模型预测控制快速梯度优化算法评估

Assessment of Fast Gradient Optimization Algorithms for Model Predictive Control

基于快速梯度法的一类在线优化算法因其可预估给定求解精度下的计算量上界而被用于实时模型预测控制的在线求解。由于各算法针对的控制问题形式不同及算法设计的差别,对于非线性模型预测控制问题,难以有效快速地选择合适的算法。首先,对各个算法的特性及适用范围进行了简要描述;然后,针对解决具有状态约束和输入约束的非线性模型预测控制问题,给出了各个算法在求解过程中的计算复杂度,通过非线性实例验证和比较了各算法的性能。研究结果可为选择合适的模型预测控制算法提供参考。

A set of optimization algorithms based on the fast gradient method had been applied to the real time model predictive control(MPC)problems as it allows one to compute a priori the worst case bound required to find a solution with pre-specified accuracy.Due to different control problem formulations and algorithmic design,it is difficult to select the appropriate algorithm effectively and quickly.Firstly,the characteristics and application scope of each algorithm are briefly described.Then,the computational complexity of each algorithm in solving the nonlinear MPC problem with state and input constraints is given.The performance of each algorithm is verified and then compared by a nonlinear MPC example.The appropriate algorithm for online MPC can be selected according to the results of the paper.