Control of nonholonomic mobile mechanical multi-agent systems under complex conditions

What is it about?

This paper studies a distributed optimal tracking control method for nonholonomic mobile mechanical multi-agent systems under complex conditions such as input constraints, the presence of both kinematic and dynamic disturbances, and uncertain interconnections. Initially, novel feed-forward control inputs are proposed to transform the inherently separate systems of kinematics and dynamics into an equivalent integrated system. Successively, an online distributed L2-bounded optimal control algorithm is designed by utilizing adaptive dynamic programming and the theory of cooperative differential graphical games. In the algorithm, a single neural network instead of three for each agent is chosen, and the online weight-tuning laws for which are designed without identifying uncertain parameters directly or indirectly. Additionally, the optimal control and worst disturbance policies are synchronously updated in only one iterative loop. It is shown that during the convergence of the value functions to the approximate optimal values when the agents perform the algorithm, overall tracking and function approximation errors are uniformly ultimately bounded. Finally, as a successful application of the study, control of the wheeled mobile multi-robot system is discussed through simulations.

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Why is it important?

- By designing novel feed-forward control inputs, the inherently separate system of kinematics and dynamics in the presence of input constraints uncertain interconnection, and both kinematic and dynamic disturbances is transformed into an equivalent integrated system. Although this transformation is based on a backstepping technique, it relaxes identification procedures for unknown functions, while the others require identifiers that make the computational complexity high. -To overcome three drawbacks of low converge speed due to using many NNs for the algorithms based on the ACD structures as mentioned in the previous page, the distributed L2-bounded optimal feedback control algorithm is proposed with only one NN for each agent. It updates online parameters in only one iterative loop without identification of unknown dynamics. Moreover, it does not any initially stable controllers. - Applying Lyapunov theory to the case of input saturation, disturbance, and uncertain interconnection, it is proven that when the agents perform the proposed algorithm, the overall tracking and function approximation errors are uniformly ultimately bounded (UUB) along with the convergence of the value functions to the approximate optimal values.