Distributed Optimization for Resource Allocation Problems Under Large Delays

In this paper, the distributed resource allocation problem over undirected networks, considering box constraints and demand–supply constraints, is studied. Furthermore, each agent has one private cost function that is only known by itself. The aim is to minimize the sum of all local cost functions in a distributed manner while meeting the constraints. To solve the dispatch problem, a continuous‐time distributed algorithm with fixed step‐size is proposed. After that, a modified distributed algorithm of discrete‐time multi‐agent system is provided. Moreover, the proposed algorithms obtain the global optimal solution with an exponential convergence speed by the conventional Lyapunov methods. Finally, several simulations of IEEE‐14 bus are presented to validate and illustrate the proposed designed algorithm.

Energy-efficiency, high transmission data rates and Quality of Service (QoS) awareness are the major challenges for resource management in the uplink of Visible Light Communication Personal Area Networks (VPANs). This paper investigates the problem of Optical Access Point (OAP) selection and resource allocation in the uplink of VPANs under two different transmission techniques, namely Orthogonal Frequency Division Multiple Access (OFDMA) and Non-Orthogonal Multiple Access (NOMA). Each user is associated with a generic utility function, which represents his perceived satisfaction with respect to the overall resource allocation problem. OAP selection adopts Maximum Gain Selection (MGS) policy, i.e. users select an OAP to connect to based on the highest path gain. A distributed resource allocation problem in VPANs is formulated and solved as an optimization problem. Following this analysis, a decentralized iterative and low-complexity algorithm for determining OAP selection and resource allocation is proposed, while the overall approach’s efficiency is illustrated via modeling and simulation, highlighting and assessing the advantages and drawbacks of each adopted transmission technique, i.e. OFDMA and NOMA.

Observer-based guaranteed-cost bipartite time-varying formation tracking control for multiagent systems subject to communication delays

Guaranteed cost load frequency control for a class of uncertain power systems with large delay periods

In this technical note, the problem of delay-independent minimum dwell time for exponential stability of uncertain switched delay systems is considered. Piecewise time-varying Lyapunov functionals/functions which are decreasing at switching times by construction are introduced to investigate exponential stability of switched delay systems with constant or time-varying delays. This type of delicately constructed Lyapunov functionals/functions can efficiently eliminate the “jump” phenomena of adjacent Lyapunov functionals/functions at switching times without imposing any restriction on the sizes of time-delays. By applying this type of Lyapunov functionals/functions, it is shown that if each subsystem is delay-independently exponentially stable, then under some conditions there exists a delay-independent minimum dwell time in the sense that the switched delay system with such minimum dwell time is exponentially stable irrespective of the sizes of the time-delays. Two numerical examples are provided to demonstrate the efficiency of the proposed approach.

In this paper, the asymptotic stability problem of neural networks with time-varying delays is investigated. First, a new sufficient and necessary condition on a general polynomial inequality was developed. Then, a novel augmented Lyapunov–Krasovskii functional (LKF) was constructed, which efficiently introduces some new terms related to the previous information of neuron activation function. Furthermore, based on the suitable LKF and the stated negative condition of the general polynomial, two criteria with less conservatism were derived in the form of linear matrix inequalities. Finally, two numerical examples were carried out to confirm the superiority of the proposed criteria, and a larger allowable upper bound of delays was achieved.

Multiuser Orthogonal Frequency Division Multiple Access (OFDMA) networks, such as Long Term Evolution networks, use the frequency reuse-1 model to face the tremendous increase of mobile traffic demands, and to increase network capacity. However, inter-cell interference problems are generated, and they have a negative impact on cell-edge users performance. Resource and power allocation should be managed in a manner that alleviates the negative impact of inter-cell interference on system performance. In this paper, we formulate a novel centralized multi-cell resource and power allocation problem for multiuser OFDMA networks. The objective is to maximize system throughput while guaranteeing a proportional fair rate for all the users. We decompose the joint problem into two independent problems: a resource allocation problem and a power allocation problem. We prove that each of these problems is a convex optimization problem, and that their optimal solution is also an optimal solution to the original joint problem. Lagrange duality theory and subgradient projection method are used to solve the centralized power allocation problem. We study the convergence of our centralized approach, and we find out that it reduces inter-cell interference, and increases system throughput and spectral efficiency in comparison with the frequency reuse-1 model, reuse-3 model, fractional frequency reuse, and soft frequency reuse techniques.

