Discrete Laguerre-based model predictive control for dynamic consensus of a vehicle platoon with time delay

Dynamic consensus of linear time-invariant multi-agent systems (MASs) using distributed model predictive control under the influence of input delay is addressed in this technical note. Model predictive control (MPC) is well suited to solve the consensus problem with its ability to handle multivariable systems and constraints. However, the increased computational complexity of MPC restricts its area of applications. An attempt to bridge this gap is made by proposing a Laguerre-based MPC design to bring down the computational load and make it viable for implementation. The effect of input delay on consensus is examined and the stability margin of a MAS with input delay is computed using the location of the closed-loop poles. A comparison of the proposed algorithm with conventional MPC establishes its superiority in convergence time, robustness to input delay and smoothness of the trajectories. The effectiveness of the proposed design is validated through the simulation of dynamic consensus on the benchmark problem of platoon configuration of vehicles.Abbreviations DLQR: discrete linear quadratic regulator; DMPC: distributed model predictive control; LMI: linear matrix inequality; LTI: linear time invariant; SISO: single-input single-output; MAS: multi-agent system; MIMO: multi-input multi-output; MPC: model predictive control