Distributed Model-Predictive Control Using Exponentially Weighted Laguerre Functions and Periodic Time Triggering for Dynamic Consensus of Linear Multiagent Systems

Model-predictive control (MPC) is becoming increasingly popular in addressing the consensus problem of multiagent systems (MASs) due to its ability to manage constraints in a multivariable control framework and to perform online optimization. However, in order to achieve the desired closed-loop performance, longer prediction and control horizons are essential for conventional MPC. This increases the computational complexity and causes the numerical instability of the optimization problem. This concern is addressed in this article by introducing an exponential-data-weighted Laguerre-based control design that minimizes computational burden, improves numerical conditioning, and provides a specified degree of closed-loop stability of the MAS. The proposed design, which incorporates an embedded integrator model, rejects constant disturbances, avoiding the need for a separate disturbance model. Furthermore, periodic time-triggered control is incorporated with the consensus algorithm, enabling a relaxation in the overusage of resources. An explicit formula for computing the upper bound of triggering interval is also derived. The proposed algorithm outperforms current methods in terms of numerical conditioning, stability margins, and rejection of deterministic disturbances. The validation of the proposed strategy is performed through the simulation of dynamic consensus on a cluster of grounded vehicles.