Local lipschitzness of reachability maps for hybrid systems with applications to safety

Motivated by the safety problem, several definitions of reachability maps, for hybrid dynamical systems, are introduced. It is well established that, under certain conditions, the solutions to continuous-time systems depend continuously with respect to initial conditions. In such setting, the reachability maps considered in this paper are locally Lipschitz (in the Lipschitz sense for set-valued maps) when the right-hand side of the continuous-time system is locally Lipschitz. However, guaranteeing similar properties for reachability maps for hybrid systems is much more challenging. Examples of hybrid systems for which the reachability maps do not depend nicely with respect to their arguments, in the Lipschitz sense, are introduced. With such pathological cases properly identified, sufficient conditions involving the data defining a hybrid system assuring Lipschitzness of the reachability maps are formulated. As an application, the proposed conditions are shown to be useful to significantly improve an existing converse theorem for safety given in terms of barrier functions. Namely, for a class of safe hybrid systems, we show that safety is equivalent to the existence of a locally Lipschitz barrier function. Examples throughout the paper illustrate the results

Nonsmooth Control Barrier Function design of continuous constraints for network connectivity maintenance

This paper considers the problem of maintaining global connectivity of a multi-robot system while executing a desired coordination task. Our approach builds on optimization-based feedback design formulations, where the nominal cost function and constraints encode desirable control objectives for the resulting input. We take advantage of the flexibility provided by control barrier functions to produce additional constraints that guarantee that the resulting optimization-based controller is continuous and maintains network connectivity. Our solution uses the algebraic connectivity of the multi-robot interconnection topology as a control barrier function and critically embraces its nonsmooth nature. The technical treatment combines elements from set-valued theory, nonsmooth analysis, and algebraic graph theory to imbue the proposed constraints with regularity properties so that they can be smoothly combined with other control constraints. We provide simulations and experimental results illustrating the effectiveness and continuity of the proposed approach in a resource gathering problem.Comment: submitted to Automatic

Unified Framework for the Propagation of Continuous-Time Enclosures for Parametric Nonlinear ODEs

Abstract This paper presents a framework for constructing and analyzing enclosures of the reachable set of nonlinear ordinary differential equations (ODEs) using continuous-time setpropagation methods. The focus is on convex enclosures that can be characterized in terms of their support functions. A generalized differential inequality is introduced, whose solutions describe such support functions for a convex enclosure of the reachable set under mild conditions. It is shown that existing continuous-time bounding methods that are based on standard differential inequalities or ellipsoidal set propagation techniques can be recovered as special cases of this generalized differential inequality. A way of extending this approach for the construction of nonconvex enclosures is also described, which relies on Taylor models with convex remainder bounds. This unifying framework provides a means for analyzing the convergence properties of continuous-time enclosure methods. The enclosure techniques and convergence results are illustrated with numerical case studies throughout the paper, including a six-state dynamic model of anaerobic digestion

Advancements in Adversarially-Resilient Consensus and Safety-Critical Control for Multi-Agent Networks

The capabilities of and demand for complex autonomous multi-agent systems, including networks of unmanned aerial vehicles and mobile robots, are rapidly increasing in both research and industry settings. As the size and complexity of these systems increase, dealing with faults and failures becomes a crucial element that must be accounted for when performing control design. In addition, the last decade has witnessed an ever-accelerating proliferation of adversarial attacks on cyber-physical systems across the globe. In response to these challenges, recent years have seen an increased focus on resilience of multi-agent systems to faults and adversarial attacks. Broadly speaking, resilience refers to the ability of a system to accomplish control or performance objectives despite the presence of faults or attacks. Ensuring the resilience of cyber-physical systems is an interdisciplinary endeavor that can be tackled using a variety of methodologies. This dissertation approaches the resilience of such systems from a control-theoretic viewpoint and presents several novel advancements in resilient control methodologies. First, advancements in resilient consensus techniques are presented that allow normally-behaving agents to achieve state agreement in the presence of adversarial misinformation. Second, graph theoretic tools for constructing and analyzing the resilience of multi-agent networks are derived. Third, a method for resilient broadcasting vector-valued information from a set of leaders to a set of followers in the presence of adversarial misinformation is presented, and these results are applied to the problem of propagating entire knowledge of time-varying Bezier-curve-based trajectories from leaders to followers. Finally, novel results are presented for guaranteeing safety preservation of heterogeneous control-affine multi-agent systems with sampled-data dynamics in the presence of adversarial agents.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168102/1/usevitch_1.pd

