arXiv subjects

Valery Ugrinovskii

Publications and source records attributed to Valery Ugrinovskii.

At least 19 recordsLinked to original sources

arXiv2026

A two-disk approach to the synthesis of coherent passive equalizers for linear quantum systems

The coherent equalization problem consists in designing a quantum system acting as a mean-square near-optimal filter for a given quantum communication channel. The paper develops an improved method for the synthesis of transfer functions for such equalizing filters, based on a linear quantum system model of the channel. The method draws on a connection with the two-disk problem of ${H}_{\infty}$ control for classical (i.e., non-quantum) linear uncertain systems. Compared with the previous methods, the proposed method applies to a broader class of linear quantum communication channels.

quant-ph↗

arXiv2025

Simultaneous estimations of quantum state and detector through multiple quantum processes

The estimation of all the parameters in an unknown quantum state or measurement device, commonly known as quantum state tomography (QST) and quantum detector tomography (QDT), is crucial for comprehensively characterizing and controlling quantum systems. In this paper, we introduce a framework, in two different bases, that utilizes multiple quantum processes to simultaneously identify a quantum state and a detector. We develop a closed-form algorithm for this purpose and prove that the mean squared error (MSE) scales as $O(1/N) $ for both QST and QDT, where $N $ denotes the total number of state copies. This scaling aligns with established patterns observed in previous works that addressed QST and QDT as independent tasks. Furthermore, we formulate the problem as a sum of squares (SOS) optimization problem with semialgebraic constraints, where the physical constraints of the state and detector are characterized by polynomial equalities and inequalities. The effectiveness of our proposed methods is validated through numerical examples.

quant-ph↗

arXiv2024

An online optimization algorithm for tracking a linearly varying optimal point with zero steady-state error

In this paper, we develop an online optimization algorithm for solving a class of nonconvex optimization problems with a linearly varying optimal point. The global convergence of the algorithm is guaranteed using the circle criterion for the class of functions whose gradient is bounded within a sector. Also, we show that the corresponding Luré-type nonlinear system involves a double integrator, which demonstrates its ability to track a linearly varying optimal point with zero steady-state error. The algorithm is applied to solving a time-of-arrival based localization problem with constant velocity and the results show that the algorithm is able to estimate the source location with zero steady-state error.

math.OC↗

arXiv2022

Global convergence and asymptotic optimality of the heavy ball method for a class of non-convex optimization problems

In this letter we revisit the famous heavy ball method and study its global convergence for a class of non-convex problems with sector-bounded gradient. We characterize the parameters that render the method globally convergent and yield the best $R$-convergence factor. We show that for this family of functions, this convergence factor is superior to the factor obtained from the triple momentum method.

math.OC↗

arXiv2022

Continuous-Time Channel Gain Control for Minimum-Information Kalman-Bucy Filtering

We consider the problem of estimating a continuous-time Gauss-Markov source process observed through a vector Gaussian channel with an adjustable channel gain matrix. For a given (generally time-varying) channel gain matrix, we provide formulas to compute (i) the mean-square estimation error attainable by the classical Kalman-Bucy filter, and (ii) the mutual information between the source process and its Kalman-Bucy estimate. We then formulate a novel "optimal channel gain control problem" where the objective is to control the channel gain matrix strategically to minimize the weighted sum of these two performance metrics. To develop insights into the optimal solution, we first consider the problem of controlling a time-varying channel gain over a finite time interval. A necessary optimality condition is derived based on Pontryagin's minimum principle. For a scalar system, we show that the optimal channel gain is a piece-wise constant signal with at most two switches. We also consider the problem of designing the optimal time-invariant gain to minimize the average cost over an infinite time horizon. A novel semidefinite programming (SDP) heuristic is proposed and the exactness of the solution is discussed.

