Optimal control via weighted congestion game with linear cost functions

This paper considers the optimal control via weighted congestion game with linear cost functions. First, the weighted congestion game is converted into a matrix form for the sake of simplicity of computation. Second, a system performance criteria is proposed in order to minimize individual cost, and by designing proper parameters of linear cost functions, the given system performance criterion is converted into weighted potential function of a weighted congestion game. Then the profile dynamics is expressed into an algebraic form and potential-based stability of weighted congestion game is considered by using the Lyapunov-based approaches. Finally, an example is given to illustrate the theoretical results.