A Boolean network consists of a set of Boolean variables whose state is determined by other variables in the network. Boolean networks have been studied extensively as models for simple artificial neural networks. Recently, Boolean networks gained considerable interest as models for biological systems composed of elements that can be in one of two possible states. Examples include genetic regul...

We present a generalization of the Pontryagin Maximum Principle, in which the usual adjoint equation, which contains derivatives of the system vector fields with respect to the state, is replaced by an integrated form, containing only differentials of the reference flow maps. In this form, the conditions of the maximum principle make sense for a number of control dynamical laws whose right-hand...

This paper develops a reduction theory for Dirac structures that includes in a unified way, reduction of both Lagrangian and Hamiltonian systems. It includes the reduction of variational principles and in particular, the Hamilton–Pontryagin variational principle. It also includes reduction theory for implicit Lagrangian systems that could be degenerate and have constraints. In this paper we foc...

<p style='text-indent:20px;'>Due to the propagation of new coronavirus (COVID-19) on community, global researchers are concerned with how minimize impact COVID-19 world. Mathematical models effective tools that help prevent and control this disease. This paper mainly focuses optimal problems an epidemic system governed by a class singular evolution equations. The mild solutions such equat...

We study an optimal control problem arising from a resource allocation problem in cellular metabolism. A minimalistic model that describes the production of enzymatic vs. non-enzymatic biomass components from a single nutrient source is introduced. The basic growth modes with this model are linear growth, where only the non-enzymatic component is produced, and exponential growth with only enzym...

Abstract. A basic idea of the classical approach for obtaining necessary optimality conditions in optimal control is to construct suitable “needle-like control variations.” We use this idea it to prove the main result of the present paper—a Pontryagin maximum principle for infinite-dimensional optimal control problems with pointwise terminal constraints in arbitrary Banach state space. By refin...

We consider scheduling data tra c for the downlink of a wireless network A draining problem is formulated where the goal is to transmit a given set of packets Each packet is assigned a utility that depends on the delay incurred We propose a simple gradient based scheduling rule which attempts to maximize the average utility per packet A deterministic analysis of this rule is given by considerin...