Cooperative Coevolutionary Algorithm-Based Model Predictive Control Guaranteeing Stability of Multirobot Formation

Abstract

This paper proposes a novel cooperative coevolutionary algorithm (CCEA)-based distributed model predictive control (MPC) that guarantees asymptotic stability of multiagent systems whose state vectors are coupled and nonseparable in a cost function. While conventional evolutionary algorithm-based MPC approaches cannot guarantee stability, the proposed CCEA-based MPC approach guarantees asymptotic stability regardless of the optimality of the solution that the CCEA-based algorithm generates with a small number of individuals. To guarantee stability, a terminal state constraint is found, and then a repair algorithm is applied to all candidate solutions to meet the constraint. Furthermore, as the proposed CCEA-based algorithm finds the Nash-equilibrium state in a distributed way, robots can quickly move into a desired formation from their locations. A novel dynamic cooperatively coevolving particle swarm optimization (CCPSO), dynamic CCPSO (dCCPSO) in short, is proposed to deal with the formation control problem based on the conventional CCPSO, which was the most recently developed algorithm among CCEAs. Numerical simulations and experimental results demonstrate that the CCEA-based MPC greatly improves the performance of multirobot formation control compared with conventional particle swarm optimization-based MPC.