Fuzzy adaptive dynamic programming-based optimal leader-following consensus for heterogeneous nonlinear multi-agent systems

In this paper, a novel online iterative scheme, based on fuzzy adaptive dynamic programming, is proposed for distributed optimal leader-following consensus of heterogeneous nonlinear multi-agent systems under directed communication graph. This scheme combines game theory, adaptive dynamic programming together with generalized fuzzy hyperbolic model (GFHM). Firstly, based on precompensation technique, an appropriate model transformation is proposed to convert the error system into augmented error system, and an exquisite performance index function is defined for this system. Secondly, on the basis of Hamilton–Jacobi–Bellman (HJB) equation, the optimal consensus control is designed and a novel policy iteration (PI) algorithm is put forward to learn the solutions of the HJB equation online. Here, the proposed PI algorithm is implemented on account of GFHMs. Compared with dual-network model including critic network and action network, the proposed scheme only requires critic network. Thirdly, the augmented consensus error of each agent and the weight estimation error of each GFHM are proved to be uniformly ultimately bounded, and the stability of our method has been verified. Finally, some numerical examples and application examples are conducted to demonstrate the effectiveness of the theoretical results.