We consider a problem where multiple agents participate in solving a quadratic optimization problem subject to linear inequality constraints in a privacy-preserving manner. Several variables of the objective function as well as the constraints are privacy-sensitive and are known to different agents. We propose a privacy-preserving protocol based on partially homomorphic encryption where each agent encrypts its own information before sending it to an untrusted cloud computing infrastructure. To find the optimal solution the cloud applies a gradient descent algorithm on the encrypted data without the ability to decrypt it. The privacy of the proposed protocol against coalitions of colluding agents is analyzed using the cryptography notion of zero knowledge proofs.
We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented, and their accuracy is shown to depend on the underlying system 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-approximative reachable set containing the true reachable set. Multiple numerical examples show the applicability of the introduced algorithms, and accuracy comparisons are made between algorithms.
is demo abstract presents PrOLoc, a localization system that combines partially homomorphic encryption with a new way of structuring the localization problem to enable e cient and accurate computation of a target's location while preserving the privacy of the observers.
The tight coupling of information technology with physical sensing and actuation in cyber-physical systems (CPS) has given rise to new security vulnerabilities and attacks with potentially life-threatening consequences. These attacks are designed to transfer the physical system into unstable and insecure states by providing corrupted sensor readings. In this work, we present an approach for distributed secure linear state estimation in the presence of modeling and measurement noise between a network of nodes with pairwise measurements. We provide security against measurement attacks and simplify the traditional distributed secure state estimation problem. Reachability analysis is utilized to establish a security layer providing secure estimate shares for the distributed diffusion Kalman filter. Furthermore, we consider not only attacks on the link level but also on the sensor level. The proposed combined filter protects against measurement and diffusion attacks without requiring specialized hardware or cryptographic techniques. The effectiveness of the approach is demonstrated by a localization example of a rotating target.
We present a robust data-driven control scheme for unknown linear systems with a bounded process and measurement noise. Instead of depending on a system model as in traditional predictive control, a controller utilizing datadriven 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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