基于Armijo准则和BFGS算法的运载火箭控制重分配

以某型运载火箭为研究对象,研究了伺服机构故障下的重构控制问题。将该问题转化为有约束二次规划问题,采用一种Armijo准则和BFGS算法相结合的控制分配方法来求解。Armijo准则可以保证优化算法的收敛性,而BFGS算法则避免了迭代过程对Hesse阵的求逆运算,且具有收敛快的优点。将该重构方法与不动点迭代算法进行了对比,该算法经过8次迭代收敛,目标函数值和误差值分别收敛到${\mathrm{10}}^{\mathrm{2}}$量级左右和${\mathrm{10}}^{-\mathrm{5}}$量级;而不动点迭代算法经过30次迭代尚未完全收敛,目标函数值和误差分别收敛到${\mathrm{10}}^{\mathrm{3}}$量级左右和${\mathrm{10}}^{-\mathrm{2}}$量级。结果表明该重构方法比不动点迭代算法收敛快且收敛精度高。以单台发动机发生卡死故障为例对该方法进行了仿真验证,得到了与无故障情况下相同的控制效果,验证了该重构方法的有效性和正确性。 

Reconfiguration control of launch vehicle based on Armijo criterion and BFGS algorithm

Taking a new type of launch vehicle as the research object,the problem of reconfiguration control under servo mechanism fault was studied.The problem was transformed into a constrained quadratic programming problem,and then a control allocation method combining the Armijo criterion and BFGS algorithm was used to solve the problem.Armijo criterion can ensure the convergence of the optimization algorithm,while BFGS algorithm avoided the inversion of Hesse matrix in the iterative process,and had the advantage of fast convergence.The proposed reconstruction method was compared with the fixed point iterative algorithm.After 8 iterations,the objective function value and error value converged to about ${\mathrm{10}}^{\mathrm{2}}$ magnitude and ${\mathrm{10}}^{-\mathrm{5}}$ magnitude,respectively.However,the fixed point iterative algorithm was not completely converged after 30 iterations,and the objective function value and error converged to about ${\mathrm{10}}^{\mathrm{3}}$ magnitude and ${\mathrm{10}}^{-\mathrm{2}}$ magnitude,respectively.The results showed that the reconstruction method converged faster and had higher convergence precision than the fixed point iterative algorithm.Taking a single engine stuck fault as an example,the simulation results showed that the control effect was the same as that in the case of no fault,which verified the validity and correctness of the proposed method.