Optimal Impulsive Control Problem with Application to Human Immunodeficiency Virus Treatment

A class of impulsive differential variational inequalities in finite dimensional spaces

“…The impulse effects occur in a host of dynamic problems such as, physics, population dynamics, ecology, industrial robotic, pharmacokinetics, optimal control (see, for example, [1,4,21,22,30,33]). …”

“…It is known that a prey-predator system and a Human Immunodeficiency Virus (HIV) treatment problem can be formulated as an impulsive differential equation with impulses at fixed time (see, for example, [20,21] and the references therein).…”

Infinite horizon optimal impulsive control with applications to Internet congestion control

“…For example many control problems in queueing theory, population dynamics, mathematical epidemiology, financial mathematics etc can be formulated as the impulsively controlled systems: see Hordijk and van der Duyn Schouten (1983), Hou and Wong (2011), Korn (1999), Palczewski and Stettner (2007), Piunovskiy (2004), Xiao et al (2006) and the references therein. Roughly speaking, an impulse (or intervention) means the instant change of the state of the system.…”

“…Nevertheless, it is possible to adjust the dynamic programming method for such models: see Bardi and Capuzzo-Dolcetta (1997), Bensoussan and Lions (1984), Christensen (2014), Davis (1993), Motta and Rampazzo (1996), Yushkevich (1989). The Pontryagin maximum principle (or the closely related Lagrangian approach) can also be used for solving impulsive optimal control problems: see Dufour and Miller (2007), Hou and Wong (2011), Miller and Rubinovich (2003), Taringoo and Caines (2013), Xiao et al (2006).…”

“…In the current paper, we consider deterministic models similar to those investigated in Bardi and Capuzzo-Dolcetta (1997), Hou and Wong (2011), Miller and Rubinovich (2003), Motta and Rampazzo (1996), Taringoo and Caines (2013), Xiao et al (2006). Note that in Hou and Wong (2011), Miller and Rubinovich (2003), Motta and Rampazzo (1996), Taringoo and Caines (2013) only the finite-horizon case was studied.…”