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对于已知目标信号的空间广义连续系统的预见跟踪问题,首先使用受限等价变换使其变为一般的连续系统,再将它们视为子系统做进一步的整合,之后定义它的状态变量、跟踪误差以及同步误差为新的状态变量,构造扩大误差系统,将跟踪问题转化成调节问题。对于复杂目标轨迹跨过不同坐标轴的情况,采用了基于同步误差的切换系统的方法,最后根据最优控制理论,求出原系统的最优反馈输入,实现了目标轨迹的跟踪。其数值仿真说明了其有效性。
For the problem of predictive tracking for a class of generalized continuous-time systems with known target signals, we first transform them into general continuous systems using constrained equivalent transformations and then treat them as further consolidation of the subsystems, then define their state variables, Tracking error and synchronization error as a new state variable, construct an extended error system, and convert the tracking problem into a regulation problem. For complex target trajectories across different axes, the method of switching system based on synchronization error is adopted. Finally, according to the optimal control theory, the optimal feedback input of the original system is obtained and the target trajectory is tracked. Its numerical simulation shows its effectiveness.