The task of inducing, via continuous static state-feedback, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to a so-called point-to-point maneuver in an underactuated mechanical system. Namely, to a smooth curve in its state--control space, which is consistent with the system dynamics and connects two (linearly) stabilizable equilibrium points. The proposed method uses a particular parameterization, together with a state projection onto the maneuver as to combine two linearization techniques for this purpose: the Jacobian linearization at the equilibria on the boundaries and a transverse linearization along the orbit. This allows for the computation of stabilizing control gains offline by solving a semidefinite programming problem. The resulting nonlinear controller, which simultaneously asymptotically stabilizes both the orbit and the final equilibrium, is time-invariant, locally Lipschitz continuous, requires no switching, and has a familiar feedforward plus feedback--like structure. The method is also complemented by synchronization function--based arguments for planning such maneuvers for mechanical systems with one degree of underactuation. Numerical simulations of the non-prehensile manipulation task of a ball rolling between two points upon the "butterfly" robot demonstrates the efficacy of the synthesis.

翻译：在非线性控制系统中,通过连续静止的静态状态回溯,将非线性控制系统中的静态稳定的间歇性轨道诱导到非线性控制系统中,这一任务在本文中得到了考虑。主要动机来自确保与所谓的点对点操作趋同的问题,即确保在一个不活跃的机械系统中与所谓的点对点操纵趋同。也就是说,进入其州控制空间的平稳曲线,该曲线与系统动态一致,并连接两个(线性)可稳定平衡点。拟议方法使用特定的参数化,同时将状态投射到操控中,为此目的将两种线性技术结合起来:在边界的equiliblibria的Jacobian线性线性化,以及轨道上的反向线性线性线化。这样可以通过解决半不固定的机械化的编程问题来计算离线性控制增益。由此产生的非线性控制器,它同时稳定轨道和最后平衡点,是时性变的,本地的Libschitzitz持续,不需要转换,并且有一个熟悉的反馈和反馈的两种类似结构的反馈结构。这个方法也由同步的机性机性滚动的机性滚动的滚动操作系统在一个方向上,在模拟的机式的机式的机式的模性操作中,在一种方向上得到补充。