In this paper we use an optimal control approach to analyze time dependent enzyme concentrations that minimize the transition time of a metabolic pathway while respecting the natural constraints imposed by a limited biosynthetical capacity. Our main result states that, under appropriate assumptions, at each time instant all the available enzyme production capacity is allocated to a single react...

The rapid growth of space utilization requires extensive construction, and maintenance of space structures and satellites in orbit. &#10This will, in turn, substantiate application of robotic systems in space. In this paper, a near-minimum-time optimal control law is developed for a rigid space platform with flexible links during an orientating maneuver with large angle of rotation. The time op...

The rapid growth of space utilization requires extensive construction, and maintenance of space structures and satellites in orbit. This will, in turn, substantiate application of robotic systems in space. In this paper, a near-minimum-time optimal control law is developed for a rigid space platform with flexible links during an orientating maneuver with large angle of rotation. The time opti...

We provide sufficient optimality conditions for optimal control problems with bang-bang controls. Building on a structural assumption on the adjoint state, we additionally need a weak second-order condition. This second-order condition is formulated with functions from an extended critical cone, and it is equivalent to a formulation posed on measures supported on the set where the adjoint state...

The distance from the convex hull of the range of an n-dimensional vector-valued measure to the range of that measure is no more than an/2, where a is the largest (one-dimensional) mass of the atoms of the measure. The case a = 0 yields Lyapounov's Convexity Theorem; applications are given to the bisection problem and to the bang-bang principle of optimal control theory.

In this paper, the time and norm optimal control problems of controlled heat equations with a weight function are considered. For the time optimal problems, we study the following two cases: one is for equations with multi-domain control under null controllability, and the other is for equations under approximate null controllability. We prove the solvability, and obtain the bang-bang principle...

*Correspondence: [email protected] 1College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, 201620, P.R. China Full list of author information is available at the end of the article Abstract This paper investigates the lag projective synchronization and anti-synchronization problems for a general master-slave chaotic system with bounded nonlinearity. An adaptive cont...