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Although the development of Internet of Things (IoT) provides a significant boost for the applications of deep learning algorithms, it is generally hard to fully implement the deep learning algorithms by IoT devices due to their limited calculation capacity. The problem could be alleviated by deploying the deep learning system with edge computing. Herein, we propose a kind of distributed long short-term memory (DLSTM) neural networks and deploy them on the IoT environment to handle the large-scale spatiotemporal correlation regression tasks. Specifically, the presented DLSTM neural networks adopt the collaborative computing architecture with the terminals, edges and cloud, in order to realize the lightweight deep learning on the IoT devices and improve the learning efficiency. The generalization ability of LSTM neural networks is promoted through introducing the distributed memory cells to implement the information sharing between different edge servers and employing the attention mechanism in LSTM neural networks. Meanwhile, the deep fully connected networks are deployed among the cloud to extract the spatiotemporal correlations in the variety of data from different time and space regions, which enhances the transferability of LSTM neural networks.

Time and energy costs are two important indicators to evaluate the consensus protocols of networking agent systems. However, the relationship between time and energy costs for achieving consensus is far from clear. In this paper, combining the benefits of the linear feedback and finite-time control technologies, a new switching protocol is proposed to solve the finite-time consensus problem of multi-agent networks with undirected and detail-balanced directed topologies. The analytical estimates of time and energy costs are obtained, which unveil the network characteristics and control parameters that can reduce the time and energy costs. Especially, it is shown, both analytically and numerically, that there is a trade-off between time and energy costs, i.e., reducing the time cost will inevitably increase the energy cost.

In this work, we consider the local relative measurement based leader-follower formation navigation problem of nonholonomic robots with globally bounded inputs and collision avoidance constraints. It is assumed that each robot can only measure the relative distances and bearings of its leaders in its local coordinate frame. No global coordinate information is available. Digital communication between robots is also prohibited considering payload or transmission medium restrictions. Under these conditions, two novel globally bounded leader-follower formation controllers are first proposed for both the distance-bearing and the distance-distance formation cases assuming known leaders’ state information. Then, the unavailable information of the leader/leaders is handled by Extended Kalman Filters (EKFs). To guarantee the global boundedness of the observer-based distance-distance formation navigation controller, a switching control strategy is designed and analyzed. Barrier function based collision avoidance method is then employed to guarantee the safety of the robots during the whole formation navigation process. Simulation examples are provided to illustrate the effectiveness of the proposed controllers.

This paper studies a nonsmooth resource allocation problem with network resource constraints and local set constraints, where the interaction graphs among agents are generally strongly connected digraphs. First, we design a centralized continuous-time proximal gradient algorithm, where each agent uses the global Lagrangian multipliers and the global values of constraint functions. For the case that the agents’ private information could not be leaked and the global Lagrangian multipliers are not available, the agents are endowed with some additional variables to estimate those global information via consensus protocols. Then, we construct a class of continuous-time distributed proximal gradient algorithms by using a two-time scale mechanism to integrate the proposed proximal gradient algorithm and consensus protocols. By adopting Lyapunov stability theory and convex optimization theory, we prove that the decision variables asymptotically converge to the optimal solution of the nonsmooth resource allocation problem. Finally, numerical simulations are applied to illustrate the effectiveness of the proposed algorithms.

Existing resilient consensus algorithms are mainly developed based on the mean subsequence reduced (MSR) method, which relies on the assumption that there exist at most $f$ malicious agents in the entire network or each neighborhood (i.e., $f$ -total or $f$ -local model). However, in some practical cases, it may be impossible to estimate an appropriate upper bound on the number of malicious agents. This paper proposes a novel method, called trusted-region subsequence reduction (TSR), for designing resilient consensus algorithm without the $f$ -total/local model assumption. The main idea of the TSR method is to filter out the received information beyond a dynamic trusted region, determined by the current relative positions of the neighboring trusted nodes. Based on the TSR method, we design a sampled-data resilient consensus algorithm for double-integrator multi-agent networks. A necessary and sufficient graph-theoretic condition is obtained to achieve resilient consensus. Finally, simulations are conducted to illustrate the effectiveness of the proposed algorithm and the faster convergence rate of the TSR-based algorithm than the classical MSR-based algorithm.

