A New Developed Q‐Learning Algorithm for Consensusability Problem of Model Unavailable Multi‐Agent System via Modified Riccati Design

ABSTRACT This paper solves the consensusability problem of the model unavailable discrete‐time single‐input multi‐agent system (MAS) over directed graphs by the modified Riccati design method. Firstly, a new iterative method is proposed to solve the modified algebraic Riccati equation (MARE) for synthesizing the stabilized feedback control gain which permits an arbitrary selection of the initial values. Then, the maximum guaranteed gain margin (GGM) yielded by the feedback control gain is rigorously derived for the first time and used to establish the necessary and sufficient condition for consensusability of the MAS. Furthermore, it is proved that in the sense of the radial projection, the maximum GGM is completely independent of the characteristic parameter of the MARE and identical to that of the standard discrete‐time algebraic Riccati equation (DARE). Benefit from the structure of the developed method, the Q‐Learning (QL) algorithm is employed to establish the consensusability criterion and implement the distributed design when the system model is entirely unavailable. Finally, the effectiveness of the proposed theoretical result and developed algorithm is verified by the numerical simulation.