High Confidence Sets for Trajectories of Stochastic Time-Varying Nonlinear Systems

We analyze stochastic differential equations and their discretizations to derive novel high probability tracking bounds for exponentially stable time varying systems which are corrupted by process noise. The bounds have an explicit dependence on the rate of convergence for the unperturbed system and the dimension of the state space. The magnitude of the stochastic deviations have a simple intuitive form, and our perturbation bounds also allow us to derive tighter high probability bounds on the tracking of reference trajectories than the state of the art. The resulting bounds can be used in analyzing many tracking control schemes.