Finite-horizon Approximate Optimal Consensus Control for Discrete-time Nonlinear Multi-Agent Systems with Unknown Dynamics

In this paper, a finite-horizon optimal control scheme is studied to realize consensus of nonlinear multi-agent systems (MAS) by using adaptive dynamic programming (ADP). By introducing an extra compensator, an augmented error system is obtained to circumvent the requirement of system dynamics. An optimal consensus control parameter is obtained by using iterative ADP algorithm, which not only makes the cost function close to the optimal value but also drives MAS realize consensus. Several properties of the finite-horizon iterative algorithm are proved theoretically. Then, the action network and the critic network are introduced to realize the proposed algorithm. The critic network approximates the cost function and the control parameter is constructed by action network. Finally, a simulation example is given to verify the effectiveness of the control scheme proposed in this paper.