Backward Iterative Algorithm Research Articles

Joint optimization of component reassignment and working intensity adjusting strategy for multi-state systems with periodic inspection in a shock environment

For some engineering systems performing a mission with long duration, the component positions and working intensity can be dynamically adjusted to improve the efficiency of mission completion and system reliability. Motivated by this reality, a joint strategy of component reassignment and working intensity adjusting is proposed for a multi-component system. Components at different positions can be functionally exchanged. When at least one component fails completely, the system fails. The system operates under a shock environment and the probability that a shock is valid to a component is affected by its position and working intensity. The system can complete more tasks per unit time in a higher working intensity, but the probability that a shock is valid to a component is also larger. The mission is divided into multiple phases, and the action of component reassignment and working intensity adjusting needs to be decided at the beginning of each phase. A Markov decision process is constructed and the optimal mission phase number and strategy are obtained by a finite stage backward recursive iterative algorithm. An Unmanned Aerial Vehicle (UAV) swarm performing an emergency rescue mission is taken as an example to verify the effectiveness of the proposed joint strategy.

Energy Trading and Power Allocation Strategies for Relay-Assisted Smart Grid Communications: A Three-Stage Game Approach

In smart grid, serious packet loss often occurs in the process of information interaction between the Utilities and customers, which results in supply-demand deviation and further increases the cost of the Utilities. In order to improve the information transmission performance of communication networks, the Utilities purchase relay service from telecom operator to help data aggregator units (DAU) transfer information to gateway (GW), so as to improve communication quality and reduce the cost of the Utilities. Secondly, in order to solve the problem of telecom operators' energy reduction and reduce the cost of purchasing energy, we utilize energy supply point (ESP) to collect the surplus energy of retail customers for energy supply, and telecom operator pays a certain amount of remuneration to ESP in exchange for ESP to continuously supply energy to telecom operator. Then, we establish a three-stage game method and system model between the Utilities, telecom operator and ESP, and propose the relay power allocation and energy transaction pricing strategy. Due to the real-time change of energy demand, we consider two situations of energy oversupply and conservative supply, and use the backward induction method and iterative algorithm to obtain the equilibrium solution of the Stackelberg game, including the unit energy price of ESP, total power of telecom operator, the proportion of transmission power allocated to the relay service, and payment scheme of the Utilities. Simulation results show that the proposed algorithm can quickly and accurately converge to the optimal solution of the problem, and the method can improve the stability of demand-side regulation, reduce the cost of the Utilities and increase the profit of telecom operator.

Utility Optimization for Multi-User Task Offloading in Mobile Ad Hoc Cloud: A Stochastic Game Approach

Offloading tasks to the mobile ad hoc cloud (MAHC) can improve the utility of mobile devices in scenarios without infrastructure. However, when multiple resource demanders (RDs) offload tasks to multiple resource providers (RPs) in the MAHC with task random generation, how to optimize the utility of RDs and the service quality of the MAHC is an issue worth researching. To this end, we investigate this issue from the stochastic game perspective. Firstly, we combine the obtained time, energy, and monetary revenue as the utility of each RD and construct the utility improvement of each RD as a static non-cooperative game. Secondly, according to the randomness of RD’s task generation, we transform the single-shot non-cooperative game into a stochastic game in an infinite time horizon to obtain the long-term utility. Thirdly, to reduce the computational complexity for achieving Nash equilibrium, we propose an action reduction alternate backward iteration algorithm according to the games characteristics and prove its convergence. Finally, we compare the utility obtained from the static game with the stochastic game, the numerical results indicating that the utility of each RD can be effectively improved by utilizing the stochastic game.

APPROXIMATION OF ZEROS OF SUM OF MONOTONE MAPPINGS WITH APPLICATIONS TO VARIATIONAL INEQUALITY AND IMAGE RESTORATION PROBLEMS

In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.

Blockchain Storage and Computation Offloading for Cooperative Mobile-Edge Computing

To enable more Internet-of-Things (IoT) devices for participating in the Proof-of-Work (PoW) mining process of public blockchains, we propose a cooperative mobile-edge computing (MEC)-aided blockchain network. In the network, devices can offload computation-intensive PoW mining tasks to base stations and store their block data to the cloud service provider. Then, we study the joint computation offloading, block storage, and resource service pricing problem as a three-stage Stackelberg game. We analyze the subgame optimization problem in each stage and propose an iterative algorithm based on backward induction to achieve the Nash equilibrium of the Stackelberg game. Furthermore, we derive the upper bound of the ergodic throughput of the cooperative scheme and the maximum number of devices connected to the network. The analysis shows that the proposed cooperative MEC-aided blockchain network can significantly improve the system throughput, and more devices can access the blockchain network. Analytical results show that the proposed backward induction-based iterative algorithm can efficiently attain the Nash equilibrium of the game. Numerical results show that our proposed backward induction-based iterative algorithm has fast convergence and good stability, and the proposed cooperative scheme can serve more devices in comparison with other noncooperative schemes.

