Combinatorial problem arising in chaotic control (Q1886200)

For nonlinear discrete time control systems, the problem to reach a given subset of the state space is considered when an optimality criterion involving the states and the controls is satisfied. A discretization of the state space leads to a discrete optimization problem on a directed graph. Then a variant of Dijkstra's algorithm is used to compute the set of Pareto optima. The complexity of this optimization problem is analyzed. Two numerical experiments are documented.