可精确实现的期望轨迹
Exactly realizable desired trajectories
AI总结：
研究非线性动力系统在具有仿射开环控制下的轨迹跟踪问题，提出可精确实现的期望轨迹概念，通过Moore-Penrose投影器进行数学表征，并简化了系统逆相关的计算。
摘要：
非线性动力系统在具有仿射开环控制下的轨迹跟踪问题被研究。控制任务是使系统状态尽可能接近给定的期望轨迹。我们引入了可精确实现的期望轨迹，这些轨迹可通过适当的控制精确跟踪。通过构造来自输入矩阵的Moore-Penrose投影器进行数学表征。该方法导致微分代数方程组，比相关系统的逆概念更简单。此外，我们识别出一个特别简单的非线性仿射控制系统类别。此类系统满足所谓的线性化假设，并与线性控制系统共享许多性质。例如，可控性条件可以以可控性矩阵的秩条件形式提出，类似于线性时不变系统的Kalman秩条件。
英文摘要：
Trajectory tracking of nonlinear dynamical systems with affine open-loop controls is investigated. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible. We introduce exactly realizable desired trajectories as these trajectories which can be tracked exactly by an appropriate control. Exactly realizable trajectories are characterized mathematically by means of Moore-Penrose projectors constructed from the input matrix. The approach leads to differential-algebraic systems of equations and is considerably simpler than the related concept of system inversion. Furthermore, we identify a particularly simple class of nonlinear affine control systems. Systems in this class satisfy the so-called linearizing assumption and share many properties with linear control systems. For example, conditions for controllability can be formulated in terms of a rank condition for a controllability matrix analogously to the Kalman rank condition for linear time-invariant systems.
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