Receding Horizon Control of a two-agent system with competitive objectives

We consider the problem of controlling two dynamically decoupled agents which can cooperate or compete. Agents are modelled as linear discrete time systems, and collect each other´s state information without delays. Control actions are computed using a Receding Horizon framework, where each agent´s controllers are computed by minimizing a linear, quadratic cost function which depends on both agents´ states. Cooperation or competition is specified throught the state tracking objectives of each agent. We do not consider state constraints. The simplicity of our framework allows us to provide the following results analytically: 1) When agents compete, their states converge to an equilibrium trajectory where the steady state tracking error is finite. 2) Limit-cycles cannot occur. Numerical simulations and experiments done with a LEGO Mindstorm multiagent platform match our analytical results.