This article considers distributed optimization by a group of agents over an undirected network. The objective is to minimize the sum of a twice differentiable convex function and two possibly nonsmooth convex functions, one of which is composed of a bounded linear operator. A novel distributed primal-dual fixed point algorithm is proposed based on an adapted metric method, which exploits the second-order information of the differentiable convex function. Furthermore, by incorporating a randomized coordinate activation mechanism, we propose a randomized asynchronous iterative distributed algorithm that allows each agent to randomly and independently decide whether to perform an update or remain unchanged at each iteration, and thus alleviates the communication cost. Moreover, the proposed algorithms adopt nonidentical stepsizes to endow each agent with more independence. Numerical simulation results substantiate the feasibility of the proposed algorithms and the correctness of the theoretical results.

This paper considers the problem of designing adaptive learning algorithms to seek the Nash equilibrium (NE) of the constrained energy trading game among individually strategic players with incomplete information. In this game, each player uses the learning automaton scheme to generate the action probability distribution based on his/her private information for maximizing his own averaged utility. It is shown that if one of admissible mixed-strategies converges to the NE with probability one, then the averaged utility and trading quantity almost surely converge to their expected ones, respectively. For the given discontinuous pricing function, the utility function has already been proved to be upper semicontinuous and payoff secure which guarantee the existence of the mixed-strategy NE. By the strict diagonal concavity of the regularized Lagrange function, the uniqueness of NE is also guaranteed. Finally, an adaptive learning algorithm is provided to generate the strategy probability distribution for seeking the mixed-strategy NE.

In this paper, trajectory tracking of multi-input multi-output underactuated nonlinear systems with dead-zone band and time delays is synthesized and analyzed using robust control technique based on adaptive fuzzy control. Fuzzy logic systems with online adaptations are utilized to evaluate each unknown nonlinear subsystem. It is assumed that the system includes a combined backlash and hysteresis resulting in a dead-zone band. Moreover, the gain from the delayed states and the upper bounds of the uncertainties caused by the fuzzy modeling errors are estimated online. H∞control technique is developed to overcome the effects of the slopes of the dead-zone band and external disturbances. The stability analysis and tracking performance of the closed-loop system are verified based on the Lyapunov stability theory and Ricatti inequality, such that all the states of the system are uniformly ultimately bounded. Finally, a tower crane system is used as a case study in the simulations to validate the effectiveness and robustness of the proposed control scheme.

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.