cs.IT↗

arXiv2019

Distributed $H_\infty$ Estimation Resilient to Biasing Attacks

We consider the distributed $H_\infty$ estimation problem with an additional requirement of resilience to biasing attacks. An attack scenario is considered where an adversary misappropriates some of the observer nodes and injects biasing signals into observer dynamics. The paper proposes a procedure for the derivation of a distributed observer which endows each node with an attack detector which also functions as an attack compensating feedback controller for the main observer. Connecting these controlled observers into a network results in a distributed observer whose nodes produce unbiased robust estimates of the plant. We show that the gains for each controlled observer in the network can be computed in a decentralized fashion, thus reducing vulnerability of the network.

eess.SY↗

arXiv2018

Detection and Mitigation of Biasing Attacks on Distributed Estimation Networks

The paper considers a problem of detecting and mitigating biasing attacks on networks of state observers targeting cooperative state estimation algorithms. The problem is cast within the recently developed framework of distributed estimation utilizing the vector dissipativity approach. The paper shows that a network of distributed observers can be endowed with an additional attack detection layer capable of detecting biasing attacks and correcting their effect on estimates produced by the network. An example is provided to illustrate the performance of the proposed distributed attack detector.

eess.SY↗

arXiv2018

A Systems Theory Approach to the Synthesis of Minimum Noise Phase-Insensitive Quantum Amplifiers

We present a systems theory approach to the proof of a result bounding the required level of added quantum noise in a phase-insensitive quantum amplifier. We also present a synthesis procedure for constructing a quantum optical phase-insensitive quantum amplifier which adds the minimum level of quantum noise and achieves a required gain and bandwidth. This synthesis procedure is based on a singularly perturbed quantum system and leads to an amplifier involving two squeezers and two beamsplitters.

eess.SY↗

arXiv2017

Modelling and Filtering for Non-Markovian Quantum Systems

This paper presents an augmented Markovian system model for non-Markovian quantum systems. In this augmented system model, ancillary systems are introduced to play the role of internal modes of the non-Markovian environment converting white noise to colored noise. Consequently, non-Markovian dynamics are represented as resulting from direct interaction of the principal system with the ancillary system. To demonstrate the utility of the proposed augmented system model, it is applied to design whitening quantum filters for non-Markovian quantum systems. Examples are presented to illustrate how whitening quantum filters can be utilized for estimating non-Markovian linear quantum systems and qubit systems. In particular, we showed that the augmented Markovian formulation can be used to theoretically model the environment for an observed non-Markovian behavior in a recent experiment on quantum dots [ Phys. Rev. Lett., 108:046807, 2012]

quant-ph↗

arXiv2016

Detection of Biasing Attacks on Distributed Estimation Networks

The paper addresses the problem of detecting attacks on distributed estimator networks that aim to intentionally bias process estimates produced by the network. It provides a sufficient condition, in terms of the feasibility of certain linear matrix inequalities, which guarantees distributed input attack detection using an $H_\infty$ approach.

eess.SY↗

arXiv2016

LQG feedback control of a class of linear non-Markovian quantum systems

In this paper we present a linear quadratic Gaussian (LQG) feedback control strategy for a class of linear non-Markovian quantum systems. The feedback control law is designed based on the estimated states of a whitening quantum filter for an augmented Markovian model of the non-Markovian open quantum systems. In this augmented Markovian model, an ancillary system plays the role of internal modes of the environment converting white noise into Lorentzian noise and a principal system obeys non-Markovian dynamics due to the direct interaction with the ancillary system. The simulation results show the LQG controller with the whitening filter obtains a better control performance than that with a Markovian filter in the problem of minimizing the photon numbers of the principal system when the ancillary system is disturbed by thermal noise.

quant-ph↗

arXiv2016

Quantum filter for a class of non-Markovian quantum systems

In this paper we present a Markovian representation approach to constructing quantum filters for a class of non-Markovian quantum systems disturbed by Lorenztian noise. An ancillary system is introduced to convert white noise into Lorentzian noise which is injected into a principal system via a direct interaction. The resulting dynamics of the principal system are non-Markovian, which are driven by the Lorentzian noise. By probing the principal system, a quantum filter for the augmented system can be derived from standard theory, where the conditional state of the principal system can be obtained by tracing out the ancillary system. An example is provided to illustrate the non-Markovian dynamics of the principal system.

