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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)
— 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)
The dynamics of hybrid systems with mode dynamics of different dimensions is described. The first part gives some deterministic examples of such multi-mode multi-dimensional (M 3 D) systems. The second part considers such models under sequential switching at random times. More specifically, the backward Kolmogorov equation is derived, and Lie-algebraic(More)
— In this paper, we study hybrid models that not only undergo mode transitions, but also experience changes in dimensions of the state and input spaces. An algorithmic framework for the optimal control of such Multi-Mode, Multi-Dimension (or M 3 D) systems is presented. We moreover derive a detailed M 3 D model for an ice-skater, and demonstrate the use of(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)