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为非完整链式系统提出了两种全局连续反馈控制律,即连续时变反馈控制律和动态时不变反馈控制律.第1种控制律通过引入一个与状态初值有关的指数衰减项,来保证控制律的连续性和渐近性.第2种控制律通过引入一个可自由设定初值的辅助状态,来保证系统的可控性以及控制律的连续性和渐近性.这两种控制律可以保证系统所有状态以指数速度渐近地、连续地收敛到原点,克服了以往控制律不能同时具有连续性、渐近性和指数收敛速度的缺陷.所得控制律应用于移动机器人系统和一个4维链式系统的镇定,仿真结果表明:状态轨迹和控制轨迹的光滑度和收敛速度都要优于以往控制律.
Two global continuous feedback control laws are proposed for nonholonomic chained systems, namely continuous time-varying feedback control law and dynamic time-invariant feedback control law. The first kind of control law introduces an exponential decay term related to the state initial value, To ensure the continuity and asymptotic behavior of the control law.The second kind of control law ensures the controllability of the system and the continuity and asymptotic behavior of the control law by introducing an auxiliary state that is free to set the initial value This kind of control law can ensure that all states of the system converge to the origin asymptotically and exponentially with exponential speed and overcomes the defect that the control law can not have the continuity, asymptotic property and the convergence rate of the exponential at the same time. The obtained control law is applied to the mobile robot system And a four-dimensional chaotic system, the simulation results show that the smoothness and convergence speed of state trajectory and control trajectory are better than those of the previous control law.