On the Connections Between Stabilization, Network Routing and Receding Horizon Optimal Control Problems

The paper is devoted to a general nonlinear regulator design problem. In this context some connections between discrete version of the receding horizon control problem and the generalized network routing problem are considered. Except “standard” definition of the Lyapunov function with the help of the Bellman optimal cost-to-go function, it is shown, that the optimizing mapping corresponds to the Bellman-Ford routing algorithm. As such, it can be implemented asynchronously, e.g. in a Hopfield type neural network. The obtained routing tables will be control rules of an optimal receding horizon regulator. At the end some results of the application of this approach to an inverted pendulum control problem are presented.