Model-Free Optimal Consensus Control of Networked Euler-Lagrange Systems

This paper considers the model-free optimal consensus problem of networked Euler-Lagrange systems without velocity measurements. By employing the position information, a novel neural network-based velocity observer is built for each agent to estimate the unmeasurable velocity vector and unknown system model. Based on the estimated velocity information, we propose distributed optimal control policies depended on the solutions to the coupled Hamilton-Jacobi-Bellman (HJB) equations. Then, a model-free policy iteration (PI) algorithm is provided to learn the coupled HJB equations online. To implement the PI algorithm, the critic-action neural networks are built and their weights are updated based on the gradient descent method. The uniform ultimate boundedness of the integrated observer estimation errors, the integrated consensus errors, and the weight estimation errors for the observer-critic-action neural networks is demonstrated by the Lyapunov technique. Finally, the numerical simulation on a directed network with six nonlinear manipulators is presented to validate the theoretical results.