Title: Decentralized Tube-based Model Predictive Control of Uncertain Nonlinear Multi-Agent Systems,
Abstract: This paper addresses the problem of decentralized tube-based nonlinear Model
Predictive Control (NMPC) for a class of uncertain nonlinear continuous-time
multi-agent systems with additive and bounded disturbance. In particular, the
problem of robust navigation of a multi-agent system to predefined states of
the workspace while using only local information is addressed, under certain
distance and control input constraints. We propose a decentralized feedback
control protocol that consists of two terms: a nominal control input, which is
computed online and is the outcome of a Decentralized Finite Horizon Optimal
Control Problem (DFHOCP) that each agent solves at every sampling time, for its
nominal system dynamics; and an additive state feedback law which is computed
offline and guarantees that the real trajectories of each agent will belong to
a hyper-tube centered along the nominal trajectory, for all times. The volume
of the hyper-tube depends on the upper bound of the disturbances as well as the
bounds of the derivatives of the dynamics. In addition, by introducing certain
distance constraints, the proposed scheme guarantees that the initially
connected agents remain connected for all times. Under standard assumptions
that arise in nominal NMPC schemes, controllability assumptions as well as
communication capabilities between the agents, we guarantee that the
multi-agent system is ISS (Input to State Stable) with respect to the
disturbances, for all initial conditions satisfying the state constraints.
Simulation results verify the correctness of the proposed framework.