This article addresses the event-triggered consensus tracking control problem for complex heterogeneous multiagent systems with multiple unknown. The systems under consideration involve fully unknown time-varying control directions (CDs), unknown time-varying input delays (UTVDs) and functions, making the problem particularly challenging. To reduce the effects of UTVDs, an auxiliary system is constructed to produce a compensation signal. Building upon this, a novel adaptive proportional-integral (PI) control approach is developed through the backstepping method and a series of Nussbaum functions. It is demonstrated that the tracking error can meet predefined transient and steady-state performance criteria, ensuring asymptotic tracking and global boundedness of all signals in the closed-loop system. The key advantage of this solution lies in its simplicity of controller design and improved control performance, without requiring prior information about the unknown functions. Finally, a simulation example validates the validity of the proposed approach.

This article investigates the distributed online optimization problem in a zero-sum game between two distinct time-varying multiagent networks. At each iteration, the agents not only communicate with their neighbors but also gather information about agents in the opposing network through a time-varying network, assigning weights accordingly. Moreover, we consider quantized communication and bandit feedback mechanisms, with agents transmitting quantized information and adopting one-point estimators. At each iteration, agents make and submit decisions and then receive the cost function values near their decision points rather than the full cost function information. To guarantee the payoff of each network, we design an algorithm named quantized distributed online bandit optimization in two-network (QDOBO-TN). We use dynamic Nash equilibrium regret to measure the positive payoff discrepancy between the decision sequence produced by Algorithm QDOBO-TN and the Nash equilibrium sequence. Furthermore, we propose a multiepoch version of Algorithm QDOBO-TN. The regret bounds for both algorithms are sublinear with respect to the iteration count T. Finally, we conduct a series of simulation experiments that further validate the effectiveness of the algorithms.

This article focuses on a decentralized online optimization problem over multiagent systems, where the interactions are modeled by a strongly connected directed graph. The objective of each agent is to minimize the global loss function accumulated by all agents' local loss functions, which are time-varying and only known by themselves. To address the communication bottleneck caused by the high-dimensional data and large-scale networks, we design a decentralized online algorithm with compressed communication, decentralized online gradient push-sum with compressed communication (CC-DOGPS). For strongly convex functions, a sublinear regret bound $\mathcal {O}((\ln T)^{2})$ of our designed algorithm is obtained, where $T$ is the time horizon. Finally, two numerical simulations are given to validate the theoretical results and illustrate the efficiency of our designed algorithm.

This article provides a novel framework for the concurrent development of asynchronous observers and controllers for discrete-time nonlinear semi-Markov jump singularly perturbed systems subjected to mismatched modes, states, and premise variables between controlled systems and observer-based controllers. Aiming at characterizing nonlinearity with parameter uncertainty, the interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy technique is implemented in system modeling. Meanwhile, it is supposed that both observer and controller modes can just be acquired via a hidden Markov mode detector in the first attempt. Then, following the concept of non-parallel distribution compensation (non-PDC), the observer-based IT2 fuzzy asynchronous controllers are constructed with observers and controllers sharing the same fuzzy membership function but different from that in systems, which improves the designed flexibility. In accordance with semi-Markov kernel approach and the Lyapunov function contingent upon both system modes and sojourn times, sufficient criteria are established for the functioning of expected mode-dependent IT2 fuzzy observers and controllers such that the σ-mean-square stability for the resulting nonlinear augmented semi-Markov jump singularly perturbed systems comprised of the controlled systems and observation error systems is guaranteed. Furthermore, from the perspective of fuzzy processing, parameters and relaxation matrices that comply with fuzzy rules are added to ensure system stability while further reducing the conservatism of conditions. Ultimately, a circuit model and comparison examples are shown to substantiate the necessity and superiority of the suggested technique.

This article focuses on the online distributed optimization with privacy protection in time-varying unbalanced networks. We consider the case where there exist potential passive attackers in the network, having access to all communication channels. The attackers attempt to deduce the privacy of participating nodes. In this case, the differential privacy approach is leveraged to enable privacy protection. Based on this privacy-preserving approach and the stochastic subgradient method, a novel differentially private distributed online stochastic subgradient descent (DP-DOSSD) algorithm is devised for addressing the considered problem. Unlike the existing algorithms that require the weight matrices to be doubly stochastic, our algorithm only depends on two different weight matrices that are column-stochastic and row-stochastic, respectively. Moreover, a stochastic subgradient rescaling technique is adopted to tackle the unbalancedness of time-varying directed networks. It proves that our algorithm not only guarantees ϵ-differential privacy but also establishes an expected regret of orderO(√T) in convex settings, where ϵ andTare the privacy level and the time horizon, respectively. The established result matches the optimal regret bound derived by state-of-the-art algorithms. The fundamental tradeoff between convergence performance and privacy level is also studied. Finally, simulation results for the sensor network-based online distributed estimation problem and the distributed online ridge regression problem are provided to confirm the effectiveness of our approach.

