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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 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.

In this paper we address the problem of exploitingthe distributed energy resources (DER) available in a smartmicro-grid to minimize the power distribution losses via optimalreactive power compensation. Due to their typically smallsize, the amount of reactive power provided by each micro-generator is subject to tight saturation constraints. As aconsequence, it might be impossible to achieve convergence tothe global optimum based on algorithms that rely on short-range, gossip-type communication. We therefore propose arandomized multi-hop protocol that guarantees convergence ofthe distributed optimization algorithm also when only short-range communications are possible, at the expense of someadditional communication overhead.