| 1. |
- Alanwar, Amr, et al.
(författare)
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Data-Driven Reachability Analysis From Noisy Data
- 2023
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Ingår i: IEEE Transactions on Automatic Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523. ; 68:5, s. 3054-3069
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing over-approximated reachable sets based on matrix zonotopes is proposed for linear systems. Constrained matrix zonotopes are introduced to provide less conservative reachable sets at the cost of increased computational expenses and utilized to incorporate prior knowledge about the unknown system model. Then we extend the approach to polynomial systems and, under the assumption of Lipschitz continuity, to nonlinear systems. Theoretical guarantees are given for these algorithms in that they give a proper over-approximate reachable set containing the true reachable set. Multiple numerical examples and real experiments show the applicability of the introduced algorithms, and comparisons are made between algorithms.
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| 2. |
- Alanwar, Amr, et al.
(författare)
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Data-Driven Reachability Analysis Using Matrix Zonotopes
- 2021
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Ingår i: Proceedings of the 3rd Conference on Learning for Dynamics and Control, L4DC 2021. - : ML Research Press. ; , s. 163-175
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Konferensbidrag (refereegranskat)abstract
- In this paper, we propose a data-driven reachability analysis approach for unknown system dynamics. Reachability analysis is an essential tool for guaranteeing safety properties. However, most current reachability analysis heavily relies on the existence of a suitable system model, which is often not directly available in practice. We instead propose a data-driven reachability analysis approach from noisy data. More specifically, we first provide an algorithm for over-approximating the reachable set of a linear time-invariant system using matrix zonotopes. Then we introduce an extension for Lipschitz nonlinear systems. We provide theoretical guarantees in both cases. Numerical examples show the potential and applicability of the introduced methods.
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| 3. |
- Alanwar, Amr, et al.
(författare)
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Data-driven Set-based Estimation of Polynomial Systems with Application to SIR Epidemics
- 2022
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Ingår i: 2022 European Control Conference (ECC). - : IEEE. ; , s. 888-893
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Konferensbidrag (refereegranskat)abstract
- This paper proposes a data-driven set-based estimation algorithm for a class of nonlinear systems with polynomial nonlinearities. Using the system's input-output data, the proposed method computes a set that guarantees the inclusion of the system's state in real-time. Although the system is assumed to be a polynomial type, the exact polynomial functions, and their coefficients are assumed to be unknown. To this end, the estimator relies on offline and online phases. The offline phase utilizes past input-output data to estimate a set of possible coefficients of the polynomial system. Then, using this estimated set of coefficients and the side information about the system, the online phase provides a set estimate of the state. Finally, the proposed methodology is evaluated through its application on SIR (Susceptible, Infected, Recovered) epidemic model.
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| 4. |
- Alanwar, Amr, et al.
(författare)
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Data-Driven Set-Based Estimation using Matrix Zonotopes with Set Containment Guarantees
- 2022
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Ingår i: 2022 EUROPEAN CONTROL CONFERENCE (ECC). - : IEEE. ; , s. 875-881
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Konferensbidrag (refereegranskat)abstract
- We propose a method to perform set-based state estimation of an unknown dynamical linear system using a data-driven set propagation function. Our method comes with set-containment guarantees, making it applicable to safety-critical systems. The method consists of two phases: (1) an offline learning phase where we collect noisy input-output data to determine a function to propagate the state-set ahead in time; and (2) an online estimation phase consisting of a time update and a measurement update. It is assumed that known finite sets bound measurement noise and disturbances, but we assume no knowledge of their statistical properties. These sets are described using zonotopes, allowing efficient propagation and intersection operations. We propose a new approach to compute a set of models consistent with the data and noise-bound, given input-output data in the offline phase. The set of models is utilized in replacing the unknown dynamics in the data-driven set propagation function in the online phase. Then, we propose two approaches to perform the measurement update. Simulations show that the proposed estimator yields state sets comparable in volume to the 3 sigma confidence bounds obtained by a Kalman filter approach, but with the addition of state set-containment guarantees. We observe that using constrained zonotopes yields smaller sets but with higher computational costs than unconstrained ones.
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| 5. |
- Alanwar, Amr, et al.
(författare)
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Distributed set-based observers using diffusion strategies
- 2023
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Ingår i: Journal of the Franklin Institute. - : Elsevier BV. - 0016-0032 .- 1879-2693. ; 360:10, s. 6976-6993
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Tidskriftsartikel (refereegranskat)abstract
- We propose two distributed set-based observers using strip-based and set-propagation approaches for linear discrete-time dynamical systems with bounded modeling and measurement uncertainties. Both algorithms utilize a set-based diffusion step, which decreases the estimation errors and the size of estimated sets, and can be seen as a lightweight approach to achieve partial consensus between the distributed estimated sets. Every node shares its measurement with its neighbor in the measurement update step. In the diffusion step, the neighbors intersect their estimated sets using our novel lightweight zonotope intersection technique. A localization example demonstrates the applicability of our algorithms.
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| 6. |
- Alanwar, Amr, et al.
(författare)
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Enhancing Data-Driven Reachability Analysis using Temporal Logic Side Information
- 2022
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Ingår i: Proceedings. - : Institute of Electrical and Electronics Engineers Inc..
