2022/09/22 by Ji, Zhengping, Zhang, Xiao, Cheng, Daizhan
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2209.11278
In this article, we give a condition for the global controllability of affine nonlinear control systems with drifts on Euclidean spaces. Under regularity assumptions, the condition is necessary and sufficient in the codimension-1 and codimension-2 cases, and holds for systems of higher codimensions under mild restrictions. We then investigate motion planning problems for codimension-1 affine systems, and give proof of the global existence of the lift to control curves for certain drifted systems using the homotopy continuation method.