In this paper, we consider cyber-physical system (CPS) with multiple remote state estimation under denial-of-service (DoS) attack in infinite time-horizon. The sensors monitor the system and send their local state estimate to remote estimators by choosing the local channels in “State 0” or “State 1”. The aim of sensors is to find policies for choosing local channel in a specific state to transmit message to minimize the total estimation error covariance on account of energy-saving in an infinite time-horizon. The DoS attacker aims to achieve the opposite goal by choosing channels to attack or not. The games between sensors and DoS attacker under two different structures of public information are investigated, that is the open-loop case (where sensors and attacker cannot observe others’ behaviors) and the closed-loop case (where sensors and attacker can observe the others’ behaviors causally). For the open-loop case with assumption that the DoS attacker can get the information from the remote estimators to the sensors, the distributed reinforcement learning algorithms for sensors and attacker based on local information are proposed to find their Nash equilibrium policies, respectively. Further, we consider in closed loop case that the DoS attacker cannot get the information from the remote estimators to the sensors which leads to asymmetric information between the sensors and attacker. To derive Nash equilibrium policies for sensors and attacker, we convert the original game into a belief-based continuous-state stochastic game. The convergence of distributed reinforcement learning method is proved. Some simulations are presented to demonstrate its effectiveness.

The structural balance preserving problem is studied in this article for heterogeneous agents in the state-dependent cooperation-competition network. The heterogeneous agents considered are described by second-order integrator systems with different intrinsic nonlinear dynamics, and velocity damping terms, and the initial network is structurally balanced, and connected, which can be divided into two cooperation subnetworks. To solve this problem, a novel classification strategy is applied, where two kinds of evolution rules among agents, and the distributed protocol based on a class of potential functions are proposed, respectively. Under this strategy, the heterogeneous multi-agent system can not only maintain the structural balance of cooperation-competition networks but also achieve bipartite static consensus. Finally, a numerical example is delivered to demonstrate the effectiveness of the theoretical analysis.

In this work, we consider the coordination control of second-order multi-agent systems subject to both velocity and input constraints with only relative output information. First, the leaderless consensus problem is considered where a nonlinear distributed controller is proposed which achieves asymptotic consensus of the agents using only local velocity and relative output information. Then, generalization to the leader-following formation control with known leader's input is studied. For the case of unknown leader's input, a finite-time observer-based controller is proposed using sliding mode control ideas. Finally, the collision avoidance requirement for the leader-following formation control is handled by employing control barrier functions. Necessary modifications to the nominal formation controllers are obtained by properly formulating some quadratic problems and the velocity and input constraints are met during the entire operation. Several simulation examples are provided to illustrate the developed controllers and the effectiveness of the collision avoidance strategy.

The finite-time stability (FTS) is crucial for the network systems with high requirements on the convergence rate. When the finite-time settling time is globally bounded, the fixed-time stability (FxTS) is introduced. This paper focuses on the FTS/FxTS of the network systems with nonlinear protocols over signed digraphs. Sufficient criteria are obtained for ensuring the FTS/FxTS of the investigated network systems with general weighted matrices from a unified framework. Particularly, the proposed distributed nonlinear protocol is fully distributed with flexible heterogeneous coefficients. The explicit bounds on the finite/fixed-time settling time are also derived analytically. Moreover, the FTS/FxTS of the perturbed network systems is guaranteed with the technique of the sliding mode controller. As an application, the obtained results are used to achieve finite/fixed-time network modulus consensus over signed digraphs. Finally, two numerical examples are presented to verify the analytical results.