Optimal Controller and Security Parameter for Encrypted Control Systems Under Least Squares Identification

Encrypted control is a framework for the secure outsourcing of controller computation using homomorphic encryption that allows to perform arithmetic operations on encrypted data without decryption. In a previous study, the security level of encrypted control systems was quantified based on the difficulty and computation time of system identification. This study investigates an optimal design of encrypted control systems when facing an attack attempting to estimate a system parameter by the least squares method from the perspective of the security level. This study proposes an optimal $H_2$ controller that maximizes the difficulty of estimation and an equation to determine the minimum security parameter that guarantee the security of an encrypted control system as a solution to the design problem. The proposed controller and security parameter are beneficial for reducing the computation costs of an encrypted control system, while achieving the desired security level. Furthermore, the proposed design method enables the systematic design of encrypted control systems.Comment: 6 pages, 1 figur

Multiple concurrent recursive least squares identification with application to on-line spacecraft mass-property identification

The present invention is a method for identifying unknown parameters in a system having a set of governing equations describing its behavior that cannot be put into regression form with the unknown parameters linearly represented. In this method, the vector of unknown parameters is segmented into a plurality of groups where each individual group of unknown parameters may be isolated linearly by manipulation of said equations. Multiple concurrent and independent recursive least squares identification of each said group run, treating other unknown parameters appearing in their regression equation as if they were known perfectly, with said values provided by recursive least squares estimation from the other groups, thereby enabling the use of fast, compact, efficient linear algorithms to solve problems that would otherwise require nonlinear solution approaches. This invention is presented with application to identification of mass and thruster properties for a thruster-controlled spacecraft

Robust adaptive regulation without persistent excitation

A globally convergent adaptive regulator for minimum or nonminimum phase systems subject to bounded distrubances and unmodeled dynamics is presented. The control strategy is designed for a particular input-output representation obtained from the state space representation of the system. The leading coefficient of the new representation is the product of the observability and controllability matrices of the system. The controller scheme uses a Least Squares identification algorithm with a dead zone. The dead zone is chosen to obtain convergence properties on the estimates and on the covariance matrix as well. This allows the definition of modified estimates which secure well-conditioned matrices in the adaptive control law. Explicit bounds on the plant output are given

Detection and evaluation of events in EEG dynamics in post-surgery patients with physiological-based mathematical models

As part of the new directions for vision and mission of Europe, patient well-being and healthcare become core features of a modern and prosperous society. That is, healthcare costs are optimized towards patient benefit and sideways effects such as cost-related reduction in medication, in frequency of post-operatory interventions, in recovery times and in comorbidity risk. In this paper, we address the incidence of events related to stroke, epileptic seizures and tools to possibly predict their presence from Electroencephalography (EEG) signal acquired in post-surgery patients. Wavelet analysis and spectrogram indicate graphically changes in the energy content of the EEG signal. Physiologically based neuronal dynamic pathway is used to derive fractional order impedance models. Nonlinear least squares identification technique is used to identify model parameters, with results suggesting parameter redundancy. There is a significant difference in model parameter values between EEG signal with/-out events

Integrated adaptive filtering and design for control experiments of flexible structures

A novel method is presented of identifying a state space model and a state estimator for linear stochastic systems from input and output data. The method is primarily based on the relations between the state space model and the finite difference model for linear stochastic systems derived through projection filters. It is proven that least squares identification of a finite difference model converges to the model derived from the projection filters. System pulse response samples are computed from the coefficients of the finite difference model. In estimating the corresponding state estimator gain, a z-domain method is used. First the deterministic component of the output is subtracted out, and then the state estimator gain is obtained by whitening the remaining signal. Experimental example is used to illustrate the feasibility of the method

Regularised Volterra series models for modelling of nonlinear self-excited forces on bridge decks

