Showing papers on "Upper and lower bounds published in 2021"

Data-Driven Model Predictive Control With Stability and Robustness Guarantees

Abstract: We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input–output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multistep fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme.

Linearized two-layers neural networks in high dimension

Abstract: We consider the problem of learning an unknown function f⋆ on the d-dimensional sphere with respect to the square loss, given i.i.d. samples {(yi,xi)}i≤n where xi is a feature vector uniformly distributed on the sphere and yi=f⋆(xi)+ei. We study two popular classes of models that can be regarded as linearizations of two-layers neural networks around a random initialization: the random features model of Rahimi–Recht (RF); the neural tangent model of Jacot–Gabriel–Hongler (NT). Both these models can also be regarded as randomized approximations of kernel ridge regression (with respect to different kernels), and enjoy universal approximation properties when the number of neurons N diverges, for a fixed dimension d. We consider two specific regimes: the infinite-sample finite-width regime, in which n=∞ while d and N are large but finite, and the infinite-width finite-sample regime in which N=∞ while d and n are large but finite. In the first regime, we prove that if dl+δ≤N≤dl+1−δ for small δ>0, then RF effectively fits a degree-l polynomial in the raw features, and NT fits a degree-(l+1) polynomial. In the second regime, both RF and NT reduce to kernel methods with rotationally invariant kernels. We prove that, if the sample size satisfies dl+δ≤n≤dl+1−δ, then kernel methods can fit at most a degree-l polynomial in the raw features. This lower bound is achieved by kernel ridge regression, and near-optimal prediction error is achieved for vanishing ridge regularization.

Implementable tensor methods in unconstrained convex optimization.

Abstract: In this paper we develop new tensor methods for unconstrained convex optimization, which solve at each iteration an auxiliary problem of minimizing convex multivariate polynomial. We analyze the simplest scheme, based on minimization of a regularized local model of the objective function, and its accelerated version obtained in the framework of estimating sequences. Their rates of convergence are compared with the worst-case lower complexity bounds for corresponding problem classes. Finally, for the third-order methods, we suggest an efficient technique for solving the auxiliary problem, which is based on the recently developed relative smoothness condition (Bauschke et al. in Math Oper Res 42:330–348, 2017; Lu et al. in SIOPT 28(1):333–354, 2018). With this elaboration, the third-order methods become implementable and very fast. The rate of convergence in terms of the function value for the accelerated third-order scheme reaches the level $$O\left( {1 \over k^4}\right) $$ , where k is the number of iterations. This is very close to the lower bound of the order $$O\left( {1 \over k^5}\right) $$ , which is also justified in this paper. At the same time, in many important cases the computational cost of one iteration of this method remains on the level typical for the second-order methods.

Adversary Instantiation: Lower Bounds for Differentially Private Machine Learning

Abstract: Differentially private (DP) machine learning allows us to train models on private data while limiting data leakage. DP formalizes this data leakage through a cryptographic game, where an adversary must predict if a model was trained on a dataset D, or a dataset D′ that differs in just one example. If observing the training algorithm does not meaningfully increase the adversary's odds of successfully guessing which dataset the model was trained on, then the algorithm is said to be differentially private. Hence, the purpose of privacy analysis is to upper bound the probability that any adversary could successfully guess which dataset the model was trained on.In our paper, we instantiate this hypothetical adversary in order to establish lower bounds on the probability that this distinguishing game can be won. We use this adversary to evaluate the importance of the adversary capabilities allowed in the privacy analysis of DP training algorithms.For DP-SGD, the most common method for training neural networks with differential privacy, our lower bounds are tight and match the theoretical upper bound. This implies that in order to prove better upper bounds, it will be necessary to make use of additional assumptions. Fortunately, we find that our attacks are significantly weaker when additional (realistic) restrictions are put in place on the adversary's capabilities. Thus, in the practical setting common to many real-world deployments, there is a gap between our lower bounds and the upper bounds provided by the analysis: differential privacy is conservative and adversaries may not be able to leak as much information as suggested by the theoretical bound.

