State Decomposition Research Articles

Fractal dimension and the counting rule of the Goldstone modes

Abstract It is argued that there are a set of orthonormal basis states, which appear as highly degenerate ground states arising from spontaneous symmetry breaking with a type-B Goldstone mode, and they are scale-invariant, with a salient feature that the entanglement entropy S(n) scales logarithmically with the block size n in the thermodynamic limit. As it turns out, the prefactor is half the number of type-B Goldstone modes N B . This is achieved by performing an exact Schmidt decomposition of the orthonormal basis states, thus unveiling their self-similarities in the real space—the essence of a fractal. Combining with a field-theoretic prediction (Castro-Alvaredo and Doyon 2012 Phys. Rev. Lett. 108 120401), we are led to the identification of the fractal dimension d f with the number of type-B Goldstone modes N B for the orthonormal basis states in quantum many-body systems undergoing spontaneous symmetry breaking.

Leader-following privacy-preserving consensus control of nonlinear multi-agent systems: a state decomposition approach

This paper focuses on a nonlinear multi-agent system (MAS) in the presence of unknown dynamics and eavesdroppers. An output consensus control strategy is proposed based on an extended state observer, which achieves leader-following privacy-preserving consensus in a backstepping framework. Different from existing distributed average consensus approaches that require each follower to exchange and expose state information to its neighbours, our strategy avoids the requirement for communication during information interaction by decomposing each follower's state information into two sub-states. The status information is leaked, thereby achieving privacy preservation. Furthermore, for this class of MAS with unknown dynamics, we use an extended state observer to estimate the unknown dynamics and design an auxiliary system. The auxiliary variables generated by this auxiliary system combined with the back-stepping method can effectively compensate for dynamics. By combining graph theory knowledge and techniques such as Lyapunov functions, it is proven that the output-consensus tracking error of an MAS is ultimately bounded. Finally, the effectiveness of the control strategy is verified via an example.

Ultra-broad Schmidt modes for biphoton states generated by SPDC in the chirped QPM crystals

In the realm of quantum optics, the manipulation and characterization of biphoton states hold significant importance for advancing quantum information processing and communication technologies. This study explores the Schmidt decomposition of ultra-broad biphoton states, revealing that most modes are fulfilled with the frequency response points, and certain modes exhibit exceptionally broad Schmidt spectra. These Schmidt modes in frequency domain are significantly reshaped and widened by a crystal at a moderate chirp-rate when pump bandwidth is about several Giga-Hertz.

Linear–quadratic mean-field game for stochastic systems with partial observation

This paper is concerned with a class of linear–quadratic stochastic large-population problems with partial information, where the individual agent only has access to a noisy observation process related to the state. The dynamics of each agent follows a linear stochastic differential equation driven by the individual noise, and all agents are coupled together via the control average term. By studying the associated mean-field game and using the backward separation principle with a state decomposition technique, the decentralized optimal control can be obtained in the open-loop form through a forward–backward stochastic differential equation with the conditional expectation. The optimal filtering equation is also provided. Thanks to the decoupling method, the decentralized optimal control can also be further presented as the feedback of state filtering via the Riccati equation. The explicit solution of the control average limit is given, and the consistency condition system is discussed. Moreover, the related ɛ-Nash equilibrium property is verified. To illustrate the good performance of theoretical results, an example in finance is studied.

Improved simulation of quantum circuits dominated by free fermionic operations

We present a classical algorithm for simulating universal quantum circuits composed of "free" nearest-neighbour matchgates or equivalently fermionic-linear-optical (FLO) gates, and "resourceful" non-Gaussian gates. We achieve the promotion of the efficiently simulable FLO subtheory to universal quantum computation by gadgetizing controlled phase gates with arbitrary phases employing non-Gaussian resource states. Our key contribution is the development of a novel phase-sensitive algorithm for simulating FLO circuits. This allows us to decompose the resource states arising from gadgetization into free states at the level of statevectors rather than density matrices. The runtime cost of our algorithm for estimating the Born-rule probability of a given quantum circuit scales polynomially in all circuit parameters, except for a linear dependence on the newly introduced FLO extent, which scales exponentially with the number of controlled-phase gates. More precisely, as a result of finding optimal decompositions of relevant resource states, the runtime doubles for every maximally resourceful (e.g., swap or CZ) gate added. Crucially, this cost compares very favourably with the best known prior algorithm, where each swap gate increases the simulation cost by a factor of approximately 9. For a quantum circuit containing arbitrary FLO unitaries and k controlled-Z gates, we obtain an exponential improvement O(4.5k) over the prior state-of-the-art.

