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This paper investigates the elliptic localization for moving object problem from time delay (TD) and Doppler frequency shift (DFS) measurements, where the transmitter position and velocity are unknown. The transmitter is not perfectly time syncronized such that unknown offsets exist in the TD and DFS measurements. We propose to jointly estimate the object and transmitter positions and velocities and the offsets. Using the TD and DFS measurements from both the indirect and direct paths between the transmitter and the receivers, we formulate a non-convex weighted least squares (WLS) problem. Local convergence may occur when solving the non-convex WLS problem, implying that good estimate is not guaranteed. Thus, we relax the non-convex WLS problem into a convex semidefinite program by applying semidefinite relaxation (SDR). Moreover, we theoretically show that the performance can be improved by using multiple transmitters as compared to that using single transmitter, although more unknown parameters are introduced. We then extend the proposed SDR method to handle the multiple transmitters case. Finally, the mean square error analysis is provided to show that the proposed WLS method reaches the Cramer-Rao lower bound accuracy under small Gaussian noise condition. Simulation results validate the theoretical analysis and show the superior performance over the existing methods.

Temperature field control is crucial for the comprehensive performance of Ni-Co-Mn layered cathode material that is the most important part of lithium-ion batteries. Starting from the aspect of a class of distributed parameter systems described by highly dissipative partial differential equations (PDEs), an event-triggered optimal control (ETOC) method based on adaptive dynamic programming (ADP) for the roller kiln temperature field is proposed. First, we formulate the event-triggered control problem of the temperature field under the general framework of PDE systems. Then, an event-triggered condition is designed based on the stability of the closed-loop PDE system, which also guarantees the upper bound of the performance index. Subsequently, ADP technology is adopted to realize the ETOC, where the critic network is employed to approximate the optimal value function. Since the studied system can be regarded as an impulsive dynamic system with flow dynamics and jump dynamics simultaneously, the stability of the impulsive dynamic system combined with the ADP-based closed-loop PDE system is proved. Finally, simulation results on the temperature field verify the effectiveness of the proposed method.

This paper addresses the problem of computing valuations of the Dieudonne determinants of matrices over discrete valuation skew fields (DVSFs). This problem is an extension of computing degrees of determinants of polynomial matrices and has an application to the analysis of degrees of freedom of linear time-varying systems. Under a reasonable computational model, we propose two algorithms for a kind of DVSFs, called split. Our algorithms are extensions of the combinatorial relaxation of Murota (1995) and the matrix expansion by Moriyama-Murota (2013), both of which are based on combinatorial optimization. While our algorithms require an upper bound on the output, we show that the bound is easily obtained if the input is skew polynomial matrices.

As a category of the recurrent neural network (RNN), zeroing neural network (ZNN) can effectively handle time-variant optimization issues. Compared with the fixed-parameter ZNN that needs to be adjusted frequently to achieve good performance, the conventional variable-parameter ZNN (VPZNN) does not require frequent adjustment, but its variable parameter will tend to infinity as time grows. Besides, the existing noise-tolerant ZNN model is not good enough to deal with time-varying noise. Therefore, a new-type segmented VPZNN (SVPZNN) for handling the dynamic quadratic minimization issue (DQMI) is presented in this work. Unlike the previous ZNNs, the SVPZNN includes an integral term and a nonlinear activation function, in addition to two specially constructed time-varying piecewise parameters. This structure keeps the time-varying parameters stable and makes the model have strong noise tolerance capability. Besides, theoretical analysis on SVPZNN is proposed to determine the upper bound of convergence time in the absence or presence of noise interference. Numerical simulations verify that SVPZNN has shorter convergence time and better robustness than existing ZNN models when handling DQMI.

