Leader-following consensus for lower-triangular nonlinear multi-agent systems with unknown controller and measurement sensitivities

summary:In this paper, a novel consensus algorithm is presented to handle with the leader-following consensus problem for lower-triangular nonlinear MASs (multi-agent systems) with unknown controller and measurement sensitivities under a given undirected topology. As distinguished from the existing results, the proposed consensus algorithm can tolerate to a relative wide range of controller and measurement sensitivities. We present some important matrix inequalities, especially a class of matrix inequalities with multiplicative noises. Based on these results and a dual-domination gain method, the output consensus error with unknown measurement noises can be used to construct the compensator for each follower directly. Then, a new distributed output feedback control is designed to enable the MASs to reach consensus in the presence of large controller perturbations. In view of a Lyapunov function, sufficient conditions are presented to guarantee that the states of the leader and followers can achieve consensus asymptotically. In the end, the proposed consensus algorithm is tested and verified by an illustrative example

Consensus of Multi-agent Reinforcement Learning Systems: The Effect of Immediate Rewards

This paper studies the consensus problem of a leaderless, homogeneous, multi-agent reinforcement learning (MARL) system using actor-critic algorithms with and without malicious agents. The goal of each agent is to reach the consensus position with the maximum cumulative reward. Although the reward function converges in both scenarios, in the absence of the malicious agent, the cumulative reward is higher than with the malicious agent present. We consider here various immediate reward functions. First, we study the immediate reward function based on Manhattan distance. In addition to proposing three different immediate reward functions based on Euclidean, $n$-norm, and Chebyshev distances, we have rigorously shown which method has a better performance based on a cumulative reward for each agent and the entire team of agents. Finally, we present a combination of various immediate reward functions that yields a higher cumulative reward for each agent and the team of agents. By increasing the agents’ cumulative reward using the combined immediate reward function, we have demonstrated that the cumulative team reward in the presence of a malicious agent is comparable with the cumulative team reward in the absence of the malicious agent. The claims have been proven theoretically, and the simulation confirms theoretical findings

Robust neurooptimal control for a robot via adaptive dynamic programming

We aim at the optimization of the tracking control of a robot to improve the robustness, under the effect of unknown nonlinear perturbations. First, an auxiliary system is introduced, and optimal control of the auxiliary system can be seen as an approximate optimal control of the robot. Then, neural networks (NNs) are employed to approximate the solution of the Hamilton-Jacobi-Isaacs equation under the frame of adaptive dynamic programming. Next, based on the standard gradient attenuation algorithm and adaptive critic design, NNs are trained depending on the designed updating law with relaxing the requirement of initial stabilizing control. In light of the Lyapunov stability theory, all the error signals can be proved to be uniformly ultimately bounded. A series of simulation studies are carried out to show the effectiveness of the proposed control

Bayesian estimation of human impedance and motion intention for human-robot collaboration

This article proposes a Bayesian method to acquire the estimation of human impedance and motion intention in a human-robot collaborative task. Combining with the prior knowledge of human stiffness, estimated stiffness obeying Gaussian distribution is obtained by Bayesian estimation, and human motion intention can be also estimated. An adaptive impedance control strategy is employed to track a target impedance model and neural networks are used to compensate for uncertainties in robotic dynamics. Comparative simulation results are carried out to verify the effectiveness of estimation method and emphasize the advantages of the proposed control strategy. The experiment, performed on Baxter robot platform, illustrates a good system performance