Linear Systems Research Articles

Adaptive Auxiliary Loop for Output-Based Compensation of Perturbations in Linear Systems

Adaptive Auxiliary Loop for Output-Based Compensation of Perturbations in Linear Systems

SOLUTION OF THE SPECTRUM ALLOCATION PROBLEM FOR A LINEAR CONTROL SYSTEM WITH CLOSED FEEDBACK

The method for constructing a feedback matrix to solve the problem spectrum allocation (spectrum control, pole assignment) for linear dynamic system is given. A new proof of the well-known theorem about the connection between the complete controllability of a dynamic system with existence of the feedback matrix is formed in the process of construction by the cascade decomposition method. The entire set of arbitrary elements that influence the non-uniqueness of the matrix is identified. Examples of constructing a feedback matrix in the case of a real spectrum and in the presence of complex conjugate eigenvalues, as well as for the case of multiple eigenvalues, are given. The stability of the specified spectrum under small perturbations of the system parameters with a fixed feedback matrix is studied.

On an Approach to Solving the Time-Optimization Problem for Linear Discrete-Time Systems Based on Krotov Method

On an Approach to Solving the Time-Optimization Problem for Linear Discrete-Time Systems Based on Krotov Method

REGULATORS OF FINITE STABILIZATION FOR HYBRID LINEAR CONTINUOUS-DISCRETE SYSTEMS

For hybrid linear autonomous continuous-discrete systems, methods for designing two types of regulators that provide finite stabilization are proposed. The implementation of one of them, a regulators for finite stabilization by state, is based on knowledge of the values of the control system solution at discrete moments of time, multiples of the quantization step. For this purpose, an observer has been built that makes it possible to obtain the necessary solution values based on the observed output signal in real time and with zero error. The second type of regulator — the regulator of finite stabilization by output — uses the observed output signal as feedback, and its design is a modification of the finite state stabilization regulator by state by including the above observer in its circuit.

Unconditional quantum magic advantage in shallow circuit computation

Quantum theory promises computational speed-ups over classical approaches. The celebrated Gottesman-Knill Theorem implies that the full power of quantum computation resides in the specific resource of “magic” states—the secret sauce to establish universal quantum computation. However, it is still questionable whether magic indeed brings the believed quantum advantage, ridding unproven complexity assumptions or black-box oracles. In this work, we demonstrate the first unconditional magic advantage: a separation between the power of generic constant-depth or shallow quantum circuits and magic-free counterparts. For this purpose, we link the shallow circuit computation with the strongest form of quantum nonlocality—quantum pseudo-telepathy, where distant non-communicating observers generate perfectly synchronous statistics. We prove quantum magic is indispensable for such correlated statistics in a specific nonlocal game inspired by the linear binary constraint system. Then, we translate generating quantum pseudo-telepathy into computational tasks, where magic is necessary for a shallow circuit to meet the target. As a by-product, we provide an efficient algorithm to solve a general linear binary constraint system over the Pauli group, in contrast to the broad undecidability in constraint systems. We anticipate our results will enlighten the final establishment of the unconditional advantage of universal quantum computation.

High Performance Bounded Finite Time Control for Linear Systems With Input Saturation

ABSTRACTReal‐world dynamical controlled systems are often subject to input saturation due to the physical constraints of actuators. This causes the response performance of the system to be degraded. To this end, we propose a high‐performance bounded finite time control (HP‐BFTC) method based on sliding mode control for finite time tracking of linear systems with input saturation. In this method, a novel concept of rate regulation finite‐time stability is proposed to achieve better steady‐state performance. A bounded controller based on sliding mode control is proposed to achieve finite‐time stability in rate regulation, wherein a finite time approach rate based on an inverse tangent function is presented to alleviate chattering caused by sign function, and two control parameters are introduced to improve response performance. The rate regulation finite‐time stability of the system is proved in the estimated domain of attraction. In addition, a parameter tuning principle is given to enhance the response performance of the closed‐loop system in transient and steady state. The superiority of the proposed method in performance is verified by a case study.

Aerothermodynamics of a sphere in a monatomic gas based on ab initio interatomic potentials over a wide range of gas rarefaction: subsonic flows

Aerothermodynamic characteristics of a sphere in a subsonic flow are calculated over a broad range of gas rarefaction by the direct simulation Monte Carlo method based on ab initio interatomic potentials and Cercignani–Lampis surface scattering kernel. Calculations of the drag and average energy transfer coefficients are performed for various noble gases in the range of Mach number from 0.1 to 1. The obtained results point out that the influence of the interatomic potential is weak in subsonic flows. A comparison of the present results with a linear theory shows that the numerical solutions at Mach number equal to 0.1 are close to those obtained from the linearized kinetic equation in the transitional and free-molecular regimes. In the near-continuum flow regime, the difference between the present solution and the linear theory is significant. To reveal the effects of the gas–surface accommodation, a few sets of the tangential momentum and normal energy accommodation coefficients are considered in simulations. It is shown that the effect of the accommodation coefficients on the sphere drag is not trivial, and, for non-diffuse scattering, the drag coefficient can be either larger or smaller than that for diffuse scattering. The effect of the sphere temperature is also investigated and the calculated values of the average energy transfer coefficient are used to find the Stanton number, recovery factor and adiabatic surface temperature. The numerical results for the sphere drag and energy transfer are compared with the semi-empirical fitting equations known from the literature.

