A controller synthesis setting for systems with controlled singularities under incomplete information is extended to the cases characterized by a constraint on the total physical impulse as well as on the time interval between the adjacent engagement phases. The use of this setting for the optimal control law calculation is illustrated on the ball/racket system representative of a large class of controlled impact problems, where there are two separate bodies interacting through controlled viscoelastic force.
Bentsman, J., Miller, B., Rubinovich, E., & Mazumder, S. K. (2012). Modeling and control of systems with active singularities under energy constraints: single- and multi-impact sequences. IEEE Transactions on Automatic Control, 57(7), 1854 - 1859. https://doi.org/10.1109/TAC.2012.2186401