Parameter Privacy versus Control Performance: Fisher Information Regularized Control

Ziemann, Ingvar

doi:10.23919/acc45564.2020.9147690

Cited by 12 publications

(10 citation statements)

References 13 publications

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“…Remark 4: We have introduced the expectation of a lower bound of Λ−1 because the computation of the inverse of Λ, in general, requires a large number of computation resources, and it cannot be computed in advance of the control system's operation. A similar approach can be found in [40]- [43], and the studies employed the inverse of a trace of the Fisher information matrix as a lower bound of the precision of general unbiased estimator for dynamical systems. Unfortunately, the approach is not specialized in our attack scenario, i.e., it would give a loose lower bound of tr( Λ−1 ), and the lower bound cannot be computed without the system's operating data.…”

Section: A Sample Identifying-complexity Curvementioning

confidence: 99%

Designing Optimal Key Lengths and Control Laws for Encrypted Control Systems based on Sample Identifying Complexity and Deciphering Time

Teranishi¹,

Sadamoto²,

Chakrabortty³

et al. 2021

Preprint

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In the state-of-the-art literature on cryptography and control theory, there has been no systematic methodology of constructing cyber-physical systems that can achieve desired control performance while being protected against eavesdropping attacks. In this paper, we tackle this challenging problem. We first propose two novel notions referred to as sample identifying complexity and sample deciphering time in an encrypted-control framework. The former explicitly captures the relation between the dynamical characteristics of control systems and the level of identifiability of the systems while the latter shows the relation between the computation time for the identification and the key length of a cryptosystem. Based on these two tractable new notions, we propose a systematic method for designing the both of an optimal key length to prevent system identification with a given precision within a given life span of systems, and of an optimal controller to maximize both of the control performance and the difficulty of the identification. The efficiency of the proposed method in terms of security level and realtime-ness is investigated through numerical simulations. To the best of our knowledge, this paper first connect the relationship between the security of cryptography and dynamical systems from a control-theoretic perspective.

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Section: A Sample Identifying-complexity Curvementioning

confidence: 99%

Designing Optimal Key Lengths and Control Laws for Encrypted Control Systems based on Sample Identifying Complexity and Deciphering Time

Teranishi¹,

Sadamoto²,

Chakrabortty³

et al. 2021

Preprint

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“…The statistical parameter privacy problem has been studied in [21] and [22]. Bassi et al in [21] studied the statistical parameter privacy of an independent and identically distributed (i.i.d.…”

Section: B Related Workmentioning

confidence: 99%

“…They characterized the leakage level of private information under the Bayes statistical risk as the privacy measure. The authors in [22] studied the optimal design of controller and privacy filter for a linear Gaussian plant. The system dynamics should be kept private from an adversary interested in inferring the system dynamics based on the state measurements and control inputs.…”

Section: B Related Workmentioning

confidence: 99%

“…In our set-up, the sensor measurements are processed by a nonlinear transformation, rather than a stochastic kernel, which ensures that the distribution of the output of privacy filter belongs to the same family of distributions as the measurements. This requirement is not guaranteed by the frameworks in [21] and [22] since stochastic kernels significantly alter the distribution of the measurements.…”

Section: Contributionsmentioning

confidence: 99%

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A Model Randomization Approach to Statistical Parameter Privacy

Nekouei¹,

Skoglund²,

Johansson³

2021

Preprint

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In this paper, we study a privacy filter design problem for a sequence of sensor measurements whose joint probability density function (p.d.f.) depends on a private parameter. To ensure parameter privacy, we propose a filter design framework which consists of two components: a randomizer and a nonlinear transformation. The randomizer takes the private parameter as input and randomly generates a pseudo parameter. The nonlinear mapping transforms the measurements such that the joint p.d.f. of the filter's output depends on the pseudo parameter rather than the private parameter. It also ensures that the joint p.d.f. of the filter's output belongs to the same family of distributions as that of the measurements. The nonlinear transformation has a feedforward-feedback structure that allows real-time and causal generation of the disguised measurements with low complexity using a recursive structure.The design of the randomizer is formulated as an optimization problem subject to a privacy constraint, in terms of mutual information, and it is shown that the optimal randomizer is the solution of a convex optimization problem. Using information-theoretic inequalities, we show that the performance of any estimator of the private parameter, based on the output of the privacy filter, is limited by the privacy constraint. The structure of the nonlinear transformation is studied in the special cases of independent and identically distributed, Markovian, and Gauss-Markov measurements. Our results show that the privacy filter in the Gauss-Markov case can be implemented as two one-step ahead Kalman predictors and a set of minimum mean square error predictors. The Kalman predictors significantly reduce the complexity of computing the disguised measurements. A numerical example on occupancy privacy in a building automation system illustrates the approach.

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“…• On a more technical note, our SDP characterization of the distribution optimizing the trace of inverse Fisher information may also be of independent interest, as this quantity also plays a key role in certain privacypreserving mechanisms, e.g. in [16], [17], [18]. By contrast, previous results were only able to characterize this distribution for scalar random variables, [10], or considered relaxed problems [16].…”

Section: Introductionmentioning

confidence: 99%

Resource Constrained Sensor Attacks by Minimizing Fisher Information

Ziemann

2021

2021 American Control Conference (ACC)

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We analyze the impact of sensor attacks on a linear state estimation problem subject to variance and sparsity constraints. We show that the maximum impact in a leaderfollower game where the attacker first chooses the distribution of an adversarial perturbation and the defender follows by choosing an estimator is characterized by a minimum Fisher information principle. In general, this is a nonlinear variational problem, but we show that it can be reduced to a finitedimensional mixed integer SDP.

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Parameter Privacy versus Control Performance: Fisher Information Regularized Control

Cited by 12 publications

References 13 publications

Designing Optimal Key Lengths and Control Laws for Encrypted Control Systems based on Sample Identifying Complexity and Deciphering Time

Designing Optimal Key Lengths and Control Laws for Encrypted Control Systems based on Sample Identifying Complexity and Deciphering Time

A Model Randomization Approach to Statistical Parameter Privacy

Resource Constrained Sensor Attacks by Minimizing Fisher Information

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