Sum-Rate Maximization for IRS-Assisted UAV OFDMA Communication Systems

Abstract: In this paper, we consider the application of intelligent reflecting surface (IRS) in unmanned aerial vehicle (UAV)-based orthogonal frequency division multiple access (OFDMA) communication systems, which exploits both the significant beamforming gain brought by the IRS and the high mobility of UAV for improving the system sum-rate. The joint design of UAV’s trajectory, IRS scheduling, and communication resource allocation for the proposed system is formulated as a non-convex optimization problem to maximize the system sum-rate while taking into account the heterogeneous quality-of-service (QoS) requirement of each user. The existence of an IRS introduces both frequency-selectivity and spatial-selectivity in the fading of the composite channel from the UAV to ground users. To facilitate the design, we first derive the expression of the composite channels and propose a parametric approximation approach to establish an upper and a lower bound for the formulated problem. An alternating optimization algorithm is devised to handle the lower bound optimization problem and its performance is compared with the benchmark performance achieved by solving the upper bound problem. Simulation results unveil the small gap between the developed bounds and the promising sum-rate gain achieved by the deployment of an IRS in UAV-based communication systems.

New positivity bounds from full crossing symmetry

Abstract: Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of the scattering amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: we refer to these as the P Q, Dsu, Dstu and $$ {\overline{D}}^{\mathrm{stu}} $$ bounds. While the PQ bounds and Dsu bounds only make use of the s ↔ u dispersion relation, the Dstu and $$ {\overline{D}}^{\mathrm{stu}} $$ bounds are obtained by further imposing the s ↔ t crossing symmetry. In contradistinction to the linear positivity for scalars, these inequalities can be applied to put upper and lower bounds on Wilson coefficients, and are much more constraining as shown in the lowest orders. In particular we are able to exclude theories with soft amplitude behaviour such as weakly broken Galileon theories from admitting a standard UV completion. We also apply these bounds to chiral perturbation theory and we find these bounds are stronger than the previous bounds in constraining its Wilson coefficients.

Thermodynamic Uncertainty Relation in Slowly Driven Quantum Heat Engines.

Abstract: Thermodynamic uncertainty relations express a trade-off between precision, defined as the noise-to-signal ratio of a generic current, and the amount of associated entropy production. These results have deep consequences for autonomous heat engines operating at steady state, imposing an upper bound for their efficiency in terms of the power yield and its fluctuations. In the present Letter we analyze a different class of heat engines, namely, those which are operating in the periodic slow-driving regime. We show that an alternative TUR is satisfied, which is less restrictive than that of steady-state engines: it allows for engines that produce finite power, with small power fluctuations, to operate close to reversibility. The bound further incorporates the effect of quantum fluctuations, which reduces engine efficiency relative to the average power and reliability. We finally illustrate our findings in the experimentally relevant model of a single-ion heat engine.

Fragile Topology and Flat-Band Superconductivity in the Strong-Coupling Regime.

Abstract: In flat bands, superconductivity can lead to surprising transport effects. The superfluid ``mobility'', in the form of the superfluid weight ${D}_{s}$, does not draw from the curvature of the band but has a purely band-geometric origin. In a mean-field description, a nonzero Chern number or fragile topology sets a lower bound for ${D}_{s}$, which, via the Berezinskii-Kosterlitz-Thouless mechanism, might explain the relatively high superconducting transition temperature measured in magic-angle twisted bilayer graphene (MATBG). For fragile topology, relevant for the bilayer system, the fate of this bound for finite temperature and beyond the mean-field approximation remained, however, unclear. Here, we numerically use exact Monte Carlo simulations to study an attractive Hubbard model in flat bands with topological properties akin to those of MATBG. We find a superconducting phase transition with a critical temperature that scales linearly with the interaction strength. Then, we investigate the robustness of the superconducting state to the addition of trivial bands that may or may not trivialize the fragile topology. Our results substantiate the validity of the topological bound beyond the mean-field regime and further stress the importance of fragile topology for flat-band superconductivity.

Delay Compensation-Based State Estimation for Time-Varying Complex Networks With Incomplete Observations and Dynamical Bias.

Abstract: In this article, a delay-compensation-based state estimation (DCBSE) method is given for a class of discrete time-varying complex networks (DTVCNs) subject to network-induced incomplete observations (NIIOs) and dynamical bias. The NIIOs include the communication delays and fading observations, where the fading observations are modeled by a set of mutually independent random variables. Moreover, the possible bias is taken into account, which is depicted by a dynamical equation. A predictive scheme is proposed to compensate for the influences induced by the communication delays, where the predictive-based estimation mechanism is adopted to replace the delayed estimation transmissions. This article focuses on the problems of estimation method design and performance discussions for addressed DTVCNs with NIIOs and dynamical bias. In particular, a new distributed state estimation approach is presented, where a locally minimized upper bound is obtained for the estimation error covariance matrix and a recursive way is designed to determine the estimator gain matrix. Furthermore, the performance evaluation criteria regarding the monotonicity are proposed from the analytic perspective. Finally, some experimental comparisons are proposed to show the validity and advantages of the new DCBSE approach.

