In this technical correspondence, we consider a distributed cooperative optimization problem encountered in a computational multiagent network with delay, where each agent has local access to its convex cost function, and jointly minimizes the cost function over the whole network. To solve this problem, we develop an algorithm that is based on dual averaging updates and delayed subgradient information, and analyze its convergence properties for a diminishing step-size by utilizing Bregman-distance functions. Moreover, we provide sharp bounds on the convergence rates as a function of the network size and topology embodied in the inverse spectral gap. Finally, we present a numerical example to evaluate our algorithm and compare its performance with several similar algorithms.

Reinforcement learning (RL) is essential for the computation of game equilibria and the estimation of payoffs under incomplete information. However, it has been a challenge to apply RL-based algorithms in the energy trading game among smart microgrids where no information concerning the distribution of payoffs is a priori available and the strategy chosen by each microgrid is private to opponents, even trading partners. This paper proposes a new energy trading framework based on the repeated game that enables each microgrid to individually and randomly choose a strategy with probability to trade the energy in an independent market so as to maximize his/her average revenue. By establishing the relationship between the average utility maximization and the best strategy, two learning-automaton-based algorithms are developed for seeking the Nash equilibria to accommodate the variety of situations. The novelty of the proposed algorithms is related to the incorporation of a normalization procedure into the classical linear reward-inaction scheme to provide a possibility to operate any bounded utility of a stochastic character. Finally, a numerical example is given to demonstrate the effectiveness of the algorithms.

An innovative method proposed for encrypting color images is comprised of one-time keys and chaos theory using a distinctive concept of rotor machine. The novelty of this scheme is that the rows and columns of 2-dimensional images are converted into circular object called rotor and can be rotated at 360 degrees in clockwise or anti clockwise direction. The rotation will change the existing rotor into new one and can be used in substitution process of plain image. This process can be repeated β times and each time a new rotor is created just by a simple rotation. The rotation is performed in terms of pixels so degree of angle is converted into number of pixels. Using this method, same object with new face (after rotation) is used for encryption. The pixels of color image are permuted using the sorted index of logistic sequence. Then, three pseudo-random images are created from Piecewise Linear Chaotic Map (PWLCM). For substitution, both the permuted color channels and pseudo-random images are transformed into rotors. The angle is obtained from Chen chaotic system. The one-time keys are for chaotic maps are generated by using 512-bits hash of plain image. The simulated outcomes demonstrate that the proposed system has high quality of results and requires only single round of encryption to achieve high encryption along with high robustness against the transmission noises.