In this article, the local stabilization problem is investigated for a class of memristive neural networks (MNNs) with communication bandwidth constraints and actuator saturation. To overcome these challenges, a discontinuous event-trigger (DET) scheme, consisting of the rest interval and work interval, is proposed to cut down the triggering times and save the limited communication resources. Then, a novel relaxed piecewise functional is constructed for closed-loop MNNs. The main advantage of the designed functional consists in that it is positive definite only in the work intervals and the sampling instants but not necessarily inside the rest intervals. With the aid of extended reciprocally convex combination lemma, generalized sector condition, and some inequality techniques, two local stabilization criteria are established on the basis of both the discrete- and continuous-time Lyapunov methods. The proposed analysis technique fully takes advantage of the looped-functional and the event-trigger mechanism. Moreover, two optimization schemes are, respectively, established to design the control gain and enlarge the estimates of the admissible initial conditions (AICs) and the upper bound of rest intervals. Finally, some comparison results are given to validate the superiority of the proposed method.

Bluetooth Low Energy (BLE) has become one of the enabling wireless technologies to facilitate the Internet of Things. Neighbor discovery is critical in BLE communications. BLE uses multiple (three) channels in neighbor discovery. It is challenging to achieve low-latency and low-energy-consumption BLE neighbor discovery due to the lack of analytical models for multichannel neighbor discovery. In this paper, we study BLE multichannel neighbor discovery for two advertising modes specified by BLE: periodic deterministic advertising (PDA) and pseudo-random delay advertising (RDA). We build two generic models, BLE 3-Circle model and BLE 1-Circle model, for characterizing BLE multichannel neighbor discovery. For PDA mode, we present a necessary and sufficient condition for BLE multichannel neighbor discovery, and provide a guideline for parameter setting. With the guideline, we derive the expected discovery latency in closed form, and demonstrate that the expected discovery latency is very close to a theoretical lower bound. For RDA mode, we build an analytical model based on Markov chain to accurately compute the expected discovery latency. Simulation and experimental results show accuracy of our analytical works. Interestingly, our parameter setting guideline works well for both PDA and RDA mode.

In this paper, the physical layer security aspects of a wireless framework over α − κ − μ shadowed (AKMS) fading channel are examined by acquiring closed-form novel expressions of average secrecy capacity, secure outage probability (SOP), and strictly positive secrecy capacity. The lower bound of SOP is derived along with the asymptotic expression of SOP at the high signal-to-noise ratio regime in order to achieve secrecy diversity gain. Capitalizing on these expressions, the consequences due to the simultaneous occurrence of fading and shadowing are quantified. Finally, Monte-Carlo simulations are demonstrated to assess the correctness of the expressions.

International audience; The lane-keeping assistance design for steer-by-wire road vehicles is a multi-objective control problem that addresses lane tracking, improvement of driver comfort and ensuring vehicle stability. The designed architecture must be sensitive to various driver behaviors, provide assistance to drivers whenever required and ensure a smooth transition of authority between manual and automated driving modes. In this work, we propose a novel shared lane-keeping controller-based on quasi-continuous high-order sliding mode control dealing with the above challenges. The parameters of the controller are characterized by an upper bound estimate of the lateral winds force and the road curvature which acts as disturbances. Using the sharing parameter dependent on the monitored driver attribute, the authority is smoothly transitioned between various modes while accounting for driver behaviors. Experimental results on the SHERPA vehicle simulator shows the real-time implementation feasibility. Extensive results and discussions are provided to demonstrate the effectiveness and the applicability of the proposed controller.

We consider a generalization of the recently proposed gradient coding framework where a large dataset is divided across $n$ workers and each worker transmits to a master node one or more linear combinations of the gradients over the data subsets assigned to it. Unlike the conventional framework which requires the master node to recover the sum of the gradients over all the data subsets in the presence of $s$ straggler workers, we relax the goal of the master node to computing the sum of at least some α fraction of the gradients. The broad goal of our work is to study the optimal computation and communication load per worker for this approximate gradient coding framework. We begin by deriving a lower bound on the computation load of any feasible scheme and also propose a strategy which achieves this lower bound, albeit at the cost of high communication load and a number of data partitions which can be polynomial in the number of workers n. We then restrict attention to schemes which utilize a number of data partitions equal to $n$ and propose schemes based on cyclic assignment which have a lower communication load. When each worker transmits a single linear combination, we also prove lower bounds on the computation load of any scheme using $n$ data partitions. A full version of this paper is accessible at: https://arxiv.org/abs/2102.10163