An Algorithmic Study to Maximize 5G Network Throughput Based on the Markov Decision Process

In this article, the network throughput optimization problem is investigated based on the theory of Markov decision process, combining the device-to-device direct selection problem with the finite stage discount MDP model problem. First, models for the device-to-device communication selection using MDP are built; second, the optimal mode selection strategy is derived using a finite stage backward iterative algorithm; and finally, the given mode selection strategy is evaluated by conducting a large number of simulation experiments. The results show that the MDP-based mode selection method proposed in this article has better performance in maximizing throughput and can yield better mode selection strategies with the advantage of obtaining larger system throughput.

A tuning scheme of cycle reference point for gas turbine adaptive performance simulation with field data

To minimize the simulated performance error of gas turbines, traditional adaptive methods are mainly concerned with the tuning of cycle design point and component maps given by the manufacturer, usually ignoring the fact that performance at cycle design point may not match the field data due to the deviation between test-rig conditions and field conditions. In this paper, a new tuning scheme of the cycle reference point is proposed to minimize the simulated errors simultaneously at design point and off-design points. The scheme is composed of a backward iteration algorithm and a genetic algorithm. During the backward iteration, the field data at the maximum operating condition is selected to obtain the initial cycle reference point with several undetermined parameters. Further, the genetic algorithm is used to optimize the undetermined parameters. The accuracy of the proposed method was validated by the simulated performance of a PGT25+ gas turbine.

Optimality of feedback control for qubit purification under inefficient measurement

A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However existing results suggest that such an enhancement is only possible when the measurement efficiency exceeds 0.5, which is difficult to achieve experimentally. We address the task of finding the global optimal feedback control for purifying a single qubit in the presence of measurement inefficiency. We use the Bloch vector length, a more physical and practical quantity than purity, to assess the quality of the state, and employ a backward iteration algorithm to find the globally optimal strategy. Our results show that a speedup is available for quantum efficiencies well below 0.5, which opens the possibility of experimental implementation in existing systems.

Cooperative Power Management in Energy Harvesting Communication Systems in Presence of a Helper

We investigate end-to-end throughput maximization problem for an energy harvesting (EH) single user channel in presence of an energy cooperating helper. The EH helper transfers energy to the EH battery-limited transmitter and receiver nodes. These nodes impose energy causality and energy saving constraints on the power consumption. Both of the transmitter and the receiver harvest energy from nature, and also from the helper via energy cooperation links. The EH receiver requires energy for message decoding process which is called the decoding cost. Then, based on status of the batteries at the transmitter and the receiver, five scenarios are investigated. To maximize the achievable throughput, we propose iterative directional waterfilling algorithms based on minimum and maximum constraint violations. Then as a general model, a backward iterative algorithm (based on combination of optimization in feasibility tunnel and directional waterfilling with variable minimum constraints) is presented. Finally, numerical results are presented to highlight the advantages of energy cooperating helper.

Optimal two-stage dynamic treatment regimes from a classification perspective with censored survival data.

Clinicians often make multiple treatment decisions at key points over the course of a patient's disease. A dynamic treatment regime is a sequence of decision rules, each mapping a patient's observed history to the set of available, feasible treatment options at each decision point, and thus formalizes this process. An optimal regime is one leading to the most beneficial outcome on average if used to select treatment for the patient population. We propose a method for estimation of an optimal regime involving two decision points when the outcome of interest is a censored survival time, which is based on maximizing a locally efficient, doubly robust, augmented inverse probability weighted estimator for average outcome over a class of regimes. By casting this optimization as a classification problem, we exploit well-studied classification techniques such as support vector machines to characterize the class of regimes and facilitate implementation via a backward iterative algorithm. Simulation studies of performance and application of the method to data from a sequential, multiple assignment randomized clinical trial in acute leukemia are presented.

