Decentralized Dynamic Output Feedback Controller Design for Consensus in Multi-agent system of Single Link Manipulators with Flexible Joint

In this paper, a novel method for solving consensus problem in a multi agent system consisting of single link manipulators with flexible joint is presented. This method is based on linear matrix inequalities and the objective is to design a dynamic fixed order controller that can fulfill consensus by using output feedback information and Laplacian Matrix of the network of manipulators. The exact model of a single Link manipulator is assumed thus a nonlinear Lipchitz term emerges. Each manipulator as an agent in the corresponding network obtains only its neighbors output information therefore the controller is decentralized. To guarantee consensus in this method, first the multi agent system should become one augmented system. Then, based on considered conditions on nonlinear terms, using appropriate structure conversion is necessary. The unknown controller state space matrices of the closed loop system can be achieved by using Lyapunov stability theorem. Applying special conditions on symmetric positive definite matrix in Lyapunov quadratic function, results in an LMI form, thus iterative methods of solving nonlinear matrix inequalities with less accuracy is prevented. Finally, to demonstrate the effectiveness of this algorithm and compare with similar earlier researches, a numerical example on a multi agent system consisting of three single link flexible manipulators is investigated.