Distributed Variational Representation Learning

Abstract: The problem of distributed representation learning is one in which multiple sources of information $X_1,\ldots, X_K$ X 1 , ... , X K are processed separately so as to learn as much information as possible about some ground truth $Y$ Y . We investigate this problem from information-theoretic grounds, through a generalization of Tishby's centralized Information Bottleneck (IB) method to the distributed setting. Specifically, $K$ K encoders, $K \geq 2$ K ≥ 2 , compress their observations $X_1,\ldots, X_K$ X 1 , ... , X K separately in a manner such that, collectively, the produced representations preserve as much information as possible about $Y$ Y . We study both discrete memoryless (DM) and memoryless vector Gaussian data models. For the discrete model, we establish a single-letter characterization of the optimal tradeoff between complexity (or rate) and relevance (or information) for a class of memoryless sources (the observations $X_1,\ldots, X_K$ X 1 , ... , X K being conditionally independent given $Y$ Y ). For the vector Gaussian model, we provide an explicit characterization of the optimal complexity-relevance tradeoff. Furthermore, we develop a variational bound on the complexity-relevance tradeoff which generalizes the evidence lower bound (ELBO) to the distributed setting. We also provide two algorithms that allow to compute this bound: i) a Blahut-Arimoto type iterative algorithm which enables to compute optimal complexity-relevance encoding mappings by iterating over a set of self-consistent equations, and ii) a variational inference type algorithm in which the encoding mappings are parametrized by neural networks and the bound approximated by Markov sampling and optimized with stochastic gradient descent. Numerical results on synthetic and real datasets are provided to support the efficiency of the approaches and algorithms developed in this paper.

Certified dimension reduction in nonlinear Bayesian inverse problems

Abstract: We propose a dimension reduction technique for Bayesian inverse problems with nonlinear forward operators, non-Gaussian priors, and non-Gaussian observation noise. The likelihood function is approximated by a ridge function, i.e., a map which depends non-trivially only on a few linear combinations of the parameters. We build this ridge approximation by minimizing an upper bound on the Kullback-Leibler divergence between the posterior distribution and its approximation. This bound, obtained via logarithmic Sobolev inequalities, allows one to certify the error of the posterior approximation. Computing the bound requires computing the second moment matrix of the gradient of the log-likelihood function. In practice, a sample-based approximation of the upper bound is then required. We provide an analysis that enables control of the posterior approximation error due to this sampling. Numerical and theoretical comparisons with existing methods illustrate the benefits of the proposed methodology.

Observer-Based PID Security Control for Discrete Time-Delay Systems Under Cyber-Attacks

Abstract: This article deals with the observer-based proportional-integral-derivative (PID) security control problem for a kind of linear discrete time-delay systems subject to cyber-attacks. The cyber-attacks, which include both denial-of-service and deception attacks, are allowed to be randomly occurring as regulated by two sequences of Bernoulli distributed random variables with certain probabilities. A novel observer-based PID controller is proposed such that the closed-loop system achieves the desired security level and the quadratic cost criterion (QCC) has an upper bound. Sufficient conditions are derived under which the exponentially mean-square input-to-state stability is guaranteed and the desired security level is then achieved. Subsequently, an upper bound of the QCC is obtained and the explicit expression of the desired PID controller is also parameterized. Finally, the validity of the developed design approach is verified via an illustrative example.

Synchronization of Switched Discrete-Time Neural Networks via Quantized Output Control With Actuator Fault

Abstract: This article considers global exponential synchronization almost surely (GES a.s.) for a class of switched discrete-time neural networks (DTNNs). The considered system switches from one mode to another according to transition probability (TP) and evolves with mode-dependent average dwell time (MDADT), i.e., TP-based MDADT switching, which is more practical than classical average dwell time (ADT) switching. The logarithmic quantization technique is utilized to design mode-dependent quantized output controllers (QOCs). Noticing that external perturbations are unavoidable, actuator fault (AF) is also considered. New Lyapunov–Krasovskii functionals and analytical techniques are developed to obtain sufficient conditions to guarantee the GES a.s. It is discovered that the TP matrix plays an important role in achieving the GES a.s., the upper bound of the dwell time (DT) of unsynchronized subsystems can be very large, and the lower bound of the DT of synchronized subsystems can be very small. An algorithm is given to design the control gains, and an optimal algorithm is provided for reducing conservatism of the given results. Numerical examples demonstrate the effectiveness and the merits of the theoretical analysis.

