Numerical solutions of linear quadratic control for time-varying systems via symplectic conservative perturbation

Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation is presented. It gives a uniform way to solve the linear quadratic control （LQ control） problems for linear timevarying systems accurately and efficiently, whose key points are solutions of differential Riccati equation （DRE） with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.

Market-based control strategy for long-span structures considering the multi-time delay issue

To solve the different time delays that exist in the control device installed on spatial structures, in this study, discrete analysis using a 2N precise algorithm was selected to solve the multi-time-delay issue for long-span structures based on the market-based control （MBC） method. The concept of interval mixed energy was introduced from computational structural mechanics and optimal control research areas, and it translates the design of the MBC multi-time-delay controller into a solution for the segment matrix. This approach transforms the serial algorithm in time to parallel computing in space, greatly improving the solving efficiency and numerical stability. The designed controller is able to consider the issue of time delay with a linear controlling force combination and is especially effective for large time-delay conditions. A numerical example of a long-span structure was selected to demonstrate the effectiveness of the presented controller, and the time delay was found to have a significant impact on the results.

Identification of additional QTLs for flowering time by removing the effect of the maturity gene E1 in soybean

The adaptability of soybean to be grown at a wide range of latitudes is attributed to natural variation in the major genes and quantitative trait loci （QTLs） that control flowering time and maturity. Thus, the identification of genes controlling flowering time and maturity and the understanding of their molecular basis are critical for improving soybean productivity. However, due to the great effect of the major maturity gene E1 on flowering time, it is difficult to detect other small-effect QTLs. In this study, aiming to reduce the effect of the QTL, associated with the E1 gene, on the detection of other QTLs, we divided a population of 96 recombinant inbred lines （RILs） into two sub-populations： one with the E1 allele and another with the elns allele. Compared with the results of using all 96 recombinant inbred lines, additional QTLs for flowering time were identified in the sub-populations, two （qFT-B1 and qFT-H） in RILs with the E1 allele and one （qFT-J-2） in the RILs with the elnl allele, respectively. The three QTLs, qFT-B1, qFT-H and qFT-J-2 were true QTLs and played an important role in the regulation of growth period. Our data provides valuable information for the genetic mapping and gene cloning of traits controlling flowering time and maturity and will help a better understanding of the mechanism of photoperiod-regulated flowering and molecular breeding in soybean.