In this paper, we provide a complete analysis of the Lie algebra structure of a system of n interacting spin 12 particles with different gyromagnetic ratios in an electromagnetic field. We relate the structure of this Lie algebra to the properties of a graph whose nodes represent the particles and an edge connects two nodes if and only if the interaction between the two corresponding particles ...

We analyse weak and strong controllability notions for the locomotion of the 3-link Purcell’s swimmer, the simplest possible swimmer at low Reynolds number from a geometric framework. After revisiting a purely kinematic form of the equations, we apply an extension of Chow’s theorem to analyze controllability in the strong and weak sense. Further, the connection form for the symmetric version of...

Many of the real life problems are modelled as Matrix Second Order Systems, (refer Wu and Duan [19], Hughes and Skelton [10]). Necessary and sufficient condition for controllability of Matrix Second Order Linear (MSOL) Systems has been established by Hughes and Skelton [10]. However, no scheme for computation of control was proposed. In this paper we first obtain another necessary and sufficien...

Two of the fundamental concepts appearing in the earlier studies on linear control systems are controllability and observability. In particular, it was through the work of R.E. Kalman that the notion of controllability of a linear system was shown to be of interest in itself, and not only as it was appearing in the context of optimal control. Linear controllability turns out to be of importance...

We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting) which implies that one can not go infinitely far away from the control region without tending to the boundary (if any), but also applies when the distance to the contro...

In these notes we analyze some problems related to the controllability and observability of partial differential equations and its space semidiscretizations. First we present the problems under consideration in the classical examples of the wave and heat equations and recall some well known results. Then we analyze the 1−d wave equation with rapidly oscillating coefficients, a classical problem...

Certain planning systems that deal with quantitative time constraints have used an underlying Simple Temporal Problem solver to ensure temporal consistency of plans. However, many applications involve processes of uncertain duration whose timing cannot be controlled by the execution agent. These cases require more complex notions of temporal feasibility. In previous work, various “controllabili...

Planning and acting in a dynamic environment require distinguishing controllable and contingent events and checking the dynamic controllability of plans. Known procedures for testing the dynamic controllability assume that all contingent events are observable. Often this assumption does not hold. We consider here the general case of networks with invisible as well as observable contingent point...

In this paper, we apply a successful combination of three key tools which allows to get a measure of the cost of the approximate controllability for semilinear heat equation. The first tool consists to get enough information about the approximate control for the linear heat equation with a potential depending on space-time variable. Then a fixed point method is applied. The fixed point techniqu...