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This paper presents algorithms for performingdata-driven reachability analysis under temporal logic sideinformation. In certain scenarios, the data-driven reachablesets of a robot can be prohibitively conservative due to theinherent noise in the robot’s historical measurement data. Inthe same scenarios, we often have side information about therobot’s expected motion (e.g., limits on how much a robotcan move in a one-time step) that could be useful for furtherspecifying the reachability analysis. In this work, we showthat if we can model this side information using a signaltemporal logic (STL) fragment, we can constrain the datadriven reachability analysis and safely limit the conservatismof the computed reachable sets. Moreover, we provide formalguarantees that, even after incorporating side information, thecomputed reachable sets still properly over-approximate therobot’s future states. Lastly, we empirically validate the practicality of the over-approximation by computing constrained,data-driven reachable sets for the Small-Vehicles-for-Autonomy(SVEA) hardware platform in two driving scenarios.
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| 7. |
- Alanwar, Amr, et al.
(författare)
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Logical Zonotopes : A Set Representation for the Formal Verification of Boolean Functions
- 2023
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Ingår i: 2023 62nd IEEE Conference on Decision and Control, CDC 2023. - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 60-66
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Konferensbidrag (refereegranskat)abstract
- A logical zonotope, which is a new set representation for binary vectors, is introduced in this paper. A logical zonotope is constructed by XORing a binary vector with a combination of other binary vectors called generators. Such a zonotope can represent up to 2γ binary vectors using only γ generators. It is shown that logical operations over sets of binary vectors can be performed on the zonotopes' generators and, thus, significantly reduce the computational complexity of various logical operations (e.g., XOR, NAND, AND, OR, and semi-tensor products). Similar to traditional zonotopes' role in the formal verification of dynamical systems over real vector spaces, logical zonotopes can efficiently analyze discrete dynamical systems defined over binary vector spaces. We illustrate the approach and its ability to reduce the computational complexity in two use cases: (1) encryption key discovery of a linear feedback shift register and (2) safety verification of a road traffic intersection protocol.
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| 8. |
- Alanwar, Amr, et al.
(författare)
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Privacy-preserving set-based estimation using partially homomorphic encryption
- 2023
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Ingår i: European Journal of Control. - : Elsevier BV. - 0947-3580 .- 1435-5671. ; 71, s. 100786-
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Tidskriftsartikel (refereegranskat)abstract
- The set-based estimation has gained a lot of attention due to its ability to guarantee state enclosures for safety-critical systems. However, collecting measurements from distributed sensors often requires out-sourcing the set-based operations to an aggregator node, raising many privacy concerns. To address this problem, we present set-based estimation protocols using partially homomorphic encryption that pre-serve the privacy of the measurements and sets bounding the estimates. We consider a linear discrete-time dynamical system with bounded modeling and measurement uncertainties. Sets are represented by zonotopes and constrained zonotopes as they can compactly represent high-dimensional sets and are closed under linear maps and Minkowski addition. By selectively encrypting parameters of the set repre-sentations, we establish the notion of encrypted sets and intersect sets in the encrypted domain, which enables guaranteed state estimation while ensuring privacy. In particular, we show that our protocols achieve computational privacy using the cryptographic notion of computational indistinguishability. We demonstrate the efficiency of our approach by localizing a real mobile quadcopter using ultra-wideband wireless devices.
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| 9. |
- Alanwar, Amr, et al.
(författare)
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Robust data-driven predictive control using reachability analysis
- 2022
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Ingår i: European Journal of Control. - : Elsevier BV. - 0947-3580 .- 1435-5671. ; 68
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Tidskriftsartikel (refereegranskat)abstract
- We present a robust data-driven control scheme for an unknown linear system model with bounded process and measurement noise. Instead of depending on a system model in traditional predictive con-trol, a controller utilizing data-driven reachable regions is proposed. The data-driven reachable regions are based on a matrix zonotope recursion and are computed based on only noisy input-output data of a trajectory of the system. We assume that measurement and process noise are contained in bounded sets. While we assume knowledge of these bounds, no knowledge about the statistical properties of the noise is assumed. In the noise-free case, we prove that the presented purely data-driven control scheme results in an equivalent closed-loop behavior to a nominal model predictive control scheme. In the case of measurement and process noise, our proposed scheme guarantees robust constraint satisfaction, which is essential in safety-critical applications. Numerical experiments show the effectiveness of the proposed data-driven controller in comparison to model-based control schemes.
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| 10. |
- Dawoud, Mohammed M., et al.
(författare)
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Differentially Private Set-Based Estimation Using Zonotopes
- 2023
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Ingår i: 2023 European Control Conference, ECC 2023. - : Institute of Electrical and Electronics Engineers (IEEE).
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Konferensbidrag (refereegranskat)abstract
- For large-scale cyber-physical systems, the collaboration of spatially distributed sensors is often needed to perform the state estimation process. Privacy concerns naturally arise from disclosing sensitive measurement signals to a cloud estimator that predicts the system state. To solve this issue, we propose a differentially private set-based estimation protocol that preserves the privacy of the measurement signals. Compared to existing research, our approach achieves less privacy loss and utility loss using a numerically optimized truncated noise distribution. The proposed estimator is perturbed by weaker noise than the analytical approaches in the literature to guarantee the same level of privacy, therefore improving the estimation utility. Numerical and comparison experiments with truncated Laplace noise are presented to support our approach. Zonotopes, a less conservative form of set representation, are used to represent estimation sets, giving set operations a computational advantage. The privacy-preserving noise anonymizes the centers of these estimated zonotopes, concealing the precise positions of the estimated zonotopes.
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