SU（n）上可控无漂移系统运动规划的时间周期李雅普诺夫方法
A Time-Periodic Lyapunov Approach for Motion Planning of Controllable Driftless Systems on SU(n)
摘要：
对于SU（n）上的右不变可控无漂移系统，我们考虑一个时间周期参考轨线，线性化控制系统沿着该参考轨线生成SU（n）：这样的轨线总是存在的，并且构成了Coron回归法的基本成分.我们提出的开环控制，它依赖于一个左不变的跟踪误差动态和一个类似李雅普诺夫函数，确定从有限数量的左平移的跟踪误差，他们保证全球渐近收敛的周期性参考轨迹。这些平移的作用是避免被困在这个类李雅普诺夫函数的临界区域。收敛性证明依赖于周期性版本的拉萨尔的不变原理和控制值由系统的动态的数值积分确定。模拟说明了所获得的控制$n=4$和生成的C-NOT量子门。
英文摘要：
For a right-invariant and controllable driftless system on SU(n), we consider a time-periodic reference trajectory along which the linearized control system generates su(n): such trajectories always exist and constitute the basic ingredient of Coron's Return Method. The open-loop controls that we propose, which rely on a left-invariant tracking error dynamics and on a fidelity-like Lyapunov function, are determined from a finite number of left-translations of the tracking error and they assure global asymptotic convergence towards the periodic reference trajectory. The role of these translations is to avoid being trapped in the critical region of this Lyapunov-like function. The convergence proof relies on a periodic version of LaSalle's invariance principle and the control values are determined by numerical integration of the dynamics of the system. Simulations illustrate the obtained controls for $n=4$ and the generation of the C--NOT quantum gate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
