Receding Horizon Control of Multiagents Systems with Competitive Dynamics

To my parents iv v"Questo controllo è un pò nervoso..." vi We consider the problem of controlling two agents with competitive objectives. Agents are modelled as linear discrete time systems, and collect each other’s state information without delays. The competitive problem is formulated in a classical receding horizon framework, where each agent’s controllers are computed by minimizing a linear, quadratic cost function which depends on both agents ’ states. The two agents specify their state tracking objective in a coordinated or competitive manner. 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