A Neighboring Extremal Solution for Optimal Switched Impulsive Control Problems with Large Perturbations

This paper presents an approach to compute the neighboring extremal solution for an optimal switched impulsive control problem with a pre-specified sequence of modes and a large perturbation in the initial state. The decision variables – the subsystem switching times and the control parameters – are subject to inequality constraints. Since the active status of these inequality constraints may change under the large perturbation, we add fractions of the initial perturbation separately such that the active status of the inequality constraints is invariant during each step, and compute the neighboring extremal solution iteratively by solving a sequence of quadratic programming problems. First, we compute a correction direction for the control in the perturbed system through an extended backward sweep technique. Then, we compute the maximal step size in this direction and derive the solution iteratively by using a revised active set strategy. An example problem involving a shrimp harvesting operation demonstrates that our solution approach is faster than the sequential quadratic programming approach.