Control-Lyapunov and Control-Barrier Functions based Quadratic Program for Spatio-temporal Specifications
Control-Lyapunov and Control-Barrier Functions based Quadratic Program for Spatio-temporal Specifications
复制标题
基于控制-Lyapunov 和控制-屏障函数的时空规范二次规划
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;Dimitra Panagou
提出了一种时空约束下的控制综合方法。首先，我们考虑在用户定义或规定时间t内达到集合S的问题。我们定义了一类新的控制李雅普诺夫函数，称为规定时间控制李雅普诺夫函数（PT CLF），并给出了该问题的控制器存在的充分条件。然后，我们制定了一个二次规划（QP）来计算满足这些充分条件的控制输入。其次，我们考虑时空目标下的控制综合：闭环轨迹始终保持在给定的集合s中；，当i = 0,1，⋯N时，在时间区间[ti，ti+1)内保持在特定集合Si中；在t = ti+1时或之前达到集合Si+1。我们证明了这种时空规范可以转化为时间逻辑公式。我们给出了PT - CLF和控制势垒函数存在控制输入的充分条件。然后，我们提出了一个QP来有效地计算控制输入，并在假设存在一个PT CLF的情况下证明了它的可行性。据作者所知，这是第一篇提出基于QP的方法来解决上述具有输入约束的非线性控制-仿射动力学的时空规范问题的论文。我们还讨论了提出的方法的局限性和未来工作的方向，以克服这些局限性。我们给出了数值例子来证实我们提出的方法。
This paper presents a method for control synthesis under spatio-temporal constraints. First, we consider the problem of reaching a set S in a user-defined or prescribed time T. We define a new class of control Lyapunov functions, called prescribed-time control Lyapunov functions (PT CLF), and present sufficient conditions on the existence of a controller for this problem in terms of PT CLF. Then, we formulate a quadratic program (QP) to compute a control input that satisfies these sufficient conditions. Next, we consider control synthesis under spatio-temporal objectives given as: the closed- loop trajectories remain in a given set Ss at all times; and, remain in a specific set Si during the time interval [ti,ti+1) for i = 0,1,⋯, N; and, reach the set Si+1 on or before t = ti+1. We show that such spatio-temporal specifications can be translated into temporal logic formulas. We present sufficient conditions on the existence of a control input in terms of PT CLF and control barrier functions. Then, we present a QP to compute the control input efficiently, and show its feasibility under the assumptions of existence of a PT CLF. To the best of authors’ knowledge, this is the first paper proposing a QP based method for the aforementioned problem of satisfying spatiotemporal specifications for nonlinear control-affine dynamics with input constraints. We also discuss the limitations of the proposed methods and directions of future work to overcome these limitations. We present numerical examples to corroborate our proposed methods.