Convergence speed in distributed consensus over dynamically switching random networks

Characterizing convergence speed is one of the most important research challenges in the design of distributed consensus algorithms for networked multi-agent systems. In this paper, we consider a group of agents that communicate via a dynamically switching random information network. Each link in the network, which represents the directed/undirected information flow between any ordered/unordered pair of agents, could be subject to failure with a certain probability. Hence we model the information flow using dynamically switching random graphs. We characterize the convergence speed for the distributed discrete-time consensus algorithm over a variety of random networks with arbitrary weights. In particular, we propose the asymptotic and per-step (mean square) convergence factors as measures of the convergence speed and derive the exact value for the per-step (mean square) convergence factor. Numerical examples are also given to illustrate our theoretical results.     

Delay robustness in consensus problems

We investigate the robustness of consensus schemes for linear Multi-Agent Systems (MAS) to feedback delays. To achieve this, we develop a unified framework that considers linear MAS models with different feedback delays, e.g. affecting only the neighbor’s output, or affecting both the agent’s own and its neighbors’ output. This framework has the advantage of providing scalable, simple, and accurate set-valued conditions for consensus. Using these set-valued conditions, previous results on consensus in MAS with delays can be recovered and generalized. Moreover, we use them to derive conditions for the convergence rate of single integrator MAS with feedback delays. Finally, building on this framework, we propose a scalable delay-dependent design algorithm for consensus controllers for a large class of linear MAS.     

Quantized consensus over directed networks with switching topologies

This paper studies the quantized consensus problem for a group of agents over directed networks with switching topologies. We propose an effective distributed protocol with an adaptive finite-level uniform quantized strategy, under which consensus among agents is guaranteed with weaker communication conditions. In particular, we analytically prove that each agent sending 5-level quantized information to each of its neighbors, together with 3-level quantized information to itself at each time step, which suffices for attaining consensus with an exponential convergence rate as long as the duration of all link failures in the directed network is bounded. By dropping the typical common left eigenvector requirement for the existence of common quadratic Lyapunov function, we conduct the convergence analysis based on the notion of input-to-output stability. The proposed quantized protocol has favorable merits of requiring little communication overhead and increasing robustness to link unreliability, and it fits well into the digital network framework.     

基于有向网络的多智能体系统快速一致性

针对具有二次积分动态的多智能体系统在有向网络下的快速一致性问题,提出了基于智能体当前状态和过去状态的快速一致性协议.利用矩阵理论和频域分析法,分别给出了多智能体系统达到静态一致性和动态一致性的充要条件,同时得到该协议能够使系统分别快速地达到静态一致和动态一致的过去状态区间.仿真示例验证了所提出协议的有效性.     

Consensus in multi-agent systems with random delays governed by a Markov chain

This paper investigates the consensus problem in a multi-agent system with random delays governed by a Markov chain. The communication topology is assumed to be directed and fixed. With first-order dynamics under the sampled-data setting, we first convert the original system into a reduced-order one featuring the error dynamics. Accordingly, the consensus problem is transformed into the stabilization of the error dynamic system. Thereafter, based on the theory in stochastic stability for time-delay systems, a sufficient condition is established in terms of a set of linear matrix inequalities (LMIs). The mean square stability of the error dynamics is shown to guarantee consensus of the multi-agent system. By explicitly incorporating the transition probability of the random delay into consideration, the conservativeness in control design is reduced. A delay-dependent switching control scheme is developed by redesigning the adjacency matrix. Finally, simulation results are provided to verify the effectiveness of the proposed approach.     

A new LP formulation of the admission control problem modelled as an MDP under average reward criterion

The admission control problem can be modelled as a Markov decision process (MDP) under the average cost criterion and formulated as a linear programming (LP) problem. The LP formulation is attractive in the present and future communication networks, which support an increasing number of classes of service, since it can be used to explicitly control class-level requirements, such as class blocking probabilities. On the other hand, the LP formulation suffers from scalability problems as the number C of classes increases. This article proposes a new LP formulation, which, even if it does not introduce any approximation, is much more scalable: the problem size reduction with respect to the standard LP formulation is O((C?+?1)²/2 ^C ). Theoretical and numerical simulation results prove the effectiveness of the proposed approach.     

Another set of conditions for average optimality in Markov control processes

The existence of an average cost optimal stationary policy in a countable state Markov decision chain is shown under assumptions weaker than those given by Sennott (1989). This treatment is a modification of that given by Hu (1992), and is related to conditions of Hordijk (1977). An example is given for which the new axiom set holds whereas the axiom set of Sennott (1989) fails to hold.     