We focus on the problem of distributed online constrained convex optimization with statistical privacy in multiagent systems. The participating agents aim to collaboratively minimize the cumulative system-wide cost while a passive adversary corrupts some of them. The passive adversary collects information from corrupted agents and attempts to estimate the private information of the uncorrupted ones. In this scenario, we adopt a correlated perturbation mechanism with globally balanced property to cover the local information of agents to enable privacy preservation. This work is the first attempt to integrate such a mechanism into the distributed online (sub)gradient descent algorithm, and then a new algorithm called privacy-preserving distributed online convex optimization (PP-DOCO) is designed. It is proved that the designed algorithm provides a statistical privacy guarantee for uncorrupted agents and achieves an expected regret in $\mathcal {O}(\sqrt {K})$ for convex cost functions, where K denotes the time horizon. Furthermore, an improved expected regret in $\mathcal {O}(\log (K))$ is derived for strongly convex cost functions. The obtained results are equivalent to the best regret scalings achieved by state-of-the-art algorithms. The privacy bound is established to describe the level of statistical privacy using the notion of Kullback-Leibler divergence (KLD). In addition, we observe that a tradeoff exists between our algorithm's expected regret and statistical privacy. Finally, the effectiveness of our algorithm is validated by simulation results.

This article studies the distributed online stochastic convex optimization problem with the time-varying constraint over a multiagent system constructed by various agents. The sequences of cost functions and constraint functions, both of which have dynamic parameters following time-varying distributions, are unacquainted to the agent ahead of time. Agents in the network are able to interact with their neighbors through a sequence of strongly connected and time-varying graphs. We develop the adaptive distributed bandit primal-dual algorithm whose step size and regularization sequences are adaptive and have no prior knowledge about the total iteration span T . The adaptive distributed bandit primal-dual algorithm applies bandit feedback with a one-point or two-point gradient estimator to evaluate gradient values. It is illustrated in this article that if the drift of the benchmark sequence is sublinear, then the adaptive distributed bandit primal-dual algorithm exhibits sublinear expected dynamic regret and constraint violation using both two kinds of gradient estimator to compute gradient information. We present a numerical experiment to show the performance of the proposed method.

This paper studies the problem of adaptive fuzzy tracking for a class of nonstrict feedback stochastic systems with input delay and asymmetric state constraints. Input delay is addressed based on the Pade approximation and introducing an intermediate variable, then the control problem for the original systems is transformed into one for non-delay system. For state constraints in the system, this paper proposes nonlinear state dependent function (NSDF) instead of barrier Lyapunov function (BLF), which removes the feasibility conditions. By fuzzy logic system (FLS) and variable separation technology, this paper effectively solves algebraic rings created by nonstrict feedback structures. A fuzzy adaptive controller is proposed to ensure that all variables in the system are bounded in probability and the asymmetric state constraints are well kept all the time. Finally, simulation examples confirm the effectiveness of control strategy.

This article is concerned with the distributed stochastic multiagent-constrained optimization problem over a time-varying network with a class of communication noise. This article considers the problem in composite optimization setting, which is more general in the literature of noisy network optimization. It is noteworthy that the mainstream existing methods for noisy network optimization are Euclidean projection based. Based on the Bregman projection-based mirror descent scheme, we present a non-Euclidean method and investigate their convergence behavior. This method is the distributed stochastic composite mirror descent type method (DSCMD-N), which provides a more general algorithm framework. Some new error bounds for DSCMD-N are obtained. To the best of our knowledge, this is the first work to analyze and derive convergence rates of optimization algorithm in noisy network optimization. We also show that an optimal rate of O(1/√T) in nonsmooth convex optimization can be obtained for the proposed method under appropriate communication noise condition. Moveover, novel convergence results are comprehensively derived in expectation convergence, high probability convergence, and almost surely sense.

