Approximation of Escape Time for Lagrangian Systems With Fast Noise

This note is concerned with the large deviations asymptotics estimate of the mean escape time for Lagrangian systems subjected to fast Gaussian noise. The solution to the Hamilton-Jacobi equation of the associated variational problem is derived as a sum of two terms dependent on kinetic and potential energy of the system, respectively. A closed-form solution for classes of linear and nonlinear systems is obtained. An application to a controlled pointing problem is discussed as an example.     

Controlling the One-Dimensional Motion of Hybrid Vibrational Rod Systems

A mathematical model of the one-dimensional controlled motion of a hybrid vibrational system is proposed. The plant includes an inhomogeneous elastic rod with loads concentrated at its endpoints. An analytical-numerical procedure for finding the eigenvalues (eigenfrequencies) and eigenfunctions is developed. A novel procedure to take into account the nonuniform distributed forces and forces concentrated at the endpoints using a modification of Grinberg’s approach is presented. Efficient statements and constructive approximate solutions of the problems for controlling the motion of a countably dimensional vibrational system with a complex distribution of eigenfrequencies are proposed.     

Dynamics of spacecraft with elastic and dissipative elements in the attitude control mode

Rotational motion of a spacecraft with elastic and dissipative elements as a whole about its center of mass taking into account the control elements designed as single-axis gyrostabilizers in the attitude control mode is studied. Oscillatory processes related to the spacecraft attitude control when the terms emerging due to the elastic oscillations of the structure are comparable with gyroscopic terms. A model problem of spacecraft reorientation is considered. Conditions under which the elastic oscillations do not affect the flat slew of the satellite and assumptions under which no flat slew is possible are obtained. Analytical expressions for estimating the spacecraft deviations from the programmed motion (drift of the angular velocity) are found.     

Optimal rotation deceleration of a dynamically symmetric body with movable mass in a resistant medium

A minimum-time problem on deceleration of rotation of a free rigid body is studied. The body is assumed to contain a viscous-elastic element, which is modeled as a movable point mass attached to the body via a damper. In addition, the body is subjected to a retarding torque generated by linear medium resistance forces. In an undeformed state, the body is assumed to be dynamically symmetric, with the mass being located on the symmetry axis. An optimal control law for deceleration of rotation of the body is synthesized, and the corresponding time and phase trajectories are determined.     

Quasi-optimal deceleration of rotations of a rigid body with a moving mass in a resistive medium

The problem of time quasi-optimal deceleration of the rotations of a dynamically symmetric rigid body is studied. It is assumed that the body contains a point mass connected to it with a strong viscoelastic element (damper). The body is acted on by a small linear resistance torque of the medium that is proportional to the angular momentum and a small control torque bounded by an ellipsoidal domain. An approximate synthesis of control is proposed, and an asymptotic solution based on a procedure of averaging the precession motion over the phase is obtained; numerical integration is performed. The main properties of the quasi-optimal motion are determined.     

Cytogenetic studies of the effects of 5-fluorouracil in vivo

Cytogenetic analysis was carried out of the culture of peripheral blood lymphocytes of 10 healthy donors and 40 patients with malignant tumours of digestive tract treated with 5-fluorouracil. The frequency of cells with chromosome aberrations in the lymphocyte culture of the patients before the treatment was significantly higher than that in the healthy donors. The difference in the frequency of the aberrant metaphases between treated and intact patients was statistically insignificant.     

Control of the apparent acceleration of a rigid body attached to a movable base by means of a two-degree-of-freedom gimbal

A mechanical system consisting of a movable base and an object (rigid body) connected to the base by means of a two-degree-of-freedom gimbal with mutually perpendicular axes is considered. The possibility to eliminate the projection of the apparent acceleration of a given object point on the plane perpendicular to an object-fixed axis by controlling the rotation of the gimbal frames is investigated. The apparent acceleration of a given object point is the difference between the absolute acceleration vector and the gravitational acceleration vector at this point. Sufficient conditions under which this goal is attainable in principle are formulated. Equations governing the rotation of the gimbal frames are derived. This problem is related to the development of control systems for gravity-sensitive technologies in spacecraft.     

Quasi-Optimal Braking of Rotations of a Body with a Moving Mass Coupled to It through a Quadratic Friction Damper in a Resisting Medium

This paper addresses the problem of the time-optimal braking of rotations of a dynamically symmetric rigid body under a small control moment in the ellipsoidal range with close unequal values of the ellipsoid’s semiaxes. This problem is considered a problem of quasi-optimal control