Prescribed-time Convergence with Input Constraints: A Control Lyapunov Function Based Approach
Prescribed-time Convergence with Input Constraints: A Control Lyapunov Function Based Approach
复制标题
具有输入约束的规定时间收敛：基于控制李亚普诺夫函数的方法
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Dimitra Panagou
中科院分区：
文献类型：
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作者：
Kunal Garg;E. Arabi;Dimitra Panagou
在本文中，我们提出了一类具有时空和输入约束的控制仿射非线性系统的控制框架。具体来说，所提出的控制体系结构解决了在规定的（用户定义的）时间内用有限的控制输入达到给定的最终集合S的问题。为此，利用时间转换技术将受时间约束的系统转换为不受时间约束的等效形式。对变换进行了定义，使变换后的时间尺度的渐近收敛导致原时间尺度的规定时间收敛。为了结合输入约束，我们描述了一组初始条件DM，使得闭环轨迹从这个集合开始，在规定的时间内到达集合S。我们进一步证明了系统轨迹从集合DM外出发，在有限时间内到达集合DM，这取决于初始条件和控制输入界。我们在控制器中使用了一个新的参数μ来控制闭环轨迹的收敛速度，并决定了DM集的大小。最后，我们给出了一个数值例子来证明我们所提出的方法的有效性。
In this paper, we present a control framework for a general class of control-affine nonlinear systems under spatiotemporal and input constraints. Specifically, the proposed control architecture addresses the problem of reaching a given final set S in a prescribed (user-defined) time with bounded control inputs. To this end, a time transformation technique is utilized to transform the system subject to temporal constraints into an equivalent form without temporal constraints. The transformation is defined so that asymptotic convergence in the transformed time scale results into prescribed-time convergence in the original time scale. To incorporate input constraints, we characterize a set of initial conditions DM such that starting from this set, the closed-loop trajectories reach the set S within the prescribed time. We further show that starting from outside the set DM , the system trajectories reach the set DM in a finite time that depends upon the initial conditions and the control input bounds. We use a novel parameter μ in the controller, that controls the convergence-rate of the closed-loop trajectories and dictates the size of the set DM. Finally, we present a numerical example to showcase the efficacy of our proposed method.