# Passivity analysis of higher order evolutionary dynamics and population games

@article{Mabrok2016PassivityAO, title={Passivity analysis of higher order evolutionary dynamics and population games}, author={Mohamed A. Mabrok and Jeff S. Shamma}, journal={2016 IEEE 55th Conference on Decision and Control (CDC)}, year={2016}, pages={6129-6134} }

Evolutionary dynamics describe how the population composition changes in response to the fitness levels, resulting in a closed-loop feedback system. Recent work established a connection between passivity theory and certain classes of population games, namely so-called “stable games”. In particular, it was shown that a combination of stable games and (an analogue of) passive evolutionary dynamics results in stable convergence to Nash equilibrium. This paper considers the converse question of…

## 13 Citations

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This paper shows the equivalence between a constrained, multi-agent control problem, modeled within the port-Hamiltonian framework, and an exact potential game, and a network of double-integrator agents, which can be represented as a graph.

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It is shown that convergence to a Nash distribution can be attained in a broader class of games than previously considered in the literature—namely, in games characterized by the monotonicity property of their (negative) payoff vectors.

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This dissertation proposes a step-by-step approach to the design of different types of discrete-time, continuous- time, hybrid, and stochastic controllers for different type of applications, extending and generalizing different results in the literature in the area of extremum seeking control, sampled-data extremization, robust synchronization, and Stochastic learning in networked systems.

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- Computer Science2018 IEEE Conference on Decision and Control (CDC)
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This work considers an exponentially-discounted reinforcement learning scheme, and shows that convergence can be guaranteed for the class of games characterized by the monotonicity property of their (negative) payoff.

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