Leader-Following Consensus for T-S Fuzzy Positive Multi-Agent Systems: A Model Prediction Control Approach

This paper addresses the leader-following consensus problem for T-S fuzzy positive multi-agent systems using a model predictive control (MPC) approach. First, a positive multi-agent system model with a leader-follower structure is formulated via the T-S fuzzy modeling approach. Considering that the states of agents are not fully measurable, positive observers and distributed T-S fuzzy controllers are designed to achieve leader-follower consensus. The main contributions of this work lie in the development of a novel MPC framework, which integrates a linear performance index, a co-positive Lyapunov function, and a linear programming solution technique. It has a simpler form and lower computational burden than existing methods based on quadratic indices and functions. Within this framework, an MPC algorithm is proposed to solve the min-max optimization problem associated with the performance index. Furthermore, the gain matrices for both the observer and the controller are systematically derived using a matrix decomposition technique. In view of a co-positive Lyapunov function, the positivity and consensus of the T-S fuzzy positive multi-agent system are rigorously proved under the proposed MPC strategy. Finally, an example is given to verify the effectiveness of the MPC design.