This article is concerned with the distributed convex constrained optimization over a time-varying multiagent network in the non-Euclidean sense, where the bandwidth limitation of the network is considered. To save the network resources so as to reduce the communication costs, we apply an event-triggered strategy (ETS) in the information interaction of all the agents over the network. Then, an event-triggered distributed stochastic mirror descent (ET-DSMD) algorithm, which utilizes the Bregman divergence as the distance-measuring function, is presented to investigate the multiagent optimization problem subject to a convex constraint set. Moreover, we also analyze the convergence of the developed ET-DSMD algorithm. An upper bound for the convergence result of each agent is established, which is dependent on the trigger threshold. It shows that a sublinear upper bound can be guaranteed if the trigger threshold converges to zero as time goes to infinity. Finally, a distributed logistic regression example is provided to prove the feasibility of the developed ET-DSMD algorithm.

This article aims to investigate the global stabilization for a class of stochastic continuous time-delay nonlinear systems involved with unknown control coefficients and stochastic-input-to-state-stable-like conditions. Without involving the traditional adaptive compensation approach, a dominate gain is adopted to deal with uncertain nonlinearities, which not only include unmeasurable state but also involve input and state delays. On account of homogeneous domination manner and stochastic stability theory, a delay-independent controller is developed to guarantee that the closed-loop system is globally asymptotically stable in probability. Finally, a simulation example is supplied to show the virtue of the devised strategy.

The distributed convex optimization problem over the multiagent system is considered in this article, and it is assumed that each agent possesses its own cost function and communicates with its neighbors over a sequence of time-varying directed graphs. However, due to some reasons, there exist communication delays while agents receive information from other agents, and we are going to seek the optimal value of the sum of agents’ loss functions in this case. We desire to handle this problem with the push-sum distributed dual averaging (PS-DDA) algorithm. We study the effects of communication delays on the convergence results of the PS-DDA algorithm and propose an explicit bound on the convergence rate. It is proved that this algorithm converges, and the convergence result of the PS-DDA algorithm will be worse as the maximum delay value on one edge becomes larger. Our analysis indicates that the PS-DDA algorithm can converge at a rate of${\mathcal {O}}(T^{-0.5})$with proper step size, where$T$is iteration span. We finally apply the theoretical results to numerical simulations to show the PS-DDA algorithm’s performance.

We consider a distributed online convex optimization problem when streaming data are distributed among computing agents over a connected communication network. Since the data are high-dimensional or the network is large-scale, communication load can be a bottleneck for the efficiency of distributed algorithms. To tackle this bottleneck, we apply the state-of-art data compression scheme to the fundamental GD-based distributed online algorithms. Three algorithms with difference-compressed communication are proposed for full information feedback (DC-DOGD), one-point bandit feedback (DC-DOBD), and two-point bandit feedback (DC-DO2BD), respectively. We obtain regret bounds explicitly in terms of time horizon, compression ratio, decision dimension, agent number, and network parameters. Our algorithms are proved to be no-regret and match the same regret bounds, w.r.t. time horizon, with their uncompressed versions for both convex and strongly convex losses. Numerical experiments are given to validate the theoretical findings and illustrate that the proposed algorithms can effectively reduce the total transmitted bits for distributed online training compared with the uncompressed baseline.

In this article, we concentrate on distributed online convex optimization problems over multiagent systems, where the communication between nodes is represented by a class of directed graphs that are time varying and uniformly strongly connected. This problem is in bandit feedback, in the sense that at each time only the cost function value at the committed point is revealed to each node. Then, nodes update their decisions by exchanging information with their neighbors only. To deal with Lipschitz continuous and strongly convex cost functions, a distributed online convex optimization algorithm that achieves sublinear individual regret for every node is developed. The algorithm is built on the algorithm called the push-sum scheme that releases the request of doubly stochastic weight matrices, and the one-point gradient estimator that requires the function value at only one point at every iteration, instead of the gradient information of loss function. The expected regret of our proposed algorithm scales as$\mathcal {O} (T^{2/3} \ln ^{2/3}(T))$, and$T$is the number of iterations. To validate the performance of the algorithm developed in this article, we give a simulation of a common numerical example.

This paper aims to investigate the event-based extended dissipative state estimation problem for memristor-based Markovian neural networks in the presence of hybrid time-varying delays and sensor nonlinearity. To tackle the effect caused by information latching, sudden interference and environmental variation, the Markov jump model is employed to describe the memristor-based neural network. Besides, an event-triggered scheme is introduced to economize the cost of communication. Then some novel conditions are presented, which guarantee that the augmented error system is stochastically stable with an extended dissipative performance. The existence criterion of the desired mode-dependent estimator is also obtained in terms of linear matrix inequalities. Finally, simulation results are provided to show the effectiveness of the proposed method.

