arXiv subjects

V. Ugrinovskii

Publications and source records attributed to V. Ugrinovskii.

At least 19 recordsLinked to original sources

arXiv2024

Coherent Equalization of Linear Quantum Systems

This paper introduces a $H_\infty$-like methodology of coherent filtering for equalization of passive linear quantum systems to help mitigate degrading effects of quantum communication channels. For such systems, which include a wide range of linear quantum optical devices and signals, we seek to find a near optimal equalizing filter which is itself a passive quantum system. The problem amounts to solving an optimization problem subject to constraints dictated by the requirement for the equalizer to be physically realizable. By formulating these constraints in the frequency domain, we show that the problem admits a convex $H_\infty$-like formulation. This allows us to derive a set of suboptimal coherent equalizers using $J$-spectral factorization. An additional semidefinite relaxation combined with the Nevanlinna-Pick interpolation is shown to lead to a tractable algorithm for the design of a near optimal coherent equalizer.

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arXiv2024

Design of Coherent Passive Quantum Equalizers Using Robust Control Theory

The paper develops a methodology for the design of coherent equalizing filters for quantum communication channels. Given a linear quantum system model of a quantum communication channel, the aim is to obtain another quantum system which, when coupled with the original system, mitigates degrading effects of the environment. The main result of the paper is a systematic equalizer synthesis algorithm which relies on methods of state-space robust control design via semidefinite programming.

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arXiv2023

A Robust Control Approach to Asymptotic Optimality of the Heavy Ball Method for Optimization of Quadratic Functions

Among first order optimization methods, Polyak's heavy ball method has long been known to guarantee the asymptotic rate of convergence matching Nesterov's lower bound for functions defined in an infinite-dimensional space. In this paper, we use results on the robust gain margin of linear uncertain feedback control systems to show that the heavy ball method is provably worst-case asymptotically optimal when applied to quadratic functions in a finite dimensional space.

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arXiv2019

Active versus Passive Coherent Equalization of Passive Linear Quantum Systems

The paper considers the problem of equalization of passive linear quantum systems. While our previous work was concerned with the analysis and synthesis of passive equalizers, in this paper we analyze coherent quantum equalizers whose annihilation (respectively, creation) operator dynamics in the Heisenberg picture are driven by both quadratures of the channel output field. We show that the characteristics of the input field must be taken into consideration when choosing the type of the equalizing filter. In particular, we show that for thermal fields allowing the filter to process both quadratures of the channel output may not improve mean square accuracy of the input field estimate, in comparison with passive filters. This situation changes when the input field is `squeezed'.

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arXiv2019

Planar Cooperative Extremum Seeking with Guaranteed Convergence Using A Three-Robot Formation

In this paper, a combined formation acquisition and cooperative extremum seeking control scheme is proposed for a team of three robots moving on a plane. The extremum seeking task is to find the maximizer of an unknown two-dimensional function on the plane. The function represents the signal strength field due to a source located at maximizer, and is assumed to be locally concave around maximizer and monotonically decreasing in distance to the source location. Taylor expansions of the field function at the location of a particular lead robot and the maximizer are used together with a gradient estimator based on signal strength measurements of the robots to design and analyze the proposed control scheme. The proposed scheme is proven to exponentially and simultaneously (i) acquire the specified geometric formation and (ii) drive the lead robot to a specified neighborhood disk around maximizer, whose radius depends on the specified desired formation size as well as the norm bounds of the Hessian of the field function. The performance of the proposed control scheme is evaluated using a set of simulation experiments.

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arXiv2019

Wiener Filtering for Passive Linear Quantum Systems

This paper considers a version of the Wiener filtering problem for equalization of passive quantum linear quantum systems. We demonstrate that taking into consideration the quantum nature of the signals involved leads to features typically not encountered in classical equalization problems. Most significantly, finding a mean-square optimal quantum equalizing filter amounts to solving a nonconvex constrained optimization problem. We discuss two approaches to solving this problem, both involving a relaxation of the constraint. In both cases, unlike classical equalization, there is a threshold on the variance of the noise below which an improvement of the mean-square error cannot be guaranteed.