This article is concerned with the problem of dynamic event-triggered adaptive neural network (NN) control for a class of switched strict-feedback uncertainty nonlinear systems. A novel switched command filter-based dynamic event-triggered adaptive NN control approach is set up by exploiting the backstepping and command filter and the common Lyapunov function method. Since adaptive controllers of subsystems are event triggered, then if the switching happens between any two consecutive triggering instants, asynchronous switching will arise between candidate controllers of subsystems and subsystems. Unlike the existing literature, where maximum asynchronous time is restricted, without any strict limitations on maximum asynchronous time being needed in this article, the asynchronous switching problem is directly handled by proposing a novel switching dynamic event-triggered mechanism (DETM) and event-triggered adaptive controllers of subsystems. Moreover, a piecewise constant variable is introduced into the switching DETM, which overcomes the difficulty of switched measurement error being discontinuous. Also, a strictly positive lower bound of interevent times is obtained. Finally, a continuous stirred tank reactor system and a numerical example are presented to demonstrate the effectiveness of the developed approach.

This article investigates event-triggered and self-triggered control problems for the Markov jump stochastic nonlinear systems subject to denial-of-service (DoS) attacks. When attacks prevent system devices from obtaining valid information over networks, a new switched model with unstable subsystems is constructed to characterize the effect of DoS attacks. On the basis of the switched model, a multiple Lyapunov function method is utilized and a set of sufficient conditions incorporating the event-triggering scheme (ETS) and restriction of DoS attacks are provided to preserve performance. In particular, considering that ETS based on mathematical expectation is difficult to be implemented on a practical platform, a self-triggering scheme (STS) without mathematical expectation is presented. Meanwhile, to avoid the Zeno behavior resulted from general exogenous disturbance, a positive lower bound is fixed in STS in advance. In addition, the exponent parameters are designed in STS to reduce triggering frequency. Based on the STS, the mean-square asymptotical stability and almost sure exponential stability are both discussed when the system is in the absence of exogenous disturbance. Finally, two examples are given to substantiate the effectiveness of the proposed method.

We study the reachability problem for continuous one-counter automata, COCA for short. In such automata, transitions are guarded by upper- and lower-bound tests against the counter value. Additionally, the counter updates associated with taking transitions can be (non-deterministically) scaled down by a nonzero factor between zero and one. Our three main results are as follows: we prove (1) that the reachability problem for COCA with global upper- and lower-bound tests is in NC 2 ; (2) that, in general, the problem is decidable in polynomial time; and (3) that it is NP-complete for COCA with parametric counter updates and bound tests.

The \begin{document}$ k $\end{document} -deck of a sequence is defined as the multiset of all its subsequences of length \begin{document}$ k $\end{document} . Let \begin{document}$ D_k(n) $\end{document} denote the number of distinct \begin{document}$ k $\end{document} -decks for binary sequences of length \begin{document}$ n $\end{document} . For binary alphabet, we determine the exact value of \begin{document}$ D_k(n) $\end{document} for small values of \begin{document}$ k $\end{document} and \begin{document}$ n $\end{document} , and provide asymptotic estimates of \begin{document}$ D_k(n) $\end{document} when \begin{document}$ k $\end{document} is fixed. Specifically, for fixed \begin{document}$ k $\end{document} , we introduce a trellis-based method to compute \begin{document}$ D_k(n) $\end{document} in time polynomial in \begin{document}$ n $\end{document} . We then compute \begin{document}$ D_k(n) $\end{document} for \begin{document}$ k \in \{3,4,5,6\} $\end{document} and \begin{document}$ k \leqslant n \leqslant 30 $\end{document} . We also improve the asymptotic upper bound on \begin{document}$ D_k(n) $\end{document} , and provide a lower bound thereupon. In particular, for binary alphabet, we show that \begin{document}$ D_k(n) = O\bigl(n^{(k-1)2^{k-1}+1}\bigr) $\end{document} and \begin{document}$ D_k(n) = \Omega(n^k) $\end{document} . For \begin{document}$ k = 3 $\end{document} , we moreover show that \begin{document}$ D_3(n) = \Omega(n^6) $\end{document} while the upper bound on \begin{document}$ D_3(n) $\end{document} is \begin{document}$ O(n^9) $\end{document} .

