George P. Papavassilopoulos

Ioannis Kordonis, Petros Maragos, George P. Papavassilopoulos

We study Max-Product and Max-Plus Systems with Markovian Jumps and focus on stochastic stability problems. At first, a Lyapunov function is derived for the asymptotically stable deterministic Max-Product Systems. This Lyapunov function is then adjusted to derive sufficient conditions for the stochastic stability of Max-Product systems with Markovian Jumps. Many step Lyapunov functions are then used to derive necessary and sufficient conditions for stochastic stability. The results for the Max-Product systems are then applied to Max-Plus systems with Markovian Jumps, using an isomorphism and almost sure bounds for the asymptotic behavior of the state are obtained. A numerical example illustrating the application of the stability results on a production system is also given.

Athanasios-Rafail Lagos, George P. Papavassilopoulos

A social choice procedure is modeled as a repeated Nash game between the social agents, who are communicating with each other through a social communication network modeled by an undirected graph. The agents' criteria for this game are describing a trade off between self-consistent and manipulative behaviors. Their best response strategies are resulting in two dynamics rules, one for the agents' opinions and one for their actions. The stability properties of these dynamics are studied. In the case of instability, the stabilization of these dynamics through the design of the network topology is formulated as a constrained integer programming problem. The constraints have the form of a Bilinear Matrix Inequality (BMI), which is known to result in a nonconvex feasible set in the general case. To deal with this problem a Genetic Algorithm is designed. Finally, simulations are presented for several different initial topologies and conclusions are derived concerning both the functionality of the algorithm and the advisability of the problem formulation.