Prescribed-Time Stabilization and Robust Safety

规定时间稳定和鲁棒安全性

• 批准号: 2151525
• 负责人: Miroslav Krstic
• 金额: $ 37.5万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-15 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2151525&HistoricalAwards=false
• 关键词: Prescribed; Time; Stabilization; Robust; Safety

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.

在从电网到机器人的工程应用中，自二战前奈奎斯特和博德的开创性时代以来，在反馈系统中使用恒定增益的范例就没有改变。恒定增益产生易于分析的设定点调节指数速率，但未充分利用。驱动能力：从远离设定点开始，控制信号开始很大，但随后在接近设定点时变得不必要的小（“惰性”）。在许多当代应用中，需要的不仅仅是无限时间指数收敛。目标是在有限的、用户指定的时间内实现收敛，以及平稳稳定在设定点上，“快速、平稳”的过渡是 PI 最近推出的控制技术的未来之路。时变反馈定律，增益随着时间的推移而增长，这种增长的增益可以防止控制信号过早衰减，并及时实现与初始条件无关的“规定时间稳定”（PTS）。这个想法除了渐近性能方面的变革性进步外，它还开创了“规定时间安全”（PTSf）方法，该方法使控制系统（如无人驾驶汽车中的控制系统）在避免碰撞方面更加保守，因为：正如人类驾驶员所知，过度保守会激励其他人违反安全规定。该项目将建立 PTS 反馈定律的鲁棒性来测量噪声，为随机非线性系统设计 PTS 控制器，并开发用于运行的 PTSf 控制器。特别是，该研究将针对以下挑战：（1）其安全性以相对度数高于1的控制障碍函数（CBF）为特征的系统，例如力输入下的位置约束，（2）安全滤波器的设计。它结合了反步法和二次规划（QP）方法，以及（3）安全概念的放松，从“永远安全”的无限时间概念（过于保守）到“在用户指定的范围内安全”的概念时间间隔”即，PTSf 在未知界限的干扰下，将比当前的鲁棒安全方法取得更多的成果，而当前的鲁棒安全方法让干扰始终以可容忍的量突破障碍，通过 PTSf，将实现完全的干扰抑制。终端时间 受到干扰的系统，甚至可能在不安全设置中启动，将在用户指定的时间内“恢复安全”，与系统在不安全设置中启动的程度以及干扰有多大无关。设计将是。在 7 自由度 Baxter 机器人上进行了实验测试。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。