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This paper concerns an optimal control problem defined on a class of switched-mode hybrid dynamical systems. The system's mode is changed (switched) whenever the state variable crosses a certain surface in the state space, henceforth called a switching surface. These switching surfaces are parameterized by finite-dimensional vectors called the switching… (More)

The problem of optimal switching of a multi-mode time delay system is considered. The class of multi-mode systems consists of systems where the control variables are the switching times in a sequence of fixed vector fields. We assume that the systems considered all have a refractory period, in the sense that once an action is taken, it takes a… (More)

— This paper introduces a new model for disease outbreaks. This model describes the disease evolution through a system of nonlinear differential equations with distributed-delay. The main difference between classical SIR-model resides in the fact that the recovery rate of the population is expressed as a distributed-delay term modeling the time spent being… (More)

— This paper investigates the problem of controlling epidemics through different vaccination strategies. A simple, constant vaccination rate is considered initially, followed by a more elaborate model, incorporating realistic delay effects. Recent results on optimal impulsive control for delay systems are used to determine a pulse vaccination strategy for… (More)

The optimal impulsive control problem for a system with a single discrete delay is studied. In such systems the control consists only of a sequence of modulated impulses, the control variables being the impulse times and their magnitudes. It is assumed that the systems considered all have a refractory period, in the sense that once an action is taken, it… (More)

In this paper a balanced realization for a smooth nonlin-ear system is defined. The approach is distinct from other notions of nonlinear balancing that appear in the literature and may be more computationally attractive since it avoids the need to compute the state transition matrix. 1. Introduction In this paper a balanced realization for a smooth… (More)