Necessary conditions of optimality for vector-valued impulsive control problems

Invariance for impulsive control systems

“…We adopt the concept of solution introduced in [2,24] modified in order to accommodate the unbounded time interval [0, ∞). Robustness is one of the key features of this concept.…”

“…This explains why a considerable body of theory for this class of systems (see, for example, [1,2,[8][9][10][11][12][13][14][15][16][17][18][19], and references therein) and supporting control strategies computation schemes, [20][21][22][23] have been developed so far.…”

Hamilton-Jacobi Conditions for an Impulsive Control Problem

“…Dynamic optimization problems arising in a variety of application areas such as finance, mechanics, resources management, and space navigation, (see, for example, (Brogliato, 1996), (Clark, Clarke, Munro, 1979), (DalMaso, Rampazzo, 1991), (Lawden, 1963), and (Marec, 1979)) whose solutions might involve discontinuous trajectories have been, over the years, motivating a significant research effort on the so-called Impulsive Control Problem (for a selected set of references see (Pereira, Silva, 2000) and references therein).…”

“…However, now, we consider vector valued measures without assuming commutativity of the singular vector field, similarly to the problem addressed in (Pereira, Silva, 2000). In this new context, the concept of proper solution is presented.…”

Invariance for impulsive control systems

“…A key role is played by the adopted solution concept (see, for example, [1,2], for finite time problems) which implies that any jump of a well defined solution to the measure-driven differential inclusion has to be such that there exists a path joining its endpoints that satisfies the singular dynamics. In this article, we consider an infinite time horizon version of this solution concept.…”