Long-range four-body interactions in structured nonlinear photonic waveguides

Multiphoton dynamics beyond linear optical materials are of significant fundamental and technological importance in quantum information processing. However, it remains largely unexplored in nonlinear waveguide QED. In this work, we theoretically propose a structured nonlinear waveguide in the presence of staggered photon-photon interactions, which supports two branches of gaped bands for doublons (i.e., spatially bound-photon-pair states). In contrast to linear waveguide QED systems, we identify two important contributions to its dynamical evolution, i.e., single-photon bound states (SPBSs) and doublon bound states (DBSs). Most remarkably, the nonlinear waveguide can mediate the long-range four-body interactions between two emitter pairs, even in the presence of disturbance from SPBSs. By appropriately designing system's parameters, we can achieve high-fidelity four-body Rabi oscillations mediated only by virtual doublons in DBSs. Our findings pave the way for applying structured nonlinear waveguide QED in multi-body quantum information processing and quantum simulations among remote sites. Published by the American Physical Society 2024

A Review on Data-Driven Model-Free Sliding Mode Control

Sliding mode control (SMC) has been widely used to control linear and nonlinear dynamics systems because of its robustness against parametric uncertainties and matched disturbances. Although SMC design has traditionally addressed process model-based approaches, the rapid advancements in instrumentation and control systems driven by Industry 4.0, coupled with the increased complexity of the controlled processes, have led to the growing acceptance of controllers based on data-driven techniques. This review article aims to explore the landscape of SMC, focusing specifically on data-driven techniques through a comprehensive systematic literature review that includes a bibliometric analysis of relevant documents and a cumulative production model to estimate the deceleration point of the scientific production of this topic. The most used SMC schemes and their integration with data-driven techniques and intelligent algorithms, including identifying the leading applications, are presented.

Dynamic analysis of the air–water interface instability in a wind-wave flume: Initial conditions for wave generation

This paper aims to investigate the dynamic mechanism for a previously calm water surface under a background wind field, which would lose stability due to minor perturbations. When spatial distribution and growth rate of the shear wind field satisfy a certain relationship, an Orr–Sommerfeld equation can be derived from linearized Navier–Stokes equations, for the amplitude of perturbation waves at the air–water interface. After transforming its coordinates to a finite interval, this fourth-order linear ordinary differential equation with variable coefficients can turn into a linear singular differential equation. It is solved under the background flow fields of air and water using the corrected Fourier method that we previously developed, to yield two sets of four analytical solutions with physical significance. The perturbation flow at the air–water interface must satisfy the kinematic and dynamic matching conditions (continuity of velocity and smooth transition of shear stress), which results in a fourth-order homogeneous linear algebraic equation for four undetermined constants. Setting various parameters in accordance with measured data with a wind-wave flume, the corresponding perturbation waves solution is identified. Our calculation densely distributes the most unstable and readily growing waves among perturbation waves with small phase speeds, consistent with the experimental results. Our perturbation solutions over a flat air–water interface are only applicable to the short period after instability onset, which provides an initial condition for wave generation. The consequent interaction between small-amplitude waves and wind field is beyond the scope of our linear theory, which has indeed been sufficiently addressed in the literature.

Suppression and excitation by collisions of two-stream and bump-on-tail instabilities

Two-stream (TS) and bump-on-tail (BOT) electron distributions in plasma can lead to electrostatic instabilities and turbulence, and they have been extensively studied. Collisions usually mitigate these instabilities since they tend to hinder the motion of the participating electrons. Here, we numerically solve the full Vlasov–Poisson equations with Krook collisions to reconsider the evolution of the TS and BOT instabilities. It is found that even in the stable parameter regime predicted by linear theory, during the initial evolution (i.e., damping) stage, collisions can excite the TS instability. The reason is that during the evolution, efficient Krook collisions cause rapid thermalization of the TS electrons, leading to broadening of the initial velocity distributions of the two beams and appearance of regimes with unstable velocity gradients and trapped electrons. On the contrary, such a behavior does not occur for the BOT instability.

