A soft-constrained optimization approach for model predictive control of multi-agent systems

In a non-cooperative multi-agent system (MAS), the agents which are self-interested will compete for common but limited resources. The competition leads to coupling constraints between the agents. It is possible that no feasible solutions can be found when treating such constraints as hard constraints. In this paper, a soft-constrained optimization approach is proposed to address this infeasibility problem. Auxiliary variables are introduced to relax the coupling constraints and the relaxation is penalized by a combination of a linear and a quadratic term in the objective function of each agent. Each agent uses model predictive control to derive its optimal strategy which will be provided to the neighboring agents as a reference. Based on the reference information, the neighboring agents derive their strategies for the future. A MAS with two unmanned aerial vehicles is used to demonstrate the scope of the proposed approach.