The Langberg-Medard multiple unicast conjecture claims that for any strongly reachable \begin{document}$ k $\end{document} -pair network, there exists a multi-flow with rate \begin{document}$ (1,1,\dots,1) $\end{document} . In this paper, we examine an optimization problem \begin{document}$ \mathcal P_{\mathcal S_k} $\end{document} such that its optimal value \begin{document}$ \mathcal O_{\mathcal S_k} $\end{document} naturally gives a lower bound on the multi-flow rate for the strongly reachable \begin{document}$ k $\end{document} -pair network. We first prove \begin{document}$ \lim_{k\rightarrow \infty}\mathcal O_{\mathcal S_k} = \frac{9}{8} $\end{document} and then show that the multi-flow \begin{document}$ \mathcal C^*_k $\end{document} constructed in our previous work is asymptotically optimal for \begin{document}$ \mathcal P_{\mathcal S_k} $\end{document} and optimal if and only if \begin{document}$ k = 1, 2, 6, 10 $\end{document} .

MDS matrices play an important role in the design of block ciphers, and constructing MDS matrices with fewer xor gates is of significant interest for lightweight ciphers. For this topic, Duval and Leurent proposed an approach to construct MDS matrices by using three linear operations in ToSC 2018. Taking words as elements, they found \begin{document}$ 16\times16 $\end{document} and \begin{document}$ 32\times 32 $\end{document} MDS matrices over \begin{document}$ \mathbb{F}_2 $\end{document} with only \begin{document}$ 35 $\end{document} xor gates and \begin{document}$ 67 $\end{document} xor gates respectively, which are also the best known implementations up to now. Based on the same observation as their work, we consider three linear operations as three kinds of elementary linear operations of matrices, and obtain more MDS matrices with \begin{document}$ 35 $\end{document} and \begin{document}$ 67 $\end{document} xor gates. In addition, some \begin{document}$ 16\times16 $\end{document} or \begin{document}$ 32\times32 $\end{document} involutory MDS matrices with only \begin{document}$ 36 $\end{document} or \begin{document}$ 72 $\end{document} xor gates over \begin{document}$ \mathbb{F}_2 $\end{document} are also proposed, which are better than previous results. Moreover, our method can be extended to general linear groups, and we prove that the lower bound of the sequential xor count based on words for \begin{document}$ 4 \times 4 $\end{document} MDS matrix over general linear groups is \begin{document}$ 8n+2 $\end{document} .

In 1943, Hadwiger conjectured that every graph with no K t + 1 minor is t-colorable for every t ≥ 0 . While Hadwiger's conjecture does not hold for list-coloring, the linear weakening is conjectured to be true. In the 1980 s, Kostochka and Thomason independently proved that every graph with no K t minor has average degree O ( t log ⁡ t ) and thus is O ( t log ⁡ t ) -list-colorable. Recently, the authors and Song proved that every graph with no K t minor is O ( t ( log ⁡ t ) β ) -colorable for every β > 1 4 . Here, we build on that result to show that every graph with no K t minor is O ( t ( log ⁡ t ) β ) -list-colorable for every β > 1 4 . Our main new tool is an upper bound on the number of vertices in highly connected K t -minor-free graphs: We prove that for every β > 1 4 , every Ω ( t ( log ⁡ t ) β ) -connected graph with no K t minor has O ( t ( log ⁡ t ) 7 / 4 ) vertices.