Noise Stability of Weighted Majority

Abstract: Benjamini et al. (Inst Hautes Etudes Sci Publ Math 90:5–43, 2001) showed that weighted majority functions of n independent unbiased bits are uniformly stable under noise: when each bit is flipped with probability 𝜖, the probability p𝜖 that the weighted majority changes is at most C𝜖1∕4. They asked what is the best possible exponent that could replace 1∕4. We prove that the answer is 1∕2. The upper bound obtained for p𝜖 is within a factor of \(\sqrt {\pi /2}+o(1)\) from the known lower bound when 𝜖 → 0 and n𝜖 →∞.

Coverage Probability and Ergodic Capacity of Intelligent Reflecting Surface-Enhanced Communication Systems

Abstract: This letter studies the performance of a single-input single-output (SISO) system enhanced by the assistance of an intelligent reflecting surface (IRS), which is equipped with a finite number of elements under Rayleigh fading channels. From the instantaneous channel capacity, we compute a closed-form expression of the coverage probability as a function of statistical channel information only. A scaling law of the coverage probability and the number of phase shifts is further obtained. The ergodic capacity is derived, then a simple upper bound to simplify matters of utilizing the symbolic functions and can be applied for a long period of time. Numerical results manifest the tightness and effectiveness of our closed-form expressions compared with Monte-Carlo simulations.

A New Adaptive-Robust Design for Time Delay Control Under State-Dependent Stability Condition

Abstract: This brief proposes a new adaptive-robust formulation for time-delay control (TDC) under a less-restrictive stability condition. TDC relies on estimating the unknown system dynamics via the artificial introduction of a time delay, often referred to as time-delay estimation (TDE). In conventional TDC, the estimation error, called TDE error, is taken to be upper bounded by a constant under the assumption of small time delay and, most importantly, of a priori bounded states. We highlight the issues of such a conventional methodology via an unstable counterexample. Consequently, a new less-restrictive structure for the upper bound of the TDE error is formulated, which has an explicit dependence on system states and is valid for any chosen time delay. This insight leads to a new TDC design, namely, time-delayed adaptive-robust control (TDARC). The effectiveness of TDARC is substantiated via a multiple-degrees-of-freedom robot.

Thermodynamic Uncertainty Relation for General Open Quantum Systems.

Abstract: We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the system-environment interaction, we bound the counting observables in the environment by the survival activity, which reduces to the dynamical activity in classical Markov processes. Remarkably, the relation derived herein holds for general open quantum systems with any counting observable and any initial state. Therefore, our relation is satisfied for classical Markov processes with arbitrary time-dependent transition rates and initial states. We apply our relation to continuous measurement and the quantum walk to find that the quantum nature of the system can enhance the precision. Moreover, we can make the lower bound arbitrarily small by employing appropriate continuous measurement.

Reconfigurable Intelligent Surfaces-Assisted Communications With Discrete Phase Shifts: How Many Quantization Levels Are Required to Achieve Full Diversity?

Abstract: Due to hardware limitations, the phase shifts of the reflecting elements of reconfigurable intelligent surfaces (RISs) need to be quantized into discrete values. This letter aims to unveil the minimum required number of phase quantization levels ${L}$ in order to achieve the full diversity order in RIS-assisted wireless communication systems. With the aid of an upper bound of the outage probability, we first prove that the full diversity order is achievable provided that ${L}$ is not less than three. If ${L}\,\,=$ 2, on the other hand, we prove that the achievable diversity order cannot exceed ( ${N}\,\,+$ 1)/2, where ${N}$ is the number of reflecting elements. This is obtained with the aid of a lower bound of the outage probability. Therefore, we prove that the minimum required value of ${L}$ for achieving the full diversity order is ${L}\,\,=$ 3. Simulation results verify the theoretical analysis and the impact of phase quantization levels on RIS-assisted communication systems.