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arXiv2018

Resilient Distributed $H_\infty$ Estimation via Dynamic Rejection of Biasing Attacks

We consider the distributed $H_\infty$ estimation problem with 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. Using a dynamic modelling of biasing attack inputs, a novel distributed state estimation algorithm is proposed which involves feedback from a network of attack detection filters. We show that each observer in the network can be computed in real time and in a decentralized fashion. When these controlled observers are interconnected to form a network, they are shown to cooperatively produce an unbiased estimate the plant, despite some of the nodes are compromised.

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arXiv2017

Robust Detection of Biasing Attacks on Misappropriated Distributed Observers via Decentralized $H_\infty$ synthesis

We develop a decentralized $H_\infty$ synthesis approach to detection of biasing misappropriation attacks on distributed observers. Its starting point is to equip the observer with an attack model which is then used in the design of attack detectors. A two-step design procedure is proposed. First, an initial centralized setup is carried out which enables each node to compute the parameters of its attack detector online in a decentralized manner, without interacting with other nodes. Each such detector is designed using the $H_\infty$ approach. Next, the attack detectors are embedded into the network, which allows them to detect misappropriated nodes from innovation in the network interconnections.

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arXiv2017

Pole Placement Approach to Coherent Passive Reservoir Engineering for Storing Quantum Information

Reservoir engineering is the term used in quantum control and information technologies to describe manipulating the environment within which an open quantum system operates. Reservoir engineering is essential in applications where storing quantum information is required. From the control theory perspective, a quantum system is capable of storing quantum information if it possesses a so-called decoherence free subsystem (DFS). This paper explores pole placement techniques to facilitate synthesis of decoherence free subsystems via coherent quantum feedback control. We discuss limitations of the conventional `open loop' approach and propose a constructive feedback design methodology for decoherence free subsystem engineering. It captures a quite general dynamic coherent feedback structure which allows systems with decoherence free modes to be synthesized from components which do not have such modes.

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arXiv2017

Controller-jammer game models of Denial of Service in control systems operating over packet-dropping links

The paper introduces a class of zero-sum games between the adversary and controller as a scenario for a `denial of service' in a networked control system. The communication link is modeled as a set of transmission regimes controlled by a strategic jammer whose intention is to wage an attack on the plant by choosing a most damaging regime-switching strategy. We demonstrate that even in the one-step case, the introduced games admit a saddle-point equilibrium, at which the jammer's optimal policy is to randomize in a region of the plant's state space, thus requiring the controller to undertake a nontrivial response which is different from what one would expect in a standard stochastic control problem over a packet dropping link. The paper derives conditions for the introduced games to have such a saddle-point equilibrium. Furthermore, we show that in more general multi-stage games, these conditions provide `greedy' jamming strategies for the adversary.

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arXiv2016

Quantum state transfer through time reversal of an optical channel

Rare earth ions have exceptionally long coherence times, making them an excellent candidate for quantum information processing. A key part of this processing is quantum state transfer. We show that perfect state transfer can be achieved by time reversing the intermediate quantum channel, and suggest using a gradient echo memory (GEM) to perform this time reversal. We propose an experiment with rare earth ions to verify these predictions, where an emitter and receiver crystal are connected with an optical channel passed through a GEM. We investigate the affect experimental imperfections and collective dynamics have on the state transfer process. We demonstrate superrandiant effects can enhance coupling into the optical channel and improve the transfer fidelity. We lastly discuss how our results apply to state transfer of entangled states.

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arXiv2016

Cooperative Robust Estimation with Local Performance Guarantees

The paper considers the problem of cooperative estimation for a linear uncertain plant observed by a network of communicating sensors. We take a novel approach by treating the filtering problem from the view point of local sensors while the network interconnections are accounted for via an uncertain signals modelling of estimation performance of other nodes. That is, the information communicated between the nodes is treated as the true plant information subject to perturbations, and each node is endowed with certain believes about these perturbations during the filter design. The proposed distributed filter achieves a suboptimal $H_\infty$ consensus performance. Furthermore, local performance of each estimator is also assessed given additional constraints on the performance of the other nodes. These conditions are shown to be useful in tuning the desired estimation performance of the sensor network.

