Finite horizon distributed optimal tracking control of multi-agent systems in presence of completely unknown dynamics

In this paper, a novel time-based finite horizon distributed optimal tracking control is proposed for multi-agent systems with completely unknown system dynamics. First, the distributed optimal tracking control problem has been formulated for multi-agent systems. Next, an online Neural Network (NN) identifier is introduced to approximate the control coefficient matrices of multi-agent systems which is subsequently utilized to develop distributed optimal tracking control inputs. Then, in order to achieve the optimality and satisfy the terminal cost at the fixed final time, a novel actor-critic scheme is proposed to determine the time-based finite horizon distributed optimal tracking control in a forward-in-time manner by using critic NN and actor NN efficiently. Eventually, Lyapunov theory is used to demonstrate that all closed-loop signals and NN weights are uniformly ultimately bounded (UUB) with ultimate bounds being a function of initial conditions and fixed final time. Further, the approximated distributed control signal converges close to theoretical distributed optimal value within fixed final time even while the multi-agent systems dynamics are completely unknown. Multiple-agent systems tracking example is included in simulation section to show the effectiveness of the proposed scheme.