Prescribed-Time Stabilization and Robust Safety

在从电网到机器人的工程应用中，在反馈系统中使用恒定增益的范例自二战前奈奎斯特和博德的开创性日子以来一直没有改变。恒定增益产生易于分析的设定点调节的指数速率，但未充分利用驱动能力：从远离设定点开始，控制信号开始较大，但随后变得不必要地变小(“懒惰”)，接近设定点。在许多当代应用中，期望的不仅仅是无限时间的指数收敛。目标是在有限的、用户指定的时间内收敛，以及在设定点平稳稳定的目标。从半导体制造到能源系统，“快速而平稳”的过渡是控制技术的未来之路。PI最近引入了时变反馈律，其增益会随着时间的推移而增长。这种不断增长的增益可防止控制信号过早衰减，并在与初始条件无关的时间内实现“规定时间稳定”(PTS)。该项目在多个方向上推进了这一想法。除了在渐近性能方面取得了革命性的进步外，它还开创了“规定时间安全”(PTSF)的方法，使控制系统，如无人驾驶汽车中的控制系统，在避免碰撞方面不那么保守，因为正如人类驾驶员所知道的那样，过度保守会促使其他人违反安全规定。该项目将建立PTS反馈律对测量噪声的鲁棒性，设计随机非线性系统的PTS控制器，并开发适用于干扰下运行的PTSF控制器。具体地说，这项研究将针对以下挑战：(1)其安全性的特征是相对程度高于1的控制屏障函数(CBF)，例如在力输入下的位置约束；(2)结合反推和二次规划(QP)方法的安全过滤器的设计；以及(3)安全概念的放宽，从“永远安全”的无限时间概念(过于保守)到“在用户规定的时间间隔内安全”的概念，即PTSF。在未知范围的扰动下，将比目前的稳健安全方法获得更多的结果，后者允许扰动始终以可容忍的量越过屏障。有了PTSF，在终端时间将实现完全的干扰抑制。受到干扰的系统，甚至可能在不安全设置中开始，将在用户规定的时间内被“救起到安全”，而与系统在不安全设置中启动的深度和干扰有多大无关。设计将在7自由度巴克斯特机器人上进行实验测试。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

In engineering applications ranging from power grids to robotics, the paradigm of using constant gains in feedback systems hasn’t changed since the pioneering days of Nyquist and Bode before WWII. Constant gains produce easy-to-analyze exponential rates of setpoint regulation but underutilize the actuation capability: starting far from the setpoint, the control signal begins large but then gets needlessly small (“lazy”) close to the setpoint. In many contemporary applications, more than the infinite-time exponential convergence is desired. Convergence in finite, user-prescribed time is the goal, along with the goal of smooth settling at the setpoint. From semiconductor manufacturing to energy systems, “rapid and smooth” transitions are the way of the future for control technology. The PI recently introduced time-varying feedback laws, with gains that grow over time. Such growing gains prevent the control signal from decaying prematurely and achieve ``prescribed-time stabilization’’ (PTS), in time that is independent of the initial condition. This project advances this idea in a number of directions. In addition to transformational advances in asymptotic performance, it pioneers the methodology of “prescribed-time safety” (PTSf), which enables control systems, like those in driverless cars, to be less conservative in avoiding collisions because, as human drivers know, excessive conservativeness incentivizes a breach of safety by others. The project will establish robustness of PTS feedback laws to measurement noise, design PTS controllers for stochastic nonlinear systems, and develop PTSf controllers for operation under disturbances. In particular, the research will target the following challenges: (1) systems whose safety is characterized by control barrier functions (CBFs) of relative degree higher than one, such as position constraints under force inputs, (2) design of safety filters which combine backstepping and quadratic programming (QP) approaches, and (3) the relaxation of the concept of safety from the infinite-time notion of ``safe forever'' (too conservative) to the notion of “safe over a user-prescribed time interval,” i.e., PTSf. Under disturbances of unknown bound, more will be achieved than with the current robust safety methods, which let the disturbance violate the barrier, by a tolerable amount, for all time. With PTSf, a complete disturbance rejection will be achieved by the terminal time. A system under disturbance, possibly even starting in the unsafe set, will be ``rescued to safety’’ by a time prescribed by the user, independent of how deeply in the unsafe set the system starts and how large the disturbance is. Designs will be experimentally tested on the 7 degree of freedom Baxter robot.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.