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  1. We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets. Moreover, by considering such representations in the space of states and finite input sequences we obtain closed-form expressions for controlled invariant sets. An immediate advantage is the ability to handle high-dimensional systems since the closed-form expression is computed in a single step rather than iteratively. To validate the proposed method, we present thorough case studies illustrating that in safety-critical scenarios the implicit representation suffices in place of the explicit invariant set. The proposed method is complete in the absence of disturbances, and we provide a weak completeness result when disturbances are present. 
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  2. In recent years, LiDAR sensors have become pervasive in the solutions to localization tasks for autonomous systems. One key step in using LiDAR data for localization is the alignment of two LiDAR scans taken from different poses, a process called scan-matching or point cloud registration. Most existing algorithms for this problem are heuristic in nature and local, meaning they may not produce accurate results under poor initialization. Moreover, existing methods give no guarantee on the quality of their output, which can be detrimental for safety-critical tasks. In this paper, we analyze a simple algorithm for point cloud registration, termed PASTA. This algorithm is global and does not rely on point-to-point correspondences, which are typically absent in LiDAR data. Moreover, and to the best of our knowledge, we offer the first point cloud registration algorithm with provable error bounds. Finally, we illustrate the proposed algorithm and error bounds in simulation on a simple trajectory tracking task. 
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  3. Abstract

    Runtime monitoring is commonly used to detect the violation of desired properties in safety critical cyber-physical systems by observing its executions. Bauer et al. introduced an influential framework for monitoring Linear Temporal Logic (LTL) properties based on a three-valued semantics for a finite execution: the formula is already satisfied by the given execution, it is already violated, or it is still undetermined, i.e., it can still be satisfied and violated by appropriate extensions of the given execution. However, a wide range of formulas are not monitorable under this approach, meaning that there are executions for which satisfaction and violation will always remain undetermined no matter how it is extended. In particular, Bauer et al. report that 44% of the formulas they consider in their experiments fall into this category. Recently, a robust semantics for LTL was introduced to capture different degrees by which a property can be violated. In this paper we introduce a robust semantics for finite strings and show its potential in monitoring: every formula considered by Bauer et al. is monitorable under our approach. Furthermore, we discuss which properties that come naturally in LTL monitoring—such as the realizability of all truth values—can be transferred to the robust setting. We show that LTL formulas with robust semantics can be monitored by deterministic automata, and provide tight bounds on the size of the constructed automaton. Lastly, we report on a prototype implementation and compare it to the LTL monitor of Bauer et al. on a sample of examples.

     
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  4. In this paper, we revisit the problem of learning a stabilizing controller from a finite number of demonstrations by an expert. By focusing on feedback linearizable systems, we show how to combine expert demonstrations into a stabilizing controller, provided that demonstrations are sufficiently long and there are at least n+1 of them, where n is the number of states of the system being controlled. The results are experimentally demonstrated on a CrazyFlie 2.0 quadrotor. 
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  5. We study the decentralized resilient state-tracking problem in which each node in a network has the objective of tracking the state of a linear dynamical system based on its local measurements and information exchanged with its neighboring nodes, despite an attack on some of the nodes. We propose a novel algorithm that solves the decentralized resilient state-tracking problem by relating it to the dynamic average consensus problem. Compared with existing solutions in the literature, our algorithm provides a solution for the most general class of decentralized resilient state-tracking problem instances. 
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  6. It was shown, in recent work by the authors, that it is possible to learn an asymptotically stabilizing controller from a small number of demonstrations performed by an expert on a feedback linearizable system. These results rely on knowledge of the plant dynamics to assemble the learned controller from the demonstrations. In this paper we show how to leverage recent results on data-driven control to dispense with the need to use the plant model. By bringing these two methodologies — learning from demonstrations and data-driven control — together, this paper provides a technique that enables the control of unknown nonlinear feedback linearizable systems solely based on a small number of expert demonstrations. 
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  7. This paper addresses the problem of decentralized learning in the presence of data poisoning attacks. In this problem, we consider a collection of nodes connected through a network, each equipped with a local function. The objective is to compute the global minimizer of the aggregated local functions, in a decentralized manner, i.e., each node can only use its local function and data exchanged with nodes it is connected to. Moreover, each node is to agree on the said minimizer despite an adversary that can arbitrarily change the local functions of a fraction of the nodes. This problem setting has applications in robust learning, where nodes in a network are collectively training a model that minimizes the empirical loss with possibly attacked local data sets. In this paper, we propose a novel decentralized learning algorithm that enables all nodes to reach consensus on the optimal model, in the absence of attacks, and approximate consensus in the presence of data poisoning attacks. 
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  8. In this paper, we derive closed-form expressions for implicit controlled invariant sets for discrete-time controllable linear systems with measurable disturbances. In particular, a disturbance-reactive (or disturbance feedback) controller in the form of a parameterized finite automaton is considered. We show that, for a class of automata, the robust positively invariant sets of the corresponding closed-loop systems can be expressed by a set of linear inequality constraints in the joint space of system states and controller parameters. This leads to an implicit representation of the invariant set in a lifted space. We further show how the same parameterization can be used to compute invariant sets when the disturbance is not available for measurement. 
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