A Note on the Multi-Agent Contracts in Continuous Time

Incentive contracts with multiple agents is a classical decentralized decision-making problem with asymmetric information. Contract design aims to incentivize noncooperative agents to act in the principal's interest over a planning horizon. We extend the single-agent incentive contract to a multiagent setting with history-dependent terminal conditions. Our contributions include: (a) Finding sufficient conditions for the existence of optimal multiagent incentive contracts and conditions under which they form a unique Nash Equilibrium; (b) Showing that the optimal multiagent incentive contracts can be solved by a Hamilton-Jacobi-Bellman (HJB) equation with equilibrium constraints; (c) Proposing a backward iterative algorithm to solve the problem.

Energy Management Strategy for Plug-In Hybrid Electric Vehicles via Bidirectional Vehicle-to-Grid

As a paradigm of the incoming smart grid, vehicle-to-grid (V2G) has been proposed as a promising solution to increase the adoption rate of plug-in hybrid electric vehicles (PHEVs). In this paper, we investigate the energy management strategies for PHEVs via bidirectional V2G. We first follow a cost-conscious approach from the PHEV owner point of view. To minimize the daily energy cost, we formulate the energy management problem via dynamic programming (DP). However, the “well-known” complexity in solving DP poses a computational challenge even for a small number of iterations. Therefore, we propose a state-independent four-threshold $(s,S,s^{\prime},S^{\prime})$ battery charging/discharging policy and theoretically prove the optimality of the proposed energy management strategy based on stochastic inventory theory. A backward iteration algorithm is further developed to practically implement the $(s,S,s^{\prime},S^{\prime})$ feedback policy. Second, from the distribution system operator's perspective, we aim to shave the peak load and flatten the overall load profile. To this end, we propose an optimal PHEV charging scheme and further derive a reminiscent “water-filling” solution for this scenario. Realistic PHEV battery models, time-of-use electricity pricing rate, and real data of household demand are integrated into our formulated V2G system model. The theoretical analysis and proofs are instrumental to the future large-scale PHEV adoption in smart grids.

Backward iteration algorithms for Julia sets of Möbius semigroups

We extend a result regarding the Random Backward Iteration algorithm for drawing Julia sets (known to work for certain rational semigroups containing a non-Möbius element) to a class of Möbius semigroups which includes certain settings not yet been dealt with in the literature, namely, when the Julia set is not a thick attractor in the sense given in [8].

Random backward iteration algorithm for Julia sets of rational semigroups

We provide proof that a random backward iteration algorithm for approximating Julia sets of rational semigroups, previously proven to work in the context of iteration of a rational function of degree two or more, extends to rational semigroups (of a certain type). We also provide some consequences of this result.

A Simplified Methodology for Determining Optimal Location and Capacity of Solar PV Distributed Generation to Reduce Losses

This paper presents distribution load flow analysis for balanced radial system in conjunction with Solar Photo-Voltaic (PV) distributed generation. The proposed approach utilizes Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL) carried-out on forward and backward sweep iterative algorithm for the calculation of node voltages and currents flowing in radial branches. The power generated from solar PV system is determined by developing a mathematical model of solar PV modules that adopts to the Indian meteorological conditions. The distribution load flow analysis carried out by taking into the effect of this Solar PV generation. Optimal location for the distributed generation is determined by considering total system losses that can occur in 24 hours and the capacity to be installed is based on desired voltage improvement. The proposed approach has been implemented on standard 69bus radial distribution network. The simulation results obtained with and without inclusion of Solar PV generation are compared and discussed.

H ∞ control for discrete-time nonlinear Markov jump systems with multiplicative noise and sector constraint

This paper addresses the finite horizon H ∞ control problem for a class of discrete-time nonlinear Markov jump systems with multiplicative noise and nonlinear feedback device. The system nonlinearity occurs in a random way specified by a Bernoulli process, whereas the actuator and sensor nonlinearities are restricted to a sector region. Both the state and the dynamic output feedback H ∞ controllers are devised in terms of difference LMIs. The proposed approach not only allows the resulting system to achieve a prescribed disturbance attenuation level, but also enables the output of actuator/sensor to meet the designated sector condition. Moreover, it is also shown that our approach is well-adapted for dealing with the discrete-time Markov jump systems with saturated actuator and sensor. Finally, a backward iterative algorithm is provided to solve the obtained difference LMIs and a numerical example is presented to verify the efficiency of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

IMPLEMENTATION OF AN ENCRYPTED WIRELESS COMMUNICATION SYSTEM USING NESTED CHAOTIC MAPS

This paper proposes an implementation of a synchronization method for wireless communication systems using a pseudo-True Random Bit Generator (PTRBG) based on chaotic maps. Chaos is generated using Nested Piecewise Linear Maps (NPWLM) to improve the statistical degradation introduced due to finite word length processing. Synchronization of nested maps using the backward iteration algorithm is introduced. This algorithm uses a mathematically driven formula to determine the initial condition of the nested map at the receiver in order to synchronize with the map at the transmitter. The implementation test bed for the complete wireless communication system is based on a Chipcon wireless development kit [] and an assessment of the pseudo- true random bits generated is performed using the NIST statistical test suite.

