Trajectory Approximation Near The Stability Boundary

Uncertain parameters impact the dynamic behaviour of many important nonlinear systems. Assessing the significance of parameter uncertainty is often vitally important, but traditional techniques are computationally challenging. A recent approach uses trajectory sensitivities to form a first-order approximation of perturbed trajectories. These approximate trajectories are generally quite accurate, though their quality reduces in the vicinity of the stability boundary. The paper proposes a modification that improves the accuracy of sensitivity-based approximations of marginally-stable trajectories. This modified approach generates approximate trajectories by considering the intersection of the perturbed trajectory with a hyperplane that progresses with the nominal trajectory.