This paper is an attempt to give sufficient conditions for a bang-bang extremal with multiple switches to be locally optimal in the strong topology. The conditions are the natural generalizations of the ones considered in [2, 3] and [4]. We require both the strict bang-bang Legendre condition, which takes a different form according to the multiplicity of the considered switching time, a non deg...

Abstract: It has been suggested by many supply chain practitioners that in certain cases inventory can have a stimulating effect on the demand. In mathematical terms this amounts to the demand being a function of the inventory level alone. In this work we propose a logistic growth model for the inventory dependent demand rate and solve first the continuous time deterministic optimal control pro...

Due to the nonlinear nature of the Bang-Bang phase-locked loops (BBPLLs), its transient analysis is very difficult. In this paper, new equations are proposed for expression of transient behavior of the second order BBPLLs to phase step input. This approach gives new insights into the transient behavior of BBPLLs. Approximating transient response to reasonable specific waveform the loop tran...

This paper gives sufficient conditions for a class of bang-bang extremals with multiple switches to be locally optimal in the strong topology. The conditions are the natural generalizations of the ones considered in [5, 14] and [16]. We require both the strict bang-bang Legendre condition, and the second order conditions for the finite dimensional problem obtained by moving the switching times ...

This article deals with bang-bang solutions of linear time-optimal control problems. Linear multivariable systems are considered which have one or more control components. It is shown in which way the control components act together to make the system achieve the ultimate aim (namely, the origin in the state space) as quickly as possible. The theory only applies to initial positions sufficientl...

In the article, Tikhonov regularization of control-constrained optimal control problems is investigated. Typically the solutions of such problems exhibit a so-called bang-bang structure. We develop a parameter choice rule that adaptively selects the Tikhonov regularization parameter depending on a-posteriori computable quantities. We prove that this choice leads to optimal convergence rates wit...

This paper gives sufficient conditions for a class of bang-bang extremals with multiple switches to be locally optimal in the strong topology. The conditions are the natural generalizations of the ones considered in [5, 13] and [16]. We require both the strict bang-bang Legendre condition, and the second order conditions for the finite dimensional problem obtained by moving the switching times ...

Phenological changes among plants due to climate change are well documented, but often hard to interpret. In order to assess the adaptive value of observed changes, we study how annual plants with and without growth constraints should optimize their flowering time when productivity and season length changes. We consider growth constraints that depend on the plant's vegetative mass: self-shading...

The fact that the time optimal controls for parabolic equations have the bang–bang property has been recently proved for controls distributed inside the considered domain (interior control). The main result in this article asserts that the boundary controls for the heat equation have the same property, at least in rectangular domains. This result is proved by combining methods from traditionall...

We study the minimal-time problem for a piecewise affine bistable switch. Motivated by applications in synthetic biology and biotechnology, aim is to minimize time needed this system achieve transitions between its two stable steady states. The latter represents possible states of genetic toggle switch, flip-flop device playing fundamental role biocomputing gene therapy. Results show that time-...