quant-ph↗

arXiv2015

Cooperative Estimation for Synchronization of Heterogeneous Multi-Agent Systems Using Relative Information

In this paper, we present a distributed estimation setup where local agents estimate their states from relative measurements received from their neighbours. In the case of heterogeneous multi-agent systems, where only relative measurements are available, this is of high relevance. The objective is to improve the scalability of the existing distributed estimation algorithms by restricting the agents to estimating only their local states and those of immediate neighbours. The presented estimation algorithm also guarantees robust performance against model and measurement disturbances. It is shown that it can be integrated into output synchronization algorithms.

eess.SY↗

arXiv2015

Ground-state Stabilization of Open Quantum Systems by Dissipation

Control by dissipation, or environment engineering, constitutes an important methodology within quantum coherent control which was proposed to improve the robustness and scalability of quantum control systems. The system-environment coupling, often considered to be detrimental to quantum coherence, also provides the means to steer the system to desired states. This paper aims to develop the theory for engineering of the dissipation, based on a ground-state Lyapunov stability analysis of open quantum systems via a Heisenberg-picture approach. Algebraic conditions concerning the ground-state stability and scalability of quantum systems are obtained. In particular, Lyapunov stability conditions expressed as operator inequalities allow a purely algebraic treatment of the environment engineering problem, which facilitates the integration of quantum components into a large-scale quantum system and draws an explicit connection to the classical theory of vector Lyapunov functions and decomposition-aggregation methods for control of complex systems. The implications of the results in relation to dissipative quantum computing and state engineering are also discussed in this paper.

math-ph↗

arXiv2015

Interpolation Approach to Hamiltonian-varying Quantum Systems and the Adiabatic Theorem

Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure could be taken as the error of adiabatic approximation. We prove under certain conditions, this error can be precisely estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example on which the applicability of the adiabatic theorem is questionable.

math-ph↗

arXiv2015

Distributed Filter Design for Cooperative H-Infinity-Type Estimation

In this paper, we consider the distributed robust filtering problem, where estimator design is based on a set of coupled linear matrix inequalities (LMIs). We separate the problem and show that the method of multipliers can be applied to obtain a solution efficiently and in a decentralized fashion, i.e. all local estimators can compute their filter gains locally and iteratively, with communications restricted to their neighbours. The convergence properties of the iterative algorithm are analyzed and interpreted.

eess.SY↗

arXiv2015

Quantum filter for a non-Markovian single qubit system

In this paper, a quantum filter for estimating the states of a non-Markovian qubit system is presented in an augmented Markovian system framework including both the qubit system of interest and multi-ancillary systems for representing the internal modes of the non-Markovian environment. The colored noise generated by the multi-ancillary systems disturbs the qubit system via a direct interaction. The resulting non-Markovian dynamics of the qubit is determined by a memory kernel function arising from the dynamics of the ancillary system. In principle, colored noise with arbitrary power spectrum can be generated by a combination of Lorentzian noises. Hence, the quantum filter can be constructed for the qubit disturbed by arbitrary colored noise and the conditional state of the qubit system can be obtained by tracing out the multi-ancillary systems. An illustrative example is given to show the non-Markovian dynamics of the qubit system with Lorentzian noise.

quant-ph↗

arXiv2015

Cooperative H-infinity Estimation for Large-Scale Interconnected Linear Systems

In this paper, a synthesis method for distributed estimation is presented, which is suitable for dealing with large-scale interconnected linear systems with disturbance. The main feature of the proposed method is that local estimators only estimate a reduced set of state variables and their complexity does not increase with the size of the system. Nevertheless, the local estimators are able to deal with lack of local detectability. Moreover, the estimators guarantee H-infinity-performance of the estimates with respect to model and measurement disturbances.

eess.SY↗