3-D consistency dynamic constitutive model of concrete

Based on the consistency-viscoplastic constitutive model, the static William-Warnke model with threeparameters is modified and a consistency-viscoplastic William-Warnke model with three-parameters is developed that considers the effect of strain rates. Then, the tangent modulus of the consistency viscoplastic model is introduced and an implicit backward Elure iterative algorithm is developed. Comparisons between the numerical simulations and experimental data show that the consistency model properly provides the uniaxial and biaxial dynamic behaviors of concrete. To study the effect of strain rates on the dynamic response of concrete structures, the proposed model is used in the analysis of the dynamic response of a simply-supported beam and the results show that the strain rate has a significant effect on the displacement and stress magnitudes and distributions. Finally, the seismic responses of a 278 m high arch dam are obtained and compared by using the linear elastic model, as well as rate-independent and rate-dependent William-Warnke three-parameter models. The results indicate that the strain rate affects the first principal stresses, and the maximal equivalent viscoplastic strain rate of the arch dam. Numerical calculations and analyses reveal that considering the strain rate is important in the safety assessments of arch dams located in seismically active areas.

A GPM Dual-Frequency Retrieval Algorithm: DSD Profile-Optimization Method

Abstract A new dual-frequency precipitation radar (DPR) will be included on the Global Precipitation Measurement (GPM) core satellite, which will succeed the highly successful Tropical Rainfall Measuring Mission (TRMM) satellite launched in 1997. New dual-frequency drop size distribution (DSD) and rain-rate estimation algorithms are being developed to take advantage of the enhanced capabilities of the DPR. It has been shown that the backward-iteration algorithm can be embedded within a single-loop (SL) feedback model. However, the SL model is unable to correctly estimate DSD profiles for a significant portion of global median volume diameter Do and normalized DSD intercept parameter Nw combinations in rain because of a multiple-value solution space. For the remaining Do, Nw pairs, another retrieval method is necessary. This paper proposes a supplementary profile-optimization technique to find those DSD profiles in the rain region that the SL model cannot correctly determine. The optimization method is based on a model that both Do and log(Nw) are linear vertical profiles, and that the profiles can be found using an optimization technique from the input reflectivity profiles. Using those assumptions, the optimization method finds the top and bottom Do, log(Nw) values such that a cost function related to the input-measured reflectivity is minimized. A random-restart method is used to generate random top-and-bottom DSD seed values for each optimization cycle. Example cases are shown to demonstrate the performance with and without error in the input reflectivity profiles. Limitations of the method are discussed, including its performance when the input reflectivity profiles are based on nonlinear DSD profiles and values of shape factor μ different than the algorithm assumed value.

Extension of GPM dual-frequency iterative retrieval method with DSD-profile constraint

A new Dual-Frequency Precipitation Radar (DPR) will be included on the Global Precipitation Measurement (GPM) core satellite which will succeed the highly successful Tropical Rainfall Measuring Mission satellite launched in 1997. New dual-frequency drop-size distribution (DSD) and rain-rate estimation algorithms are being developed to take advantage of the enhanced capabilities of the DPR. It has been shown previously that a backward-iteration algorithm can be embedded within a single-loop feedback model to retrieve the rain rate. However, the single-loop model is unable to correctly estimate DSD profiles for a significant portion of global median-volume-diameter, D/sub o/, and normalized DSD intercept parameter, N/sub w/, combinations in rain because of a multiple-value solution space. For the remaining D/sub o/,N/sub w/ pairs, another retrieval method is necessary. This paper proposes a dual-loop model, in which the intercept parameter, N/sub w/, of the DSD is constrained in its vertical profile, to guide the algorithm to correct convergence. This allows an additional constraint on the DSD values estimated by the iterative algorithm and helps to retrieve correct DSD values in the regions where the iterative approach alone fails. To demonstrate feasibility of the proposed method, three test cases representative of many DSD and profile combinations are discussed. The first case is a constant vertical profile of the DSD parameters. The second case examines linear variation of the DSD parameters, and the third case examines how measurement error affects the retrieval process. In each case, the proposed constraint on the intercept parameter is implemented, and the results are discussed. Using the constraint, the dual-loop algorithm is able to retrieve reasonable values for the DSDs and rain-rate profiles and extend the convergence region of the algorithm.