In this paper, the distributed Nash equilibrium (NE) searching problem is investigated, where the feasible action sets are constrained by nonlinear inequalities and linear equations. Different from most of the existing investigations on distributed NE searching problems, we consider the case where both cost functions and feasible action sets depend on actions of all players, and each player can only have access to the information of its neighbors. To address this problem, a continuous-time distributed gradient-based projected algorithm is proposed, where a leader-following consensus algorithm is employed for each player to estimate actions of others. Under mild assumptions on cost functions and graphs, it is shown that players' actions asymptotically converge to a generalized NE. Simulation examples are presented to demonstrate the effectiveness of the theoretical results.

This paper considers the problem of asynchronous distributed multi-agent optimization on server-based system architecture. In this problem, each agent has a local cost, and the goal for the agents is to collectively find a minimum of their aggregate cost. A standard algorithm to solve this problem is the iterative distributed gradientdescent (DGD) method being implemented collaboratively by the server and the agents. In the synchronous setting, the algorithm proceeds from one iteration to the next only after all the agents complete their expected communication with the server. However, such synchrony can be expensive and even infeasible in realworld applications. We show that waiting for all the agents is unnecessary in many applications of distributed optimization, including distributed machine learning, due to redundancy in the cost functions (or data). Specifically, we consider a generic notion of redundancy named (r, )-redundancy implying solvability of the original multi-agent optimization problem with accuracy, despite the removal of up to r (out of total n) agents from the system. We present an asynchronous DGD algorithm where in each iteration the server only waits for (any) n − r agents, instead of all the n agents. Assuming (r, )-redundancy, we show that our asynchronous algorithm converges to an approximate solution with error that is linear in and r. Moreover, we also present a generalization of our algorithm to tolerate some Byzantine faulty agents in the system. Finally, we demonstrate the improved communication efficiency of our algorithm through experiments on MNIST and Fashion-MNIST using the benchmark neural network LeNet.Preprint. Under review.

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The observer-based feedback controller of a new linear networked control system (NCS) with both delays and packet dropouts is designed when the state information is not fully available. With the effects of transmission delays, NCSs are modeled as a discrete-time system with time-varying parameter. The occurrence of packet dropouts is modeled as a Bernoulli event in the NCSs. Under certain conditions, the observer-based controller is proved to render the corresponding NCSs exponentially mean-square stable based on Lyapunov stability theorem and matrix inequality theory. Finally, numerical simulations are included to demonstrate the theoretical results.

The problem of a guaranteed cost controller design of networked control systems under transmission control protocol (TCP) is derived. To improve the overall performance of the networked control system, a scheme to simultaneously control the plant and the network is presented. An analytical TCP model is used to design active queue management (AQM) to achieve the desired queue length, which is helpful in reducing the variation of the network induced delay. Moreover, a new closed loop model of networked control systems is obtained by augmenting the TCP communication model with the control plant. The guaranteed cost controller is addressed in terms of a linear matrix inequality (LMI) to render the system asymptotically stable based on Lyapunov‐Krasovskii theory and weighted technology. Finally, numerical simulations are included to demonstrate the theoretical results.