达能力关系,为设计有效的回答集求解器提供了新的思路,也为进一步探索ASP在解决用凸抽象约束表示的问题中的应用提供了理论基础。展开更多
基金supported by National Natural Science Foundation of China(No.61074064)Natural Science Foundation of Tianjin(No.12JCZDJC30300)
文摘Constrained reentry trajectory optimization for hypersonic vehicles is a challenging job. In particular, this problem becomes more difficult when several objectives with preemptive priorities are expected for different purposes. In this paper, a fuzzy satisfactory goal programming method is proposed to solve the multi-objective reentry trajectory optimization problem. Firstly, direct collocation approach is used to discretize the reentry trajectory optimal-control problem with nonlinear constraints into nonlinear multiobjective programming problem with preemptive priorities, where attack angles and bank angles at nodes and collocation nodes are selected as control variables. Secondly, the preemptive priorities are transformed into the relaxed order of satisfactory degrees according to the principle that the objective with higher priority has higher satisfactory degree. Then the fuzzy satisfactory goal programming model is proposed. The balance between optimization and priorities is realized by regulating parameter λ, such that the satisfactory reentry trajectory can be acquired. The simulation demonstrates that the proposed method is effective for the multi-objective reentry trajectory optimization of hypersonic vehicles.
基金the National Natural Science Foundation of China (No.19671053).
文摘This paper derives a new constraint qualification for nondifferential convex programming problem, by using the distance between the feasible set and the perturbed feasible sets. If the feasible sot is bounded, then this constraint qualification is weaker than Stater's constrains qualification.
文摘基于回答集语义的逻辑程序(Answer Set Programming,ASP)是描述性问题求解的典范,广泛应用于规划、诊断、调度以及生物信息学等领域。为了增强ASP的表达能力,一些工作在ASP引入了数据库系统中的聚合函数约束,并提出了SPT,FLP等语义,抽象约束剥离聚合函数约束的具体形式成为研究ASP语义等性质的重要工具,并得到了抽象约束逻辑程序的各种回答集语义之间的关系和复杂性问题等的相关结果。对此,进一步研究了仅含凸抽象约束原子抽象约束逻辑的性质,证明了仅含凸抽象约束原子的正规逻辑程序判定是否存在FLP回答集是Σ_(2)^(p)完全的,其审慎推理和大胆推理分别是Π_(2)^(p)完全的和Σ_(2)^(p)完全的。这些复杂性结果进一步理清了各类逻辑程序间的表达能力关系,为设计有效的回答集求解器提供了新的思路,也为进一步探索ASP在解决用凸抽象约束表示的问题中的应用提供了理论基础。