MaxCut quantum approximate optimization algorithm performance guarantees for p > 1

Abstract: We obtain worst-case performance guarantees for $p=2$ and 3 QAOA for MaxCut on uniform 3-regular graphs. Previous work by Farhi et al. obtained a lower bound on the approximation ratio of 0.692 for $p=1$. We find a lower bound of 0.7559 for $p=2$, where worst-case graphs are those with no cycles $\ensuremath{\le}5$. This bound holds for any 3-regular graph evaluated at particular fixed parameters. We conjecture a hierarchy for all $p$, where worst-case graphs have with no cycles $\ensuremath{\le}2p+1$. Under this conjecture, the approximation ratio is at least 0.7924 for all 3-regular graphs and $p=3$. In addition, using an indistinguishable argument we find an upper bound on the worst-case approximation ratio for all $p$, which indicates classes of graphs for which there can be no quantum advantage for at least $pl6$.

Joint Transmit Beamforming and Phase Shift Design for Reconfigurable Intelligent Surface Assisted MIMO Systems

Abstract: Reconfigurable intelligent surface (RIS) becomes an increasingly important technology in sixth-generation (6G). The key aspect of RIS is smartly configuring the wireless propagation environment and providing supplementary links to enhance the signal transmission between the BS and the UE. In recent years, there has been a surge of interest in RISs in joint active and passive beamforming design to improve the system performance of RIS-assisted systems with the assumption of uncorrelated environments. To date, far too little attention has been paid to the situations that consider the correlations among the antennas and RIS reflecting elements. In this article, we focus on an RIS-assisted multiple-input multiple-output (MIMO) system under spatial fading correlations, with the statistical channel state information (CSI) known at the transmitter and the RIS. We aim to maximize the ergodic spectral efficiency (SE) of this system. At first, we derive a tight upper bound on the ergodic SE. Concise upper bounds are also shown in special cases of independent and identically distributed (i.i.d.) Rician and Rayleigh, correlated Rayleigh as well as extreme Rician MIMO channels. Next, we propose a benchmark algorithm based on the semidefinite relaxation (SDR) technique to jointly optimize the beamforming vector at the transmitter and phase shift matrix of the RIS. Alternative manner is utilised until both arrive at convergence. Furthermore, we apply the dominant eigen direction transmission scheme to do beamforming in order to reduce the complexity of the algorithm, and consider the column control of the RIS to facilitate practical hardware implementation. Numerical results show the tightness of the upper bounds and the effectiveness of our proposed algorithm for improving the ergodic SE as well as the effects of freedom degrees on performances.

Event-Based Formation Coordinated Control for Multiple Spacecraft Under Communication Constraints

Abstract: This paper addresses the relative position coordinated control problem for spacecraft formation flying under an undirected communication graph, whilst considering mass uncertainties, external disturbances, and limited communication resources. A new event-triggered information transmission mechanism is first presented, where each spacecraft only requires accessing to the states of neighbors intermittently. Subsequently, a novel event-based coordinated control scheme is proposed by combining a smooth adaptive projection rule that confines the parameter estimations to well-defined bounded convex hypercubes. Under the proposed control framework, the information exchange among spacecraft occurs only when the specified event is triggered, thereby significantly reducing the communication load and saving the onboard resources. Furthermore, a positive lower bound on interevent time intervals is guaranteed to exclude Zeno behavior. By virtue of Lyapunov stability analysis and graph theory, it is proved that the relative position tracking errors can converge to small invariant sets around the origin, and that all closed-loop signals are bounded, even in the presence of mass uncertainties and external disturbances. Finally, numerical simulations are given to evaluate the effectiveness and highlight the advantages of the developed control algorithm.

General Relativistic Simulations of the Quasicircular Inspiral and Merger of Charged Black Holes: GW150914 and Fundamental Physics Implications

Abstract: We perform general-relativistic simulations of charged black holes targeting GW150914 We show that the inspiral is most efficient for detecting black hole charge through gravitational waves and that GW150914 is compatible with having charge-to-mass ratio as high as 03 Our work applies to electric and magnetic charge and to theories with black holes endowed with U(1) (hidden or dark) charges Using our results, we place an upper bound on the deviation from general relativity in the dynamical strong-filed regime of Moffat's modified gravity

Spectral separation of the stochastic gravitational-wave background for LISA: observing both cosmological and astrophysical backgrounds