Learning for autonomy in the wild : theory, algorithms, and practice

How can autonomous systems learn to operate in the wild, i.e., complex, dynamic, and uncertain real-world environments? Despite recent and significant breakthroughs in artificial intelligence, there is still a tremendous gap between its current capabilities and what we need to do to develop systems that can autonomously operate in the wild. We aim to bridge this gap by addressing a few key challenges of learning in the wild. These challenges include learning with extremely scarce amounts of data, learning safely from a single and ongoing trial, learning to generalize to unseen situations, and learning with uncertainty-aware and explainability considerations for trustworthy human-robot interactions. We take an opinionated approach to address these challenges and argue that data are never the only source of knowledge available during training, and modern learning techniques should not treat them as such. Instead, we demonstrate that merging modern learning techniques' efficiency at extracting patterns from data with existing knowledge on how the world works is key for autonomous systems to achieve learning in the wild. This existing knowledge on how the world works may stem from structural knowledge such as fundamental principles of physics, qualitative expert knowledge such as design or mechanical constraints, or contextual knowledge such as formal specifications on the underlying task. Thus, by leveraging prior knowledge into learning through formal techniques, we propose data-driven modeling and control approaches that enable autonomous systems to operate even under severely limited amounts of data, such as streaming data from a single and ongoing trial. We additionally demonstrate that the data-driven approaches generalize beyond the training regime, improve explainability over traditional black-box models, and exhibit principled uncertainty awareness. Specifically, we focus on theoretical analyses that quantify the benefits of exploiting prior knowledge as inductive bias in terms of data efficiency, safety, computational requirements, and optimality of learning. We derive these theoretical analyses through novel ideas at the intersection of control, learning, and formal methods. Based on the theoretical insights, we develop practical and computationally efficient algorithms, some of which have provable performance, real-time, and safety guarantees. To validate the effectiveness of our algorithms, we conduct experiments in high-fidelity robotics and flight simulators, as well as on real-world hardware such as a Toyota Supra car and a custom-built hexacopter. Remarkably, when applied in real-world settings, our algorithms provide high performance for control tasks that push the system beyond the limits of the prior knowledge and data coverage, despite being trained on only a handful of system trajectories or a few minutes worth of data.Electrical and Computer Engineerin

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Local lipschitzness of reachability maps for hybrid systems with applications to safety

Motivated by the safety problem, several definitions of reachability maps, for hybrid dynamical systems, are introduced. It is well established that, under certain conditions, the solutions to continuous-time systems depend continuously with respect to initial conditions. In such setting, the reachability maps considered in this paper are locally Lipschitz (in the Lipschitz sense for set-valued maps) when the right-hand side of the continuous-time system is locally Lipschitz. However, guaranteeing similar properties for reachability maps for hybrid systems is much more challenging. Examples of hybrid systems for which the reachability maps do not depend nicely with respect to their arguments, in the Lipschitz sense, are introduced. With such pathological cases properly identified, sufficient conditions involving the data defining a hybrid system assuring Lipschitzness of the reachability maps are formulated. As an application, the proposed conditions are shown to be useful to significantly improve an existing converse theorem for safety given in terms of barrier functions. Namely, for a class of safe hybrid systems, we show that safety is equivalent to the existence of a locally Lipschitz barrier function. Examples throughout the paper illustrate the results