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- Tsiamis, Anastasios, et al.
(author)
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Decentralized Leader-Follower Control under High Level Goals without Explicit Communication
- 2015
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In: 2015 IEEE/RSJ INTERNATIONAL CONFERENCE ON INTELLIGENT ROBOTS AND SYSTEMS (IROS). - : IEEE. - 9781479999941 ; , s. 5790-5795
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Conference paper (peer-reviewed)abstract
- In this paper, we study the decentralized control problem of a two-agent system under local goal specifications given as temporal logic formulas. The agents collaboratively carry an object in a leader-follower scheme and lack means to exchange messages on-line, i. e., to communicate explicitly. Specifically, we propose a decentralized control protocol and a leader re-election strategy that secure the accomplishment of both agents' local goal specifications. The challenge herein lies in exploiting exclusively implicit inter- robot communication that is a natural outcome of the physical interaction of the robots with the object. An illustrative experiment is included clarifying and verifying the approach.
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| 3. |
- Tsiamis, Anastasios, et al.
(author)
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Learning to Control Linear Systems can be Hard
- 2022
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In: Proceedings of 35th Conference on Learning Theory, COLT 2022. - : ML Research Press. ; , s. 3820-3857
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Conference paper (peer-reviewed)abstract
- In this paper, we study the statistical difficulty of learning to control linear systems. We focus on two standard benchmarks, the sample complexity of stabilization, and the regret of the online learning of the Linear Quadratic Regulator (LQR). Prior results state that the statistical difficulty for both benchmarks scales polynomially with the system state dimension up to system-theoretic quantities. However, this does not reveal the whole picture. By utilizing minimax lower bounds for both benchmarks, we prove that there exist nontrivial classes of systems for which learning complexity scales dramatically, i.e. exponentially, with the system dimension. This situation arises in the case of underactuated systems, i.e. systems with fewer inputs than states. Such systems are structurally difficult to control and their system theoretic quantities can scale exponentially with the system dimension dominating learning complexity. Under some additional structural assumptions (bounding systems away from uncontrollability), we provide qualitatively matching upper bounds. We prove that learning complexity can be at most exponential with the controllability index of the system, that is the degree of underactuation.
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| 4. |
- Tsiamis, Anastasios, et al.
(author)
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Statistical Learning Theory for Control : A Finite-Sample Perspective
- 2023
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In: IEEE Control Systems. - : Institute of Electrical and Electronics Engineers (IEEE). - 1066-033X .- 1941-000X. ; 43:6, s. 67-97
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Journal article (peer-reviewed)abstract
- Learning algorithms have become an integral component to modern engineering solutions. Examples range from self-driving cars and recommender systems to finance and even critical infrastructure, many of which are typically under the purview of control theory. While these algorithms have already shown tremendous promise in certain applications [1], there are considerable challenges, in particular, with respect to guaranteeing safety and gauging fundamental limits of operation. Thus, as we integrate tools from machine learning into our systems, we also require an integrated theoretical understanding of how they operate in the presence of dynamic and system-theoretic phenomena. Over the past few years, intense efforts toward this goal - an integrated theoretical understanding of learning, dynamics, and control - have been made. While much work remains to be done, a relatively clear and complete picture has begun to emerge for (fully observed) linear dynamical systems. These systems already allow for reasoning about concrete failure modes, thus helping to indicate a path forward. Moreover, while simple at a glance, these systems can be challenging to analyze. Recently, a host of methods from learning theory and high-dimensional statistics, not typically in the control-theoretic toolbox, have been introduced to our community. This tutorial survey serves as an introduction to these results for learning in the context of unknown linear dynamical systems (see 'Summary'). We review the current state of the art and emphasize which tools are needed to arrive at these results. Our focus is on characterizing the sample efficiency and fundamental limits of learning algorithms. Along the way, we also delineate a number of open problems. More concretely, this article is structured as follows. We begin by revisiting recent advances in the finite-sample analysis of system identification. Next, we discuss how these finite-sample bounds can be used downstream to give guaranteed performance for learning-based offline control. The final technical section discusses the more challenging online control setting. Finally, in light of the material discussed, we outline a number of future directions.
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| 5. |
- Ziemann, Ingvar, et al.
(author)
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A Tutorial on the Non-Asymptotic Theory of System Identification
- 2023
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In: 2023 62nd IEEE Conference on Decision and Control, CDC 2023. - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 8921-8939
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Conference paper (peer-reviewed)abstract
- This tutorial serves as an introduction to recently developed non-asymptotic methods in the theory of-mainly linear-system identification. We emphasize tools we deem particularly useful for a range of problems in this domain, such as the covering technique, the Hanson-Wright Inequality and the method of self-normalized martingales. We then employ these tools to give streamlined proofs of the performance of various least-squares based estimators for identifying the parameters in autoregressive models. We conclude by sketching out how the ideas presented herein can be extended to certain nonlinear identification problems. Note: For reasons of space, proofs have been omitted in this version and are available in an online version: https://arxiv.org/abs/2309.03873.
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