This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill’s equations with nonnegative potential. By optimal control methods develo...This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill’s equations with nonnegative potential. By optimal control methods developed in 1990s, we obtain several stability criteria including Lyapunov’s criterion, Neǐgauz and Lidskiǐ’s criterion. Secondly, we present stability criteria on Hill’s equations with sign-changing potential in which Brog’s criterion and Krein’s criterion are included.展开更多
In this paper, a numerical method for solving the optimal control （OC） problems is presented. The method is enlightened by the Chebyshev-Legendre （CL） method for solving the partial differential equations （PDEs）...In this paper, a numerical method for solving the optimal control （OC） problems is presented. The method is enlightened by the Chebyshev-Legendre （CL） method for solving the partial differential equations （PDEs）. The Legendre expansions are used to approximate both the control and the state functions. The constraints are discretized over the Chebyshev-Gauss-Lobatto （CGL） collocation points. A Legendre technique is used to approximate the integral involved in the performance index. The OC problem is changed into an equivalent nonlinear programming problem which is directly solved. The fast Legendre transform is employed to reduce the computation time. Several further illustrative examples demonstrate the efficiency of the proposed method.展开更多
为获得具有优良气动性能且兼具结构强度及轻量化的复合材料飞机机翼,提出考虑气动分析和结构分析多目标多工况优化方法。分别对机翼进行气动分析及结构强度分析,以机翼展弦比、锥度比、后掠角为几何优化变量,以机翼上下机翼蒙皮的-45...为获得具有优良气动性能且兼具结构强度及轻量化的复合材料飞机机翼,提出考虑气动分析和结构分析多目标多工况优化方法。分别对机翼进行气动分析及结构强度分析,以机翼展弦比、锥度比、后掠角为几何优化变量,以机翼上下机翼蒙皮的-45°、90°、45°、0°层厚度和夹芯厚度为结构优化变量,建立以应力、位移为约束,以升阻比最大化和质量最小化为目标的协同优化模型。针对复合材料机翼多目标优化设计存在的计算量大难以取舍的问题,提出基于多准则和物理规划的自适应约束Kriging模型多目标优化算法(adaptive constraint kriging model multi-objective optimization algorithm based on multi-criteria and physical programming,AKBCP)。该算法引入了物理规划法和多准则加点,通过测试算例对比分析表明该算法具有较好的优化效果。将该算法应用到机翼多目标优化中,与初始机翼相比,优化后机翼升阻比提高3.12%,质量减轻31%,研究结果可为复合材料机翼优化设计提供参考。展开更多
基金supported by NSFC(11401089,11671071)the Scientific Technological Project of Jilin Province’s Education Department in Thirteenth Five-Year(JJKH20170535KJ)+1 种基金supported by NSFC(11571065)the National Basic Research Program of China(2013CB834102)
文摘This paper gives a tutorial on how to prove Lyapunov type criteria by optimal control methods. Firstly, we consider stability criteria on Hill’s equations with nonnegative potential. By optimal control methods developed in 1990s, we obtain several stability criteria including Lyapunov’s criterion, Neǐgauz and Lidskiǐ’s criterion. Secondly, we present stability criteria on Hill’s equations with sign-changing potential in which Brog’s criterion and Krein’s criterion are included.
基金supported by the National Natural Science Foundation of China (Grant Nos.10471089,60874039)the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘In this paper, a numerical method for solving the optimal control （OC） problems is presented. The method is enlightened by the Chebyshev-Legendre （CL） method for solving the partial differential equations （PDEs）. The Legendre expansions are used to approximate both the control and the state functions. The constraints are discretized over the Chebyshev-Gauss-Lobatto （CGL） collocation points. A Legendre technique is used to approximate the integral involved in the performance index. The OC problem is changed into an equivalent nonlinear programming problem which is directly solved. The fast Legendre transform is employed to reduce the computation time. Several further illustrative examples demonstrate the efficiency of the proposed method.
文摘为获得具有优良气动性能且兼具结构强度及轻量化的复合材料飞机机翼,提出考虑气动分析和结构分析多目标多工况优化方法。分别对机翼进行气动分析及结构强度分析,以机翼展弦比、锥度比、后掠角为几何优化变量,以机翼上下机翼蒙皮的-45°、90°、45°、0°层厚度和夹芯厚度为结构优化变量,建立以应力、位移为约束,以升阻比最大化和质量最小化为目标的协同优化模型。针对复合材料机翼多目标优化设计存在的计算量大难以取舍的问题,提出基于多准则和物理规划的自适应约束Kriging模型多目标优化算法(adaptive constraint kriging model multi-objective optimization algorithm based on multi-criteria and physical programming,AKBCP)。该算法引入了物理规划法和多准则加点,通过测试算例对比分析表明该算法具有较好的优化效果。将该算法应用到机翼多目标优化中,与初始机翼相比,优化后机翼升阻比提高3.12%,质量减轻31%,研究结果可为复合材料机翼优化设计提供参考。
