一种带梯度惩罚项的离散力学最优控制方法
IMPROVED DMOC MODEL USING GRADIENT PENALTY TERM
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摘要: 离散力学最优控制方法(discrete mechanics and optimal control, DMOC) 是最新提出的一种有效的优化控制模型. 由于原始方法在求解优化问题时容易产生控制力的震荡,不利于控制力的稳定输出. 该文首先对产生这种数值现象的原因进行了简单的分析,并提出了可行的解决路径——加入惩罚梯度项. 最后采用数值算例对该方法进行验证,数值算例表明:改进的方法可以在保证力量最小化的前提下,使得控制力连续平滑.Abstract: The discrete mechanics and optimal control (DMOC) is a recently developed effective method to solve the optimization control problem. However, the original DMOC usually leads to some numerical oscillation of the control forces, which is unfavorable for the control output. In this paper, the causes of the numerical oscillation are analyzed. Then a feasible solution by introducing a gradient penalty term to the objective function is proposed. Finally, numerical examples validate the effectiveness of the proposed method. The simulation results show that the improved algorithm can ensure smoothness of the control forces under the condition of the minimization of the total control forces.