The emerging Federated Learning (FL) enables IoT devices to collaboratively learn a shared model based on their local datasets. However, due to end devices heterogeneity, it will magnify the inherent synchronization barrier issue of FL and result in non-negligible waiting time when local models are trained with the identical batch size. Moreover, the useless waiting time will further lead to a great strain on devices limited battery life. Herein, we aim to alleviate the negative impact of synchronization barrier through adaptive batch size during model training. When using different batch sizes, stability and convergence of the global model should be enforced by assigning appropriate learning rates on different devices. Therefore, we first study the relationship between batch size and learning rate, and formulate a scaling rule to guide the setting of learning rate in terms of batch size. Then we theoretically analyze the convergence rate of global model and obtain a convergence upper bound. On these bases, we propose an efficient algorithm that adaptively adjusts batch size with scaled learning rate for heterogeneous devices to reduce the waiting time and save battery life. We conduct extensive simulations and testbed experiments, and the experimental results demonstrate the effectiveness of our method.

Almost all event-triggered control (ETC) strategies were designed for discrete-time or continuous-time systems. In order to unify these existing theoretical results of ETC and develop ETC strategies for nonlinear systems, whose state variables evolve steadily at one time and change intermittently at another time, this article investigates quasisynchronization of delayed neural networks (NNs) on time scales with discontinuous activation functions via ETC approaches. First, the existence of the Filippov solutions is proved for discontinuous NNs with finite discontinuities. Second, two static event-triggered conditions and two dynamic event-triggered conditions are established to avoid continuous communication between the master-slave systems under algebraic/matrix inequality criteria. Third, under static/dynamic event-triggered conditions, a positive lower bound of event-triggered intervals is demonstrated to be greater than a positive number for each event-based controller, which shows that the Zeno behavior will not occur. Finally, two numerical simulations are carried out to show the effectiveness of the presented theoretical results in this article.

In the wideband regime, the performance of many of the popular modulation schemes such as code division multiple access and orthogonal frequency division multiplexing falls quickly without channel state information. Obtaining the amount of channel information required for these techniques to work is costly and difficult, which suggests the need for schemes which can perform well without channel state information. In this work, we present one such scheme, called wideband time frequency coding, which achieves rates on the order of the additive white Gaussian noise capacity without requiring any channel state information. Wideband time frequency coding combines impulsive frequency shift keying with pulse position modulation, which allows for information to be encoded in both the transmitted frequency and the transmission time period. On the detection side, we propose a non-coherent decoder based on a square-law detector, akin to the optimal decoder for frequency shift keying based signals. The impacts of various parameters on the symbol error probability and capacity of wideband time frequency coding are investigated, and the results show that it is robust to shadowing and highly fading channels. When compared to other modulation schemes such as code division multiple access, orthogonal frequency division multiplexing, pulse position modulation, and impulsive frequency shift keying without channel state information, wideband time frequency coding achieves higher rates in the wideband regime, and performs comparably in smaller bandwidths.

Knowledge graph embedding is an effective way to represent knowledge graph, which greatly enhance the performances on knowledge graph completion tasks, e.g. entity or relation prediction. For knowledge graph embedding models, designing a powerful loss framework is crucial to the discrimination between correct and incorrect triplets. Margin-based ranking loss is a commonly used negative sampling framework to make a suitable margin between the scores of positive and negative triples. However, this loss can not ensure ideal low scores for the positive triplets and high scores for the negative triplets, which is not beneficial for knowledge completion tasks. In this paper, we present a double limit scoring loss to separately set upper bound for correct triplets and lower bound for incorrect triplets, which provides more effective and flexible optimization for knowledge graph embedding. Upon the presented loss framework, we present several knowledge graph embedding models including TransE-SS, TransH-SS, TransD-SS, ProjE-SS and ComplEx-SS. The experimental results on link prediction and triplet classification show that our proposed models have the significant improvement compared to state-of-the-art baselines.