Consensus of second-order multi-agent systems based on PIDD-like control protocol with time delay

This paper concentrates on investigating the consensus for general second-order linear multiagent systems subjected to time-varying delay. Initially, a novel PIDD-like consensus control protocol with time-varying delay is designed, which includes information on position and its integration, as well as velocity and its differentiation. Subsequently, based upon model transformation, the consensus problem is transformed into the asymptotic stability of the error system. Through constructing of a novel augmented vector Lyapunov-Krasovskii functional, including delay-product terms and multiple integral terms, and then by adopting auxiliary-function-based integral inequalities and the delay-dependent-matrix-based reciprocally convex inequality to address the derivative of the constructed functional, the less conservative consensus conditions for multi-agent systems are obtained. Additionally, numerical simulations are given to demonstrate that the presented consensus conditions not only ensure the consensus of position and velocity states but also exhibit better dynamic performance.

LMI-based discrete LPV controller design for systems with inherent couplings in the scheduling vector: Improved robustness and performance

This work presents the design of controllers for discrete-time linear parameter-varying systems, particularly in scenarios where uncontrollable regions emerge within the polytope obtained by convex rewriting of a certain bounded region. Two fundamental aspects are addressed: the stability of the system and the enhancement of the controller performance and robustness. The most significant results include the proposal of a strategy to isolate the regions that are not reached by the trajectories of the system due to inherent couplings in the scheduling vector. The resulting control law ensures asymptotic stability under specific conditions, along with improved performance and robustness against perturbations through the use of H∞ and linear matrix inequalities regions. A numerical example illustrates the applicability and performance of the proposal.

Noninvasive high-resolution deep-brain photoacoustic imaging with a negatively focused fiber-laser ultrasound transducer

Noninvasive high-resolution deep-brain imaging is essential to fundamental cognitive process study and neuroprotective drugs development. Although optical microscopes can resolve fine biological structures with good contrast without exposure to ionizing radiation or a strong magnetic field, the optical scattering limits the penetration depth and hinders its capability for deep-brain imaging. Here, in vivo high-resolution imaging of the whole mouse brain is demonstrated by using a photoacoustic computed tomography system with a negatively focused fiber-laser ultrasound transducer. By leveraging the high flexibility and low bending loss of the optical fiber, a rationally designed negatively focused fiber laser cavity exhibits a low detection limit down to 5.4 Pa and a broad view angle of ∼120 deg, enabling mouse brain imaging with a penetration larger than 7 mm and a nearly isotropic spatial resolution of ∼130 μm. In addition, the negative curvature of the fiber laser reduces the working distance, which facilitates the development of a compact and portable linear scanning imaging system. In vivo imaging of a mouse model with intracerebral hemorrhage is also showcased to demonstrate its capability for potential biomedical and clinical applications. With high spatial resolution and large tissue penetration, the system may provide a noninvasive, user-friendly, and high-performance imaging solution for biomedical research and preclinical/clinical diagnosis.

Limited Attention Allocation in a Stochastic Linear Quadratic System With Multiplicative Noise

Limited Attention Allocation in a Stochastic Linear Quadratic System With Multiplicative Noise

Admissible Observation Operators of Abstract Linear Viscoelastic Systems

Admissible Observation Operators of Abstract Linear Viscoelastic Systems

Asynchronous Stabilization of Discrete-Time Switched Linear Systems Under Dwell-Time Constraints

Asynchronous Stabilization of Discrete-Time Switched Linear Systems Under Dwell-Time Constraints

Comparison of Nondeterministic Stable Linear Systems by ($\gamma,\delta$)-Similarity

Comparison of Nondeterministic Stable Linear Systems by ($\gamma,\delta$)-Similarity

Comprehension of linear systems with two unknowns in secondary education

Comprehension of linear systems with two unknowns in secondary education

Convective Gravity Waves in the Stratosphere and the Mesosphere: A Case Study of Airglow Over West Africa Using the Weather Research and Forecasting Model

AbstractThe Weather Research and Forecasting (WRF) Model is employed to explore gravity waves excited by a storm complex over West Africa on 15 August 2020, propagating to the mesosphere and lower thermosphere. Although the simulation portrays gravity waves in the stratosphere in a complex structure, it reveals a concentric‐ring pattern of gravity waves in the mesosphere. The waves closely resemble the airglow image acquired by Suomi National Polar‐orbiting Partnership satellite near the mesopause. This intriguing phenomenon of the emergence of concentric rings after passing the stratopause is investigated by analyzing wave characteristics, including horizontal wavenumbers, frequency, and phase speed. The analysis reveals that the wind filtering effect directly influences the behavior of gravity waves, leading to variations in their appearance with altitude. The wind filtering effect, which typically breaks symmetric ring waves, could help reveal the ring pattern when the waves are subject to interference. Consequently, the concentric rings, propagating faster than the background winds, are shown to originate from the cloud tops of the storm complex. A wind duct at a specific location is identified through spectral analysis. This mechanism is further elucidated with the assistance of the dispersion relation of a classical linear theory.