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• Firstly, a robust discrete-time non-smooth consensus protocol solves that consensus problem for the first-order leaderless multi-agent systems with external disturbance and discrete-time feedback. • Then, a discrete-time super-twisting observer is proposed to estimate the multi-agent systems disturbance. Combining the robust discrete-time non-smooth consensus protocol and discrete-time super-twisting observer, we get a new consensus protocol. The superiorities of this method contains two aspects, i.e., the disturbance rejection ability and a smaller consensus error. To the best authors' knowledge, the presented results in this paper are novel in the literature. In this paper, we firstly consider the consensus problems of first-order leaderless multi-agent systems with external disturbance. Then, we propose a robust discrete-time non-smooth (RDTNS) consensus protocol, which makes agents reach consensus within a region. Besides, we design a disturbance observer based on the discrete-time super-twisting algorithm (DTSTA), which can improve the disturbance rejection ability and decrease the consensus error for the multi-agent systems. At last, we get a robust discrete-time disturbance rejection control consensus protocol by combining the RDTNS consensus protocol with the discrete-time super-twisting observer (DTSTO). The simulation results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• We consider the constrained stochastic convex optimization by projected subgradient algorithm. • A new convergence analysis approach is developed to prove the validity of the proposed algorithm. • Convergence rate is given without specifying the gains. This paper discusses a kind of convex optimization problem considering noises from information transmission in multi-agent systems. Different from previous works, we focus on the objective function which is a summation of strictly L 0 (F) -convex functions under random inner space. Our system is described by Itô formula, which leads to that it is hard to calculate second-order derivative when designing the projected subgradient algorithm. It is shown that all states in stochastic system will converge to the unique optimal state in the polyhedric set constraint by adopting projected subgradient algorithm and the convergence rate is also investigated. Numerical examples are provided to demonstrate the results. [ABSTRACT FROM AUTHOR]

In this paper, the optimal consensus control problem with second-order dynamics consisting of leader and follower agents is discussed. For optimal consensus problem, the optimal control policies rely on algebraic Riccati equations (AREs) equation, which are difficult to solve. Furthermore, both the follower agents' and the leader agent's dynamics are assumed to be completely unknown. As the consensus problem based on feedback control, the second-order discrete-time multi-agent systems (DT-MASs) model with directed topology is formulated to the optimal tracking control problem via online deep reinforcement learning method. Based on graph theory, matrix analysis, Lyapunov stability, deep learning and optimal control, the optimality of value function and the stability of the consensus error systems for the unknown second-order systems are guaranteed for each agent. The results show that the designed policy iteration algorithm not only stabilizes the distributed dynamic systems, but also makes all agents' position and velocity states reach consensus, respectively. Finally, the correctness of our theoretical results is illustrated under two numerical simulations based on the designing model-free actor-critic networks. [ABSTRACT FROM AUTHOR]