Volterra series models are considered an attractive approach for modelling nonlinear aerodynamic forces for bridge decks since they extend the convolution integral to higher dimensions. Optimal identification of nonlinear systems is a challenging task since there are typically many unknown variables that need to be determined, and it is vital to avoid overfitting. Several methods exist for identifying Volterra kernels from experimental data, but a large class of them put restrictions on the system inputs, making them infeasible for section model tests of bridge decks. A least-squares identification method does not restrict the inputs, but the identified model often struggles with noisy (non-smooth) kernels, which is deemed to be unphysical and a sign of overfitting. In this work, regularised least-squares identification is introduced to improve the performance of model identification using least-squares. Standard Tikhonov regularisation and other penalty techniques that impose decaying kernels are also explored. The performance of the methodology is studied using experimental data from wind tunnel tests of a twin deck section. The regularised Volterra models show equal or better results in terms of modelling the self-excited forces, and the regularisation makes the models less prone to overfitting

Decomposition-based recursive least squares identification methods for multivariate pseudo-linear systems using the multi-innovation

© 2018 Informa UK Limited, trading as Taylor & Francis Group. This paper studies the parameter estimation algorithms of multivariate pseudo-linear autoregressive systems. A decomposition-based recursive generalised least squares algorithm is deduced for estimating the system parameters by decomposing the multivariate pseudo-linear autoregressive system into two subsystems. In order to further improve the parameter accuracy, a decomposition based multi-innovation recursive generalised least squares algorithm is developed by means of the multi-innovation theory. The simulation results confirm that these two algorithms are effective

A note on the smallest eigenvalue of the empirical covariance of causal Gaussian processes

We present a simple proof for bounding the smallest eigenvalue of the empirical covariance in a causal Gaussian process. Along the way, we establish a one-sided tail inequality for Gaussian quadratic forms using a causal decomposition. Our proof only uses elementary facts about the Gaussian distribution and the union bound. We conclude with an example in which we provide a performance guarantee for least squares identification of a vector autoregression

Use of Modal Representation for the Supporting Structure in Model Based Fault Identification of Large Rotating Machinery: Part 1 – Theoretical Remarks

Fault identification by means of model-based techniques, both in frequency and time domain, is often employed in diagnostics of rotating machines, when the main task is to locate and to evaluate the severity of the malfunction. The model of the fully assembled machine is composed by the submodels of the rotor, of the bearings and of the foundation, while the effect of the faults is modelled by means of equivalent force systems. Some identification techniques, such as the least squares identification in frequency domain, proposed by the authors, have proven to be quite robust even if the submodels are not fine-tuned. Anyhow, the use of a reliable model can increase the accuracy of the identification. Normally a supporting structure is represented by means of rigid foundation or by pedestals, i.e. 2 d.o.f. mass–spring–damper systems, but these kind of models are often not able to reproduce correctly the influence of the dynamical behaviour of the supporting structure on the shaft, especially in large machines where coupled modes are present. Therefore, peculiar aspect of this paper is the use of a modal foundation to model the supporting structure of the machine and the method is discussed in detail in this first part. The modal representation of the foundation is then introduced in the least squares identification technique in frequency domain

Partial least squares identification of multi look-up table digital predistorters for concurrent dual-band envelope tracking power amplifiers

©208 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper presents a technique to estimate the coefficients of a multiple-look-up table (LUT) digital predistortion (DPD) architecture based on the partial least-squares (PLS) regression method. The proposed 3-D distributed memory LUT architecture is suitable for efficient FPGA implementation and compensates for the distortion arising in concurrent dual-band envelope tracking power amplifiers. On the one hand, a new variant of the orthogonal matching pursuit algorithm is proposed to properly select only the best LUTs of the DPD function in the forward path, and thus reduce the number of required coefficients. On the other hand, the PLS regression method is proposed to address both the regularization problem of the coefficient estimation and, at the same time, reducing the number of coefficients to be estimated in the DPD feedback identification path. Moreover, by exploiting the orthogonality of the PLS transformed matrix, the computational complexity of the parameters' identification can be significantly simplified. Experimental results will prove how it is possible to reduce the DPD complexity (i.e., the number of coefficients) in both the forward and feedback paths while meeting the targeted linearity levels.Peer ReviewedPostprint (author's final draft