With the increase in data availability, it has been widely demonstrated that neural networks (NN) can capture complex system dynamics precisely in a data-driven manner. However, the architectural complexity and nonlinearity of the NNs make it challenging to synthesize a provably safe controller. In this work, we propose a novel safety filter that relies on convex optimization to ensure safety for a NN system, subject to additive disturbances that are capable of capturing modeling errors. Our approach leverages tools from NN verification to over-approximate NN dynamics with a set of linear bounds, followed by an application of robust linear MPC to search for controllers that can guarantee robust constraint satisfaction. We demonstrate the efficacy of the proposed framework numerically on a nonlinear pendulum system.
This paper investigates the use of extended Kalman filtering to train recurrent neural networks with rather general convex loss functions and regularization terms on the network parameters, including $\ell_1$-regularization. We show that the learning method is competitive with respect to stochastic gradient descent in a nonlinear system identification benchmark and in training a linear system with binary outputs. We also explore the use of the algorithm in data-driven nonlinear model predictive control and its relation with disturbance models for offset-free closed-loop tracking.
We study the problem of safe online convex optimization, where the action at each time step must satisfy a set of linear safety constraints. The goal is to select a sequence of actions to minimize the regret without violating the safety constraints at any time step (with high probability). The parameters that specify the linear safety constraints are unknown to the algorithm. The algorithm has access to only the noisy observations of constraints for the chosen actions. We propose an algorithm, called the {Safe Online Projected Gradient Descent} (SO-PGD) algorithm, to address this problem. We s…
Online convex optimization is a sequential prediction framework with the goal to track and adapt to the environment through evaluating proper convex loss functions. We study efficient particle filtering methods from the perspective of such a framework. We formulate an efficient particle filtering methods for the non-stationary environment by making connections with the online mirror descent algorithm which is known to be a universal online convex optimization algorithm. As a result of this connection, our proposed particle filtering algorithm proves to achieve optimal particle efficiency.
Unlike conventional generators, inverter-based generation do not possess any rotational inertia. While grid-forming inverters can synthesize small (virtual) inertia via advanced feedback control loops, additional control mechanisms are needed to ensure safety and security of the power grid during transients. In this paper, we propose novel real-time safety-constrained feedback controllers ("safety filters") for droop-based (grid-forming) inverters to ensure transient security of the grid. The safety filter acts as a buffer between the network operational layer and the inverter-control layer, a…
Inverse Safety Filtering: Inferring Constraints from Safety Filters for Decentralized Coordination
Department of Electrical Engineering and Computer Sciences, University of California Berkeley（加州大学伯克利分校电气与计算机科学与工程系）；Oden Institute, University of Texas at Austin（德克萨斯大学奥斯汀分校奥登研究所）
Safety Filtering While Training: Improving the Performance and Sample Efficiency of Reinforcement Learning Agents
University of Toronto（多伦多大学）；University of Toronto Robotics Institute（多伦多大学机器人研究所）；Vector Institute for Artificial Intelligence（向量人工智能研究所）；Technical University of Munich（慕尼黑工业大学）；Munich Institute for Robotics and Machine Intelligence（慕尼黑机器人与机器智能研究所）
CBF-QP safety filters are pointwise minimizers of the control effort at a given state vector, i.e., myopically optimal at each time instant. But are they optimal over the entire infinite time horizon? What does it even mean for a controlled dynamic systems to be "optimally safe" as opposed to, conventionally "optimally stable"? When disturbances, deterministic and stochastic, have unknown upper bounds, how should safety be defined to allow a graceful degradation under disturbances? Can safety filters be designed to guarantee such weaker safety properties as well as the optimality of safety ove…
Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamics
Institute for Data Science in Mechanical Engineering (DSME), RWTH Aachen University（机械工程数据科学研究所（DSME），亚琛工业大学）；Institute of Climate and Energy Systems (ICE), Energy Systems Engineering (ICE-1), Forschungszentrum Jülich GmbH（气候与能源系统研究所（ICE），能源系统工程（ICE-1），焦耳研究中心有限公司）
Distributed Risk-Sensitive Safety Filters for Uncertain Discrete-Time Systems
Department of Electrical and Computer Engineering, College of Design and Engineering, National University of Singapore（新加坡国立大学电气与计算机工程系，设计与工程学院）；Learning & Adaptive Systems Group, Department of Computer Science, ETH Zurich（苏黎世联邦理工学院计算机科学系学习与自适应系统小组）
The growing need for high-performance controllers in safety-critical applications like autonomous driving has been motivating the development of formal safety verification techniques. In this paper, we design and implement a predictive safety filter that is able to maintain vehicle safety with respect to track boundaries when paired alongside any potentially unsafe control signal, such as those found in learning-based methods. A model predictive control (MPC) framework is used to create a minimally invasive algorithm that certifies whether a desired control input is safe and can be applied to …
Secure Safety Filter: Towards Safe Flight Control under Sensor Attacks
Department of Mechanical and Civil Engineering, California Institute of Technology（加州理工学院机械与土木工程系）；Secure Systems Research Center at Technology Innovation Institute（技术创新研究所安全系统研究中心）
Run Time Assurance (RTA) Systems are online verification mechanisms that filter an unverified primary controller output to ensure system safety. The primary control may come from a human operator, an advanced control approach, or an autonomous control approach that cannot be verified to the same level as simpler control systems designs. The critical feature of RTA systems is their ability to alter unsafe control inputs explicitly to assure safety. In many cases, RTA systems can functionally be described as containing a monitor that watches the state of the system and output of a primary contro…
Department of Mechanical and Civil Engineering, Caltech（加州理工学院机械与土木工程系）；Department of Computing and Mathematical Sciences, Caltech（加州理工学院计算与数学科学系）；Department of Mechanical Engineering, Tufts University（塔夫茨大学机械工程系）
Robotic systems navigating in real-world settings require a semantic understanding of their environment to properly determine safe actions. This work aims to develop the mathematical underpinnings of such a representation -- specifically, the goal is to develop safety filters that are risk-aware. To this end, we take a two step approach: encoding an understanding of the environment via Poisson's equation, and associated risk via Laplace guidance fields. That is, we first solve a Dirichlet problem for Poisson's equation to generate a safety function that encodes system safety as its 0-superleve…
In real-world applications, we often require reliable decision making under dynamics uncertainties using noisy high-dimensional sensory data. Recently, we have seen an increasing number of learning-based control algorithms developed to address the challenge of decision making under dynamics uncertainties. These algorithms often make assumptions about the underlying unknown dynamics and, as a result, can provide safety guarantees. This is more challenging for other widely used learning-based decision making algorithms such as reinforcement learning. Furthermore, the majority of existing approac…