We study online linear regression problems in a distributed setting, where the data is spread over a network. In each round, each network node proposes a linear predictor, with the objective of fitting the network-wide data. It then updates its predictor for the next round according to the received local feedback and information received from neighboring nodes. The predictions made at a given node are assessed through the notion of regret, defined as the difference between their cumulative network-wide square errors and those of the best off-line network-wide linear predictor. Various scenarios are investigated, depending on the nature of the local feedback (full information or bandit feedback), on the set of available predictors (the decision set), and the way data is generated (by an oblivious or adaptive adversary). We propose simple and natural distributed regression algorithms, involving, at each node and in each round, a local gradient descent step and a communication and averaging step where nodes aim at aligning their predictors to those of their neighbors. We establish regret upper bounds typically in O(T3/4) when the decision set is unbounded and in O(√T) in case of bounded decision set.

This article considers the problem of stochastic strongly convex optimization over a network of multiple interacting nodes. The optimization is under a global inequality constraint and the restriction that nodes have only access to the stochastic gradients of their objective functions. We propose an efficient distributed non-primal-dual algorithm, by incorporating the inequality constraint into the objective via a smoothing technique. We show that the proposed algorithm achieves an optimal O((1)/(T)) ( T is the total number of iterations) convergence rate in the mean square distance from the optimal solution. In particular, we establish a high probability bound for the proposed algorithm, by showing that with a probability at least 1-δ , the proposed algorithm converges at a rate of O(ln(ln(T)/δ)/ T) . Finally, we provide numerical experiments to demonstrate the efficacy of the proposed algorithm.

In this paper, we consider the problem of solving distributed constrained optimization over a multiagent network that consists of multiple interacting nodes in online setting, where the objective functions of nodes are time-varying and the constraint set is characterized by an inequality. Through introducing a regularized convex-concave function, we present a consensus-based adaptive primal-dual subgradient algorithm that removes the need for knowing the total number of iterations in advance. We show that the proposed algorithm attains an [where ] regret bound and an bound on the violation of constraints; in addition, we show an improvement to an regret bound when the objective functions are strongly convex. The proposed algorithm allows a novel tradeoffs between the regret and the violation of constraints. Finally, a numerical example is provided to illustrate the effectiveness of the algorithm.

In this paper, we study the distributed constrained optimization problem where the objective function is the sum of local convex cost functions of distributed nodes in a network, subject to a global inequality constraint. To solve this problem, we propose a consensus-based distributed regularized primal-dual subgradient method. In contrast to the existing methods, most of which require projecting the estimates onto the constraint set at every iteration, only one projection at the last iteration is needed for our proposed method. We establish the convergence of the method by showing that it achieves an O ( K (-1/4) ) convergence rate for general distributed constrained optimization, where K is the iteration counter. Finally, a numerical example is provided to validate the convergence of the propose method.

This paper studies the problem of minimizing a sum of (possible nonsmooth) convex functions that are corresponding to multiple interacting nodes, subject to a convex state constraint set. Time-varying directed network is considered here. Two types of computational constraints are investigated in this paper: one where the information of gradients is not available and the other where the projection steps can only be calculated approximately. We devise a distributed zeroth-order method, the implementation of which needs only functional evaluations and approximate projection. In particular, we show that the proposed method generates expected function value sequences that converge to the optimal value, provided that the projection errors decrease at appropriate rates.

In this brief, we consider the multiagent optimization over a network where multiple agents try to minimize a sum of nonsmooth but Lipschitz continuous functions, subject to a convex state constraint set. The underlying network topology is modeled as time varying. We propose a randomized derivative-free method, where in each update, the random gradient-free oracles are utilized instead of the subgradients (SGs). In contrast to the existing work, we do not require that agents are able to compute the SGs of their objective functions. We establish the convergence of the method to an approximate solution of the multiagent optimization problem within the error level depending on the smoothing parameter and the Lipschitz constant of each agent's objective function. Finally, a numerical example is provided to demonstrate the effectiveness of the method.

This paper studies the problem of optimizing the sum of multiple agents' local convex objective functions, subject to global convex inequality constraints and a convex state constraint set over a network. Through characterizing the primal and dual optimal solutions as the saddle points of the Lagrangian function associated with the problem, we propose a distributed algorithm, named the distributed primal-dual subgradient method, to provide approximate saddle points of the Lagrangian function, based on the distributed average consensus algorithms. Under Slater's condition, we obtain bounds on the convergence properties of the proposed method for a constant step size. Simulation examples are provided to demonstrate the effectiveness of the proposed method.