考虑控制约束和不确定性的火星最优进入制导

摘要： 针对火星进入段控制受约束、大气环境以及探测器自身参数不确定性等问题，提出控制受约束的火星最优鲁棒进入制导方法.将针对参数不确定系统的最优性能指标转换为针对标称系统的修正性能指标；同时考虑控制约束，在性能指标中引入饱和函数，将制导问题转化为求解修正Hamilton Jacobi Bellman (HJB)方程问题；由于HJB方程是偏微分方程，求解有难度，利用神经网络的逼近能力近似求解.本文制导方法保证了不确定系统有最优的性能指标上界和较强的鲁棒性.最后将其应用到火星进入制导中，仿真结果表明系统存在不确定的情况下，仍可以很好地满足火星进入段终端条件，控制量也在约束的范围内，从而验证所提方法的有效性.

Mars Optimal Entry Guidance with Constrained Control and Uncertainty

Abstract：Aiming at the problem of Mars entry guidance, considering the constrained control and uncertainty of Mars atmosphere and detector’s parameters, the optimal robust guidance method with constrained control is proposed. Considering the parameter uncertainty of system, the optimal index of uncertain nonlinear system is transformed into an index of the nominal system. In consideration of the constrained control, a saturated function is introduced, and the guidance problem is transformed into solving the modified HJB equation. The neural network has the ability of approximation. The proposed HJB equation is solved with the neural network because the HJB equation is partial differential equation and there is a great deal of difficulty in solving it. The guidance method makes sure that the uncertain nonlinear systems have an optimal upper bound of performance index and that the method has robustness. Then, the method is applied to the Mars entry guidance. The simulation results show that the terminal conditions of Mars entry phase can be well guaranteed despite uncertainty of system, and that the control is in the constrained range, so the method is effective. Keywords： uncertain system; constrained control；HJB equation； Mars entry guidance