This paper develops a safety analysis method for stochastic systems that is sensitive to the possibility and severity of rare harmful outcomes. We define risk-sensitive safe sets as sub-level sets of the solution to a non-standard optimal control problem, where a random maximum cost is assessed via Conditional Value-at-Risk (CVaR). The objective function represents the maximum extent of constraint violation of the state trajectory, averaged over a given percentage of worst cases. This problem is well-motivated but difficult to solve tractably because the temporal decomposition for CVaR is history-dependent. Our primary theoretical contribution is to derive computationally tractable under-approximations to risk-sensitive safe sets. Our method provides a novel, theoretically guaranteed, parameter-dependent upper bound to the CVaR of a maximum cost without the need to augment the state space. For a fixed parameter value, the solution to only one Markov decision process problem is required to obtain the under-approximations for any family of risk-sensitivity levels. In addition, we propose a second definition for risk-sensitive safe sets and provide a tractable method for their estimation without using a parameter-dependent upper bound. The second definition is expressed in terms of a new coherent risk functional, which is inspired by CVaR. We demonstrate our primary theoretical contribution via numerical examples.

Identifying drug-target interactions has been a key step in drug discovery. Many computational methods have been proposed to directly determine whether drugs and targets can interact or not. Drug-target binding affinity is another type of data which could show the strength of the binding interaction between a drug and a target. However, it is more challenging to predict drug-target binding affinity, and thus a very few studies follow this line. In our work, we propose a novel co-regularized variational autoencoders (Co-VAE) to predict drug-target binding affinity based on drug structures and target sequences. The Co-VAE model consists of two VAEs for generating drug SMILES strings and target sequences, respectively, and a co-regularization part for generating the binding affinities. We theoretically prove that the Co-VAE model is to maximize the lower bound of the joint likelihood of drug, protein and their affinity. The Co-VAE could predict drug-target affinity and generate new drugs which share similar targets with the input drugs. The experimental results on two datasets show that the Co-VAE could predict drug-target affinity better than existing affinity prediction methods such as DeepDTA and DeepAffinity, and could generate more new valid drugs than existing methods such as GAN and VAE.

Deep learning models have been shown to be vulnerable to adversarial attacks. Adversarial attacks are imperceptible perturbations added to an image such that the deep learning model misclassifies the image with a high confidence. Existing adversarial defenses validate their performance using only the classification accuracy. However, classification accuracy by itself is not a reliable metric to determine if the resulting image is "adversarial-free". This is a foundational problem for online image recognition applications where the ground-truth of the incoming image is not known and hence we cannot compute the accuracy of the classifier or validate if the image is "adversarial-free" or not. This paper proposes a novel privacy preserving framework for defending Black box classifiers from adversarial attacks using an ensemble of iterative adversarial image purifiers whose performance is continuously validated in a loop using Bayesian uncertainties. The proposed approach can convert a single-step black box adversarial defense into an iterative defense and proposes three novel privacy preserving Knowledge Distillation (KD) approaches that use prior meta-information from various datasets to mimic the performance of the Black box classifier. Additionally, this paper proves the existence of an optimal distribution for the purified images that can reach a theoretical lower bound, beyond which the image can no longer be purified. Experimental results on six public benchmark datasets namely: 1) Fashion-MNIST, 2) CIFAR-10, 3) GTSRB, 4) MIO-TCD, 5) Tiny-ImageNet, and 6) MS-Celeb show that the proposed approach can consistently detect adversarial examples and purify or reject them against a variety of adversarial attacks.

In online learning, the dynamic regret metric chooses the reference oracle that may change over time, while the typical (static) regret metric assumes the reference solution to be constant over the whole time horizon. The dynamic regret metric is particularly interesting for applications, such as online recommendation (since the customers' preference always evolves over time). While the online gradient (OG) method has been shown to be optimal for the static regret metric, the optimal algorithm for the dynamic regret remains unknown. In this article, we show that proximal OG (a general version of OG) is optimum to the dynamic regret by showing that the proved lower bound matches the upper bound. It is highlighted that we provide a new and general lower bound of dynamic regret. It provides new understanding about the difficulty to follow the dynamics in the online setting.