Abstract: With the goal of observing a stochastic gravitational-wave background (SGWB) with LISA, the spectral separability of the cosmological and astrophysical backgrounds is important to estimate. We attempt to determine the level with which a cosmological background can be observed given the predicted astrophysical background level. We predict detectable limits for the future LISA measurement of the SGWB. Adaptive Markov chain Monte Carlo methods are used to produce estimates with the simulated data from the LISA Data Challenge. We also calculate the Cramer-Rao lower bound on the variance of the SGWB parameter estimates based on the inverse Fisher information using the Whittle likelihood. The estimation of the parameters is done with the three LISA channels $A$, $E$, and $T$. We simultaneously estimate the noise using a LISA noise model. Assuming the expected astrophysical background around ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{GW},\mathrm{astro}}(25\text{ }\text{ }\mathrm{Hz})=0.355\ensuremath{\rightarrow}35.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$, a cosmological SGWB normalized energy density of around ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{GW},\mathrm{Cosmo}}\ensuremath{\approx}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ to $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ can be detected by LISA after 4 years of observation.

Dissipativity Analysis for T–S Fuzzy System Under Memory Sampled-Data Control

Abstract: The dissipative stability problem for a class of Takagi–Sugeno (T–S) fuzzy systems with variable sampling control is the focus of this paper. The controller signals are assumed to transmit with a constant delay. Our aim is to design the sampled-data controller such that the T–S fuzzy system is globally asymptotically stable with a $(\mathcal {Q},\mathcal {S},\mathcal {R})$ - $\gamma $ -dissipative performance index. The stability is analyzed by using a novel piecewise Lyapunov–Krasovskii functional (LKF) together with a looped-functional and free-matrix-based (FMB) inequality method. First, several useful linear matrix inequality (LMI) conditions are derived to verify the dissipative stability of the T–S fuzzy system and then the controller gains matrices are expressed by resorting the LMI approach with the maximal-allowable upper bound (MAUB) of sampling periods. The proposed LMI conditions can be easily solved by using the MATLAB tool box. Finally, the numerical example of a truck–trailer system is considered and analyzed by the proposed scheme to illustrate the benefit and superiority.

Adaptive Predefined Performance Sliding Mode Control of Motor Driving Systems With Disturbances

Abstract: In this paper, a predefined time sliding mode control with prescribed performance is presented for dual-inertia driving systems with unknown disturbances. A modified prescribed performance function (PPF) without requiring the accurate initial error is designed to guarantee that the tracking error remains within the prescribed boundary. An adaptive law is then constructed to estimate the unknown upper boundary parameters of the lumped dynamics (e.g., parameter uncertainties and external disturbances), so that the prior knowledge of the upper bound of uncertainties is not required. The parameter estimation is incorporated into the control design to eliminate the effects of the unknown dynamics. Using the sliding mode technique, an adaptive predefined time sliding mode control is developed. The proposed control method can achieve fast convergence rate of the tracking error, and the stability of the closed-loop system is proved via the Lyapunov function method. Comparative experiments are carried out based on a dual-inertia driving system to validate the efficacy of the proposed approach.

Performance Analysis of RIS-Aided Systems With Practical Phase Shift and Amplitude Response

Abstract: Reconfigurable intelligent surfaces (RISs) have drawn significant attention due to their capability of controlling the radio environment and improving the system performance. In this paper, we study the performance of an RIS-assisted single-input single-output system over Rayleigh fading channels. Differently from previous works that assume a constant reflection amplitude, we consider a model that accounts for the intertwinement between the amplitude and phase response, and derive closed-form expressions for the outage probability and ergodic capacity. Moreover, we obtain simplified expressions under the assumption of a large number of reflecting elements and provide tight upper and lower bounds for the ergodic capacity. Finally, the analytical results are verified by using Monte Carlo simulations.

Improved big bang nucleosynthesis constraints on heavy neutral leptons

Abstract: We constrain the lifetime of thermally produced heavy neutral leptons (HNLs) from big bang nucleosynthesis. We show that even a small fraction of mesons present in the primeval plasma leads to the overproduction of primordial helium-4. This constrains the lifetime of HNLs to be ${\ensuremath{\tau}}_{N}l0.02\text{ }\text{ }\mathrm{s}$ for masses above the mass of the pion (as compared to 0.1 s reported previously). In combination with accelerator searches, this allows us to put a new lower bound on the HNL masses and define the ``bottom line'' for HNL searches at the future Intensity Frontier experiments.