Optimal Leader-following Consensus of Nonlinear Heterogeneous Multi-agent Systems with Input Constraints

This paper investigates the optimal leader-following consensus for nonlinear heterogeneous multi-agent systems, namely, the dynamics of all agents including followers and one leader are different. Essentially different from the existing related literature, the protocol for each follower is restricted by a pre-specified constant. This makes the classical quadratic cost function inapplicable, from which an unconstrained protocol for each follower is obtained. To derive the optimal constrained protocol, this paper adopts a nonquadratic functional, which takes the constraints of the protocol into consideration. First of all, an augmented system consisting of the consensus error and the leader's dynamics is constructed, and the corresponding augmented discounted cost function is given. Then, based on the augmented system, an augmented Hamilton-Jacobi-Bellman equation is derived, by which the optimal protocol is obtained. Furthermore, an algorithm of solving the nonlinear Hamilton-Jacobi-Bellman equation is given.