A robust control approach to stabilization of networked control systems with time-varying delays

A delay-dependent analysis and synthesis approach is established for a class of linear discrete-time switched delay systems with convex bounded parameter uncertainties in all system matrices. New results are established for both constant and time-varying delays using switched Lyapunov---Krasovskii functionals. A delay-dependent analysis of the uncertain switched delay system is developed to guarantee that it is asymptotically stable with an ?2 gain smaller than a prescribed constant level. Delay-dependent switched control feedback is then designed, based on state and output measurements, to render the corresponding switched closed-loop system delay-dependent asymptotically stable with a prescribed ?2 gain measure. The developed results are cast as linear matrix inequalities (LMIs) and tested on representative examples.

In this article, a distributed resource allocation problem for second‐order multi‐agent systems over undirected switching topologies is investigated. For the distributed resource allocation problem, most of the existing algorithms depend on the gradient of cost function with specific expression, which may be unknown to agents. To deal with unknown cost functions, the extremum seeking control is introduced in the designed distributed resource allocation algorithm to estimate the gradient of the cost function only by the value of the cost. Besides, an estimator is proposed to estimate the optimal Lagrange multiplier associated with the equality constraint. The communication graph is supposed to be switched among a set of undirected subgraphs, which may be connected or unconnected. For undirected and connected switching graphs, the average dwell‐time constraint is used to describe the switching frequency. For the undirected graphs, containing connected and unconnected ones, both the average dwell‐time and the time‐ratio constraints are used to model the switching signal. For the two cases, the semi‐globally practically asymptotical stability of the designed algorithm is established. The obtained results are verified by an example.

This paper proposes distributed algorithms for control and coordination of loads and distributed energy resources (DERs) in distribution networks. These algorithms are relevant for load curtailment control in demand response programs, and also for coordination of DERs for provision of ancillary services. Both the distributed load-curtailment and DER coordination problems can be cast as distributed resource allocation problems with constraints on resource capacity. We focus on linear iterative algorithms in which each resource j maintains a set of values that is updated to be a weighted linear combination of the resource's own previous set of values and the previous sets of values of its neighboring resources. This set of values can be used by each node to determine its own contribution to load curtailment or to resource request.

The symmetric and weighted Shapley values for cooperative n-person games are studied. Using the semi-tensor product of matrices, it is first shown that a characteristic function can be expressed as a pseudo-Boolean function. Then, two simple matrix formulas are obtained for calculating the symmetric and weighted Shapley values. Finally, using these new formulas, a design technique for the agents’ payoff functions in distributed resource allocation problems is proposed. It is possible to design payoff functions with the weighted Shapley value by the nonsymmetric weights defined on the players, thus ensuring that the optimal allocation is a pure Nash equilibrium. Practical examples are presented to illustrate the theoretical results.

From drinking philosophers to asynchronous path-following robots

In this paper, the robust stability issue of switched uncertain multidelay systems resulting from actuator failures is considered. Based on the average dwell time approach, a set of suitable switching signals is designed by using the total activation time ratio between the stable subsystem and the unstable one. It is first proven that the resulting closed-loop system is robustly exponentially stable for some allowable upper bound of delays if the nominal system with zero delay is exponentially stable under these switching laws. Particularly, the maximal upper bound of delays can be obtained from the linear matrix inequalities. At last, the effectiveness of the proposed method is demonstrated by a simulation example.

Deployment of the Internet of Things (IoT) in industries have enabled remote control of various mechanical system over the Internet. It is known that such networked control systems (NCSs) might suffer large time-varying communication delays. Not only performance degradation of the controlled system but also stability issues may occur as a consequence. The present paper proposes a two degree-of-freedom (DOF) digital servo system that stabilizes a feedback control system under the presence of large data transmission delay. We formulated a round trip time (RTT) predictor using a recurrent neural network (RNN). We then designed a dynamic state prediction controller (DSPC) to stabilize the feedback control system under the presence of large delay without causing control performance degradation. The controller gain is determined by solving LMI-based delay-dependent optimization problem. The designed controller is applied to a virtual inverted pendulum attached to the tip of an industrial robot manipulator controlled through a network that includes a wifi router. Results of experiments revealed that the proposed controller exhibited good performance under large fluctuation of RTT.