We study the list decodability of different ensembles of codes over the real alphabet under the assumption of an omniscient adversary. It is a well-known result that when the source and the adversary have power constraints $ P $ and $ N $ respectively, the list decoding capacity is equal to $ \frac{1}{2}\log\frac{P}{N} $. Random spherical codes achieve constant list sizes, and the goal of the present paper is to obtain a better understanding of the smallest achievable list size as a function of the gap to capacity. We show a reduction from arbitrary codes to spherical codes, and derive a lower bound on the list size of typical random spherical codes. We also give an upper bound on the list size achievable using nested Construction-A lattices and infinite Construction-A lattices. We then define and study a class of infinite constellations that generalize Construction-A lattices and prove upper and lower bounds for the same. Other goodness properties such as packing goodness and AWGN goodness of infinite constellations are proved along the way. Finally, we consider random lattices sampled from the Haar distribution and show that if a certain number-theoretic conjecture is true, then the list size grows as a polynomial function of the gap-to-capacity., Comment: Significantly revised

We consider Bandits with Knapsacks (henceforth, BwK), a general model for multi-armed bandits under supply/budget constraints. In particular, a bandit algorithm needs to solve a well-known knapsack problem: find an optimal packing of items into a limited-size knapsack. The BwK problem is a common generalization of numerous motivating examples, which range from dynamic pricing to repeated auctions to dynamic ad allocation to network routing and scheduling. While the prior work on BwK focused on the stochastic version, we pioneer the other extreme in which the outcomes can be chosen adversarially. This is a considerably harder problem, compared to both the stochastic version and the "classic" adversarial bandits, in that regret minimization is no longer feasible. Instead, the objective is to minimize the competitive ratio: the ratio of the benchmark reward to the algorithm's reward. We design an algorithm with competitive ratio O(log T) relative to the best fixed distribution over actions, where T is the time horizon; we also prove a matching lower bound. The key conceptual contribution is a new perspective on the stochastic version of the problem. We suggest a new algorithm for the stochastic version, which builds on the framework of regret minimization in repeated games and admits a substantially simpler analysis compared to prior work. We then analyze this algorithm for the adversarial version and use it as a subroutine to solve the latter., The extended abstract appeared in FOCS 2019. The definitive version was published in JACM '22. V8 is the latest version with all technical changes. Subsequent versions fixes minor LATEX presentation issues

This article identifies a new upper bound norm for the intervalized interconnection matrices pertaining to delayed dynamical neural networks under the parameter uncertainties. By formulating the appropriate Lyapunov functional and slope-bounded activation functions, the derived new upper bound norms provide new sufficient conditions corresponding to the equilibrium point of the globally asymptotic robust stability with respect to the delayed neural networks. The new upper bound norm also yields the optimized minimum results as compared with some existing methods. Numerical examples are given to demonstrate the effectiveness of the proposed results obtained through the new upper bound norm method.

A multivariable finite-time control algorithm is proposed for double integrator systems with matched disturbances. The remarkable feature of the developed method is to ensure the finite-time stability of the closed-loop system with uniformly bounded control signal with respect to arbitrary initial conditions. The convergence criteria is derived by using the Lyapunov-based techniques, and the upper bound of the control signal can be calculated based on the obtained criteria. Finally, the effectiveness of the proposed algorithm is confirmed by some numerical simulations.

This technical note studies fixed-time consensus tracking with disturbance rejection for first-order multi-agent systems. The communication topology among the leader and followers contains a directed spanning tree. The control input to the leader is time-varying and unknown to the followers, except that its upper bound is known a priori. A novel fixed-time protocol is devised based on discontinuous and nonlinear control. A fixed-time stability analysis for consensus tracking with disturbance rejection is completed as a one-step control process by using non-smooth analysis. An upper bound estimate for the settling time, independent of the initial conditions, is aesthetically pleasing, in comparison to previous results derived based on two-step control design technique using sliding mode. Finally, a numeric example confirms the theoretical results.