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arXiv2016

Event-triggered leader-following tracking control for multivariable multi-agent systems

The paper considers event-triggered leader-follower tracking control for multi-agent systems with general linear dynamics. For both undirected and directed follower graphs, we propose event triggering rules which guarantee bounded tracking errors. With these rules, we also prove that the systems do not exhibit Zeno behavior, and the bounds on the tracking errors can be tuned to a desired small value. We also show that the combinational state required for the proposed event triggering conditions can be continuously generated from discrete communications between the neighboring agents occurring at event times. The efficacy of the proposed methods is discussed using a simulation example.

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arXiv2015

Distributed robust estimation over randomly switching networks using $H_\infty$ consensus

The paper considers a distributed robust estimation problem over a network with Markovian randomly varying topology. The objective is to deal with network variations locally, by switching observer gains at affected nodes only. We propose sufficient conditions which guarantee a suboptimal $H_\infty$ level of relative disagreement of estimates in such observer networks. When the status of the network is known globally, these sufficient conditions enable the network gains to be computed by solving certain LMIs. When the nodes are to rely on a locally available information about the network topology, additional rank constraints are used to condition the gains, given this information. The results are complemented by necessary conditions which relate properties of the interconnection graph Laplacian to the mean-square detectability of the plant through measurement and interconnection channels.

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arXiv2015

Leader-follower Tracking Control with Guaranteed Consensus Performance for Interconnected Systems with Linear Dynamic Uncertain Coupling

This paper considers the leader-follower tracking control problem for linear interconnected systems with undirected topology and linear dynamic coupling. Interactions between the systems are treated as linear dynamic uncertainty and are described in terms of integral quadratic constraints (IQCs). A consensus-type tracking control protocol is proposed for each system based on its state relative its neighbors. In addition a selected set of subsystems uses for control their relative states with respect to the leader. Two methods are proposed for the design of this control protocol. One method uses a coordinate transformation to recast the protocol design problem as a decentralized robust control problem for an auxiliary interconnected large scale system. Another method is direct, it does not employ coordinate transformation; it also allows for more general linear uncertain interactions. Using these methods, sufficient conditions are obtained which guarantee that the system tracks the leader. These conditions guarantee a suboptimal bound on the system consensus and tracking performance. The proposed methods are compared using a simulation example, and their effectiveness is discussed. Also, algorithms are proposed for computing suboptimal controllers.

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arXiv2015

Gain-scheduled Leader-follower Tracking Control for Interconnected Parameter Varying Systems

This paper considers the gain-scheduled leader-follower tracking control problem for a parameter varying complex interconnected system with directed communication topology and uncertain norm-bounded coupling between the agents. A gain-scheduled consensus-type control protocol is proposed and a sufficient condition is obtained which guarantees a suboptimal bound on the system tracking performance under this protocol. An interpolation technique is used to obtain a protocol schedule which is continuous in the scheduling parameter. The effectiveness of the proposed method is demonstrated using a simulation example.

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arXiv2014

Detectability of distributed consensus-based observer networks: An elementary analysis and extensions

This paper continues the study of local detectability and observability requirements on components of distributed observers networks to ensure detectability properties of the network. First, we present a sketch of an elementary proof of the known result equating the multiplicity of the zero eigenvalue of the Laplace matrix of a digraph to the number of its maximal reachable subgraphs. Unlike the existing algebraic proof, we use a direct analysis of the graph topology. This result is then used in the second part of the paper to extend our previous results which connect the detectability of an observer network with corresponding local detectability and observability properties of its node observers. The proposed extension allows for nonidentical matrices to be used in the interconnections.

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arXiv2014

Gain-scheduled synchronization of parameter varying systems via relative $H_\infty$ consensus with application to synchronization of uncertain bilinear systems

The paper considers a problem of consensus-based synchronization of uncertain parameter varying multi-agent systems. We present a method for constructing consensus-based synchronization protocol schedules for each agent to ensure it synchronizes with a reference parameter-varying system. The proposed protocol guarantees a specified level of $H_\infty$ transient consensus between the agents. The algorithm uses a consensus-preserving interpolation and produces continuous (in the scheduling parameter) coefficients for the protocol. An application to synchronization of uncertain bilinear systems is discussed.

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