In this paper, we consider a class of optimal control problems in which the dynamical system involves a finite number of switching times together with a state jump at each of these switching times. The locations of these switching times and a parameter vector representing the state jumps are taken as decision variables. We show that this class of optimal control problems is equivalent to a special class of optimal parameter selection problems. Gradient formulas for the cost functional and the constraint functional are derived. On this basis, a computational algorithm is proposed. For illustration, a numerical example is included.
Liu, Y., Teo, K. L., Jennings, L., & Wang, S. (1998). On a class of optimal control problems with state jumps. Journal of Optimization Theory and Applications, 98(1), 65-82. https://doi.org/10.1023/A:1022684730236