A note on the vanishing interest rate approach in average Markov decision chains with continuous and bounded costs

This work considers denumerable state Markov decision processes with discrete time parameter. The performance of a control policy is measured by the (lim sup) expected average cost criterion, the action sets are compact metric and the cost function is continuous and bounded. Within this framework, necessary and sufficient conditions are given so that the vanishing interest rate (VIR) method — also known as the vanishing discount effect approach — yields an average optimal stationary policy.     

Service networks with multichannel nodes in a random environment

Service networks with multichannel nodes of semi-Markovian type are considered. The parameters of a source of demands depend on the state of the Markovian random environment. For the process of servicing demands, the conditions of existence of a stationary mode are found, and the properties of stationary distribution in terms of spectral characteristics of the routing matrix are investigated. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 167–172, January–February, 2000.     

On the estimation of the consensus rate of convergence in graphs with persistent interconnections

The aim of the current article is to establish myriad convergence rate estimates to consensus for time-varying graphs with persistent interaction. Several novel analysis methodologies for consensus protocols employing the notions of persistence of excitation and Lyapunov functions are provided. The estimates are compared with each other and existing literature. Numerical simulations on test examples are illustrated to support the theoretical findings.     

Maximization of average number of correctly received symbols over multiple channels in the presence of idle periods

In this study, optimal channel switching (time sharing) strategies are investigated under average power and cost constraints for maximizing the average number of correctly received symbols between a transmitter and a receiver that are connected via multiple flat-fading channels with additive Gaussian noise. The optimal strategy is shown to correspond to channel switching either among at most three different channels with full channel utilization (i.e., no idle periods), or between at most two different channels with partial channel utilization. Also, it is stated that the optimal solution must operate at the maximum average power and the maximum average cost, which facilitates low-complexity approaches for obtaining the optimal strategy. For two-channel strategies, an upper bound is derived, in terms of the parameters of the employed channels, on the ratio between the optimal power levels. In addition, theoretical results are derived for characterizing the optimal solution for channel switching between two channels, and for comparing performance of single channel strategies. Sufficient conditions that depend solely on the systems parameters are obtained for specifying when partial channel utilization cannot be optimal. Furthermore, the proposed optimal channel switching problem is investigated for logarithmic cost functions, and various theoretical results are obtained related to the optimal strategy. Numerical examples are presented to illustrate the validity of the theoretical results.     

A pause control approach to the value iteration scheme in average Markov decision processes

This work concerns average Markov decision chains with denumerable state space. Assuming that the Lyapunov function condition holds, it is shown that the value iteration scheme yields convergent approximations to the solution of the average cost optimality equation. This result is obtained using a particular implementation of the value iteration procedure involving an artificial control action under which the system remains static.     

Parameter optimization of stochastic automata operating in random environments

Two methods of determining the lower bounds of the rate of convergence of finite stochastic automata are presented. The rate of convergence, defined as the percentage decrease in the distance between the transient probability distribution and the equilibrium probability distribution in each step, is determined as a function of the probability transition matrix. Formulas for parameter optimization for a class of stochastic automata for fast convergence and maximum expediency are derived and illustrative examples of fourth-order systems are given.     

A hybrid intelligent model for network selection in the industrial Internet of Things

Industrial Internet of Things (IIoT) plays an important role in increasing productivity and efficiency in heterogeneous wireless networks. However, different domains such as industrial wireless scenarios, small cell domains and vehicular ad hoc networks (VANET) require an efficient machine learning/intelligent algorithm to process the vertical handover decision that can maintain mobile terminals (MTs) in the preferable networks for a sufficient duration of time. The preferred quality of service parameters can be differentiated from all the other MTs. Hence, in this paper, the problem with the vertical handoff (VHO) decision is articulated as the process of the Markov decision aimed to maximize the anticipated total rewards as well as to minimize the handoffs’ average count. A rewards function is designed to evaluate the QoS at the point of when the connections take place, as that is where the policy decision for a stationary deterministic handoff can be established. The proposed hybrid model merges the biogeography-based optimization (BBO) with the Markov decision process (MDP). The MDP is utilized to establish the radio access technology (RAT) selection’s probability that behaves as an input to the BBO process. Therefore, the BBO determines the best RAT using the described multi-point algorithm in the heterogeneous network. The numerical findings display the superiority of this paper’s proposed schemes in comparison with other available algorithms. The findings shown that the MDP-BBO algorithm is able to outperform other algorithms in terms of number of handoffs, bandwidth availability, and decision delays. Our algorithm displayed better expected total rewards as well as a reduced average account of handoffs compared to current approaches. Simulation results obtained from Monte-Carlo experiments prove validity of the proposed model.