Closed-Loop Control of the Motion of a Disk–Rod System

This work deals with the guidance and control of a system which is composed of a rolling disk and a controlled slender rod that is pivoted, through its center of mass, about the disk center. There are given N points P _i, i=1, ..., N, in the horizontal plane, a set of angles _2i , i=1, ..., N, a finite-time interval [0, t _f], and a sequence of times ₁=0<₂<...< _N =t _f. Using the concept of path controllability, a closed-loop control law is derived to steer the system in such a manner that the disk center and the rod angle of rotation ₂ will pass through (P _i, _2i ) at the times _i , i=1,...,N, respectively. This system serves as a model for the motion of a simple mobile robot.     

On multiparameter ergodic and martingale theorems in infinite measure spaces

Summary A unified proof is given of several ergodic and martingale theorems in infinite measure spaces.The research of this author is in part supported by the National Science Foundation, grant MCS-8301619     

The controllability of a system of two bank-to-turn airborne vehicles

This letter deals with the controllability of the motion of a system of two bank-to-turn airborne vehicles. It is shown that the smooth manifold on which the system is controllable, is not unique.     

New fluorescent probes for the measurement of cell membrane viscosity

BACKGROUND: Molecular rotors are fluorescent molecules that exhibit viscosity-dependent fluorescence quantum yield, potentially allowing direct measurements of cell membrane viscosity in cultured cells. Commercially available rotors, however, stain not only the cell membrane, but also bind to tubulin and migrate into the cytoplasm. We synthesized molecules related to 9-(dicyanovinyl)-julolidine (DCVJ), which featured hydrocarbon chains of different length to increase membrane compatibility.RESULTS: Longer hydrocarbon chains attached to the fluorescent rotor reduce the migration of the dye into the cytoplasm and internal compartments of the cell. The amplitude of the fluorescence response to fluid shear stress, known to decrease membrane viscosity, is significantly higher than the response obtained from DCVJ. Notably a farnesyl chain showed a more than 20-fold amplitude over DCVJ and allowed detection of membrane viscosity changes at markedly lower shear stresses.CONCLUSIONS: The modification of molecular rotors towards increased cell membrane association provides a new research tool for membrane viscosity measurements. The use of these rotors complements established methods such as fluorescence recovery after photobleaching with its limited spatial and temporal resolution and fluorescence anisotropy, which has low sensitivity and may be subject to other effects such as deformation.     

Feasible command strategies for the control of motion of a simple mobile robot

The concept of feasible command strategies is introduced and its applicability is demonstrated by solving a guidance and control problem. This problem concerns the motion of a system which is composed of a rolling disk and a controlled slender rod that is pivoted, through its endpoint, about the disk center. The motion of the disk-rod system is subjected to state and control constraints, and it serves as a model for the motion of a simple mobile robot. In addition, the concept of path controllability is introduced and a condition is derived for the system motion path controllability. The derivation of this condition enables one to design closed-loop control laws for the system motion.     

Optimal investment and reinsurance policies in insurance markets under the effect of inside information

In this paper, we study the problem of optimal investment and proportional reinsurance coverage in the presence of inside information. To be more precise, we consider two firms: an insurer and a reinsurer who are both allowed to invest their surplus in a Black–Scholes‐type financial market. The insurer faces a claims process that is modeled by a Brownian motion with drift and has the possibility to reduce the risk involved with this process by purchasing proportional reinsurance coverage. Moreover, the insurer has some extra information at her disposal concerning the future realizations of her claims process, available from the beginning of the trading interval and hidden from the reinsurer, thus introducing in this way inside information aspects to our model. The optimal investment and proportional reinsurance decision for both firms is determined by the solution of suitable expected utility maximization problems, taking into account explicitly their different information sets. The solution of these problems also determines the reinsurance premia via a partial equilibrium approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Stochastic Burgers PDEs with random coefficients and a generalization of the Cole–Hopf transformation

This paper studies forward and backward versions of the random Burgers equation (RBE) with stochastic coefficients. First, the celebrated Cole–Hopf transformation reduces the forward RBE to a forward random heat equation (RHE) that can be treated pathwise. Next we provide a connection between the backward Burgers equation and a system of FBSDEs. Exploiting this connection, we derive a generalization of the Cole–Hopf transformation which links the backward RBE with the backward RHE and investigate the range of its applicability. Stochastic Feynman–Kac representations for the solutions are provided. Explicit solutions are constructed and applications in stochastic control and mathematical finance are discussed.     

Collision Avoidance by a Ship with a Moving Obstacle: Computation of Feasible Command Strategies

A ship moving from a point A to a point B detects a moving small obstacle at close range. Hence, the ship has to perform a maneuver to avoid collision with the moving obstacle. Using a realistic model of a tanker ship, a method is proposed for computing feasible rudder command strategies for performing the collision-avoidance maneuver.     

Feasible Command Strategies for the Control of Motion of a Simple Mobile Robot

An error in the model of the disk-rod system of Ref. 1 is corrected.     

Reinsurance control in a model with liabilities of the fractional Brownian motion type

We propose a model for reinsurance control for an insurance firm in the case where the liabilities are driven by fractional Brownian motion, a stochastic process exhibiting long-range dependence. The problem is transformed to a nonlinear programming problem, the solution of which provides the optimal reinsurance policy. The effect of various parameters of the model, such as the safety loading of the reinsurer and the insurer, the Hurst parameter, etc. on the optimal reinsurance program is studied in some detail. Copyright © 2007 John Wiley & Sons, Ltd.