Privacy protection-based resilient secondary control for DC microgrids under DoS attacks

In this paper, we investigate the privacy protection-based resilient secondary control problem for an isolated DC microgrid (MG) under denial-of-service (DoS) attacks. To solve the problem, a resilient privacy protection control method is proposed by introducing random noises and the state decomposition strategy. Specifically, the initial secondary control signal of each distributed generator (DG) includes two parts: one is utilized for neighbor communication and compensating for the voltage deviation caused by the droop control, while the other influences the evolution of the first part and remains undetected to the neighbors. Besides, to ensure that the true value of the transmitted current remains obscured, random noises are injected in the first part. Based on the developed privacy protection mechanism, a distributed resilient controller is designed to guarantee the deviations in current and voltage are effectively regulated within the permissible range under DoS attacks, while simultaneously safeguarding the privacy datas. Ultimately, the efficiency of our proposed method is proved through real-time experiments conducted in OPAL-RT 4510.

Privacy‐Preserving Optimization Algorithm for Distributed Energy Management Over Time‐Varying Graphs: A State Decomposition Method

ABSTRACTThe rapid advancements of intelligent technologies have brought about the potential vulnerability of confidential gradient information linked to cost functions when solving distributed optimization and its related problems. Within the context of distributed energy management, safeguarding such private information has risen to paramount importance. This article investigates a distributed energy management problem (DEMP) to minimize cost while simultaneously satisfying multiple local constraints and protecting the private gradient information of the cost function. To this end, a new privacy‐preserving distributed optimization algorithm under the framework of gradient tracking over time‐varying graphs is proposed for solving the DEMP. Specifically, the auxiliary variables are designed for each node in the algorithm to update the gradient while the original state variables are responsible for the interaction with original neighbors and auxiliary variables. Consequently, the devised algorithm can protect the confidentiality of private cost gradient information, even in the presence of eavesdroppers within the network. In contrast to the homomorphic encryption, signal masking method, and some other algorithms without utilizing the state decomposition, the designed algorithm does not require extra information or computing resources. Moreover, it is proven that the designed algorithm could theoretically converge to the exact optimum of the DEMP at a rate of under some mild assumptions.

Direct and indirect photodegradation mechanism of ractopamine in aquatic environment

As a kind of typical lean meat essences and veterinary drugs, ractopamine (RAC) has been frequently detected in agricultural sewage and livestock, posing potential risk to both aquatic ecosystems and human health. Despite its widespread occurrence, the environmental fate of RAC remains unclear. Here, the mechanisms underlying the direct and indirect photodegradation of RAC was investigated under UV light irradiation at wavelengths of 275 and 365 nm, respectively. The effect of pH, initial concentration, and co-existing ions were examined. For direct photodegradation, the quantum yield of RAC increased with increasing pH values. In solutions containing dissolved organic matter (DOM), indirect photodegradation of RAC intensified with increasing pH values, and the initial concentration of DOM accelerated the process. The presence of Cu2+ was found to inhibit both direct and indirect photodegradation of RAC. Electron spin resonance (ESR) spectrometry and quenching experiments revealed that direct photodegradation was primarily attributed to the decomposition of the triplet state of RAC. Both the triplet state of DOM (3DOM*) and singlet oxygen contributed to the indirect photodegradation of RAC. LC-MS/MS analysis indicated that oxidation of the phenol group and subsequent decarboxylation were the principal photodegradation processes. The energies of each state of RAC and the active sites of RAC molecules were computed using frontier molecular orbitals and Fukui indices based on density functional theory. Combining the analysis of photoproducts with energy calculation, pathways of the direct and indirect photodegradation of RAC were proposed. These findings unveiled the photochemical behaviors of RAC concerning the removal and attenuation in aquatic environment.

Reachable set control of singular semi-Markov jump multi-agent systems with input delay via state decomposition method

This paper addresses the challenge of reachable set estimation in singular multi-agent systems with time-delay and semi-Markov switching topologies. The primary goal is to construct an ellipsoid that encompasses all states originating from the origin. Furthermore, criteria for reachable sets with reduced conservatism are developed. The singular multi-agent systems are reduced by the Laplace matrix, then the Lyapunov–Krasovskii functional is constructed by using decomposed state vector. In addition, the sufficient conditions for the reachable set of singular multi-agent systems bounded by ellipsoids are given by matrix theory and linear matrix inequality. Numerical examples show that our results is effective.

Disturbance rejection for switched singular systems using state decomposition technique and equivalent-input-disturbance with a dynamic state observer

In this study, an equivalent-input-disturbance (EID) method with a dynamic state observer and a state decomposition technique (SDT) are used to explore the disturbance rejection of a class of linear switched singular systems. The EID approach defines an EID signal, is defined for the control input channel and has the same impact on the system as exogenous disturbances. Additionally, it employs an observer to estimate the EID and achieves good disturbance-rejection performance. However, in the EID method, the coefficient matrix of the observer needs to be consistent with the coefficient matrix of the original system, which limits the application of the method. So, a dynamic state observer is designed to reconstruct the system state and estimate the disturbance in this study. Based on the state feedback control strategy, a disturbance-rejection control law containing disturbance information is designed and a closed-loop control system structure is established. Subsequently, the state equation of the closed-loop system is reorganized and decomposed into an algebraic equation and a differential equation using the SDT. Then, a Lyapunov function with few decision variables is designed to obtain an admissible criterion for the closed-loop system and the controller gains under arbitrary switching signals. Finally, the effectiveness of the presented method is verified via numerical simulations.

Optimized deep learning modelling for predicting the diffusion range and state change of filling projects

Concealment of filling constructions poses significant challenges for quality assurance in filling engineering. Direct surveillance of fill dispersal currently remains infeasible, while conventional detection techniques suffer deficiencies in efficiency. This research proposes a framework integrating elastic wave monitoring and hybrid deep learning for predictive modelling of filling state transitions and diffusion range. During the sand filling of the immersed tunnel, elastic wave data is collected via elastic wave testing, and the response energy characteristic is derived through time-domain analysis. The trends in elastic wave response energy are correlated with three filling states: free diffusion, accumulation, and filled state, using Seasonal and Trend decomposition using Loess (STL) for seasonal trend analysis. Convolutional Neural Networks (CNN) and Long Short-Term Memory Networks (LSTM) are utilized to extract spatiotemporal features from the response energy trends, facilitating accurate prediction of the trends’ development and the sand filling state over time. The performances of the proposed strategy are illustrated through an application to the case study of the sand filling construction of the Chebeilu immersed tunnel. The CNN + LSTM model with the proposed strategy gave excellent results (MAE 0.0663, MSE 0.0071, RMSE 0.0845). The model can predict fill state changes and quantify diffusion radii to optimize and guide the construction process.

Distributed state estimation of networked systems based on state decomposition

Distributed state estimation of networked systems based on state decomposition

Estimation of real‐time reachable set on nonlinear time‐delay switched singular systems with state jump

AbstractThis article addresses the real‐time reachable set problem on nonlinear time‐delay switched singular systems with state jump, which is subject to initial state and peak‐bound disturbance. Initially, based on the system state decomposition method, a state jump lemma is proposed, which combines the nonlinear function and the system state at the switching instant. Then, a real‐time bounded lemma is developed, premised on using the idea of average dwell‐time and analyzing subinterval function changes. Afterwards, the sufficient conditions for estimating the real‐time and nonreal‐time reachable set are established, which ensures that the reachable state of system can be restricted within a real‐time or nonreal‐time closed set. Finally, simulation results of the typical Direct Current boost chopper are performed to exhibit the effectiveness of the devised estimation scheme for the real‐time reachable set of system.

Disturbance rejection analysis of singular time-delay systems based on state decomposition method

The state decomposition technique (SDT) based on memory state-feedback control (MSFC) is used in this article to provide a new disturbance-rejection (DR) method for singular time-delay systems (STSs). First, under MSFC, a singular time-delay control system with disturbance estimator is constructed. Then, a DR control law, which contains disturbance information and MSFC, is designed. Second, the STS is split into algebraic and differential subsystems based on the SDT. Next, a brand-new enhanced Lyapunov–Krasovskii function (LKF) with fewer state vectors is designed. Additionally, a new delay-dependent admissible criterion with fewer decision variables is obtained based on the LKF by combining a Jensen inequality and two zero equations. Third, the controller is designed according to the decomposition component of the controller gain. Finally, the usefulness and efficiency of the strategy are demonstrated by comparing it to a sliding mode control and a traditional control technique.

Adaptive dynamic‐surface repetitive control for uncertain nonlinear systems with mismatched disturbances and input delay

AbstractBased on additive state decomposition technique, this article presents an adaptive dynamic‐surface repetitive control method for a class of uncertain nonlinear systems with mismatched disturbances and input delay. First, the original uncertain nonlinear system is decomposed into a linear time invariant (LTI) primary system responsible for the periodic signal tracing and rejection task, and a nonlinear secondary system with input time delay responsible for the robust stabilization task. A modified repetitive controller with a small correction to the delay constant is then independently designed for the LTI primary system, while an adaptive dynamic surface controller is designed for the nonlinear secondary system. Stability analysis is performed for each subsystem and the design procedure of the whole system is presented in detail. Finally, comparative simulations with other repetitive control and dynamic surface control methods show that the presented method not only relaxes the constraints on the reference inputs and exogenous disturbances, but also ensures that the system has better disturbance rejection and periodic‐signal tracking performance in both transient and steady states. As a result, this method broadens the application of both repetitive control and dynamic surface control.

A new inequality and its application in descriptor Markovian jump systems with time-varying delays

This paper is focused on the dissipativity analysis of descriptor Markovian jump systems with time-varying delays. For achieving this aim, an augmented mode-dependent Lyapunov-Krasovskii functional (LKF) is constructed on the basis of the state decomposition method. Next, a novel integral inequality is proposed through the generalized free-weighting-matrix (GFWM) method as well as zero-valued equalities to estimate single integral terms more precisely. Then, an ameliorative stochastic admissibility and dissipative criterion is derived by utilizing the proposed integral inequality, the augmented LKF and other bounding techniques. Finally, the effectiveness and superiority of the presented results are confirmed with some numerical examples.

Sufficient Condition for Universal Quantum Computation Using Bosonic Circuits

Continuous-variable bosonic systems stand as prominent candidates for implementing quantum computational tasks. While various necessary criteria have been established to assess their resourcefulness, sufficient conditions have remained elusive. We address this gap by focusing on promoting circuits that are otherwise simulatable to computational universality. The class of simulatable, albeit non-Gaussian, circuits that we consider is composed of Gottesman-Kitaev-Preskill (GKP) states, Gaussian operations, and homodyne measurements. Based on these circuits, we first introduce a general framework for mapping a continuous-variable state into a qubit state. Subsequently, we cast existing maps into this framework, including the modular and stabilizer subsystem decompositions. By combining these findings with established results for discrete-variable systems, we formulate a sufficient condition for achieving universal quantum computation. Leveraging this, we evaluate the computational resourcefulness of a variety of states, including Gaussian states, finite-squeezing GKP states, and cat states. Furthermore, our framework reveals that both the stabilizer subsystem decomposition and the modular subsystem decomposition (of position-symmetric states) can be constructed in terms of simulatable operations. This establishes a robust resource-theoretical foundation for employing these techniques to evaluate the logical content of a generic continuous-variable state, which can be of independent interest. Published by the American Physical Society 2024

Privacy-Preserving Distributed Economic Dispatch for Microgrids Based on State Decomposition With Added Noises

Privacy-Preserving Distributed Economic Dispatch for Microgrids Based on State Decomposition With Added Noises

Privacy-Preserving Consensus-Based Distributed Economic Dispatch of Smart Grids via State Decomposition

Privacy-Preserving Consensus-Based Distributed Economic Dispatch of Smart Grids via State Decomposition

A new [formula omitted] control method of singular time-delay systems based on a variable memory state feedback

This paper is concerned with the H∞ control problem of singular time-delay systems. A variable memory state feedback is established with state decomposition. It is verified that this feedback including the traditional memory and memoryless state feedbacks as special cases, and thus it is more general than these existing feedback strategies Based on the proposed feedback, a new H∞ control method with better performance level is derived. Moreover, the yielded computational complexity is lower. The superiority is confirmed by two given examples.