Impulsive control problems with state constraints

In this chapter, in the context of the impulsive extension of the optimal control problem, the state constraints are studied. That is, it is assumed that a certain closed subset of the state space is given while feasible arcs are not permitted to take values outside of it. This set is defined functionally in our considerations. It should be noted that the state constraints are in great demand in various engineering applications. For example, an iRobot cleaning a house should be able to avoid obstacles or objects that arise in its path. These obstacles are nothing but state constraints, while the task of avoiding the obstacle represents an important class of problems with state constraints. Evidently, there is a host of other engineering problems, in which the state constraints play an important role. The chapter deals with the same problem formulation as in the previous chapter; however, the state constraints of the above type are added. For this impulsive control problem, the Gamkrelidze-like maximum principle is obtained. Conditions for nondegeneracy of the maximum principle are presented. The chapter ends with eight exercises. © 2019, Springer Nature Switzerland AG.