Superlinear Convergence Using Controls Based on Second-Order Needle Variations
Superlinear Convergence Using Controls Based on Second-Order Needle Variations
复制标题
DOI：
10.1109/cdc.2018.8619405
复制
发表时间：
2018-12
期刊：
影响因子：
--
通讯作者：
Giorgos Mamakoukas;M. A. MacIver;T. Murphey
中科院分区：
文献类型：
--
作者：
Giorgos Mamakoukas;M. A. MacIver;T. Murphey
研究了非线性仿射控制系统的二阶针变分法的收敛性能。控制解决方案有一个封闭的形式的表达，是来自第一和第二阶模式插入梯度的目标，并被证明表现出超线性收敛附近的平衡。与一阶指针变化相比，所提出的综合方案具有上级收敛性，比替代的非线性反馈控制器具有更小的计算成本。对差动驱动模型的仿真结果验证了分析，并表明二阶指针变化优于一阶变分方法和iLQR优化器附近。最后，即使在一个闭环，滚动时域设置，所提出的算法表现出上级收敛迭代线性二次高斯（iLQG）控制器。
This paper investigates the convergence performance of second-order needle variation methods for nonlinear control-affine systems. Control solutions have a closed-form expression that is derived from the first-and second-order mode insertion gradients of the objective and are proven to exhibit superlinear convergence near equilibrium. Compared to first-order needle variations, the proposed synthesis scheme exhibits superior convergence at smaller computational cost than alternative nonlinear feedback controllers. Simulation results on the differential drive model verify the analysis and show that second-order needle variations outperform first-order variational methods and iLQR near the optimizer. Last, even when implemented in a closed-loop, receding horizon setting, the proposed algorithm demonstrates superior convergence against the iterative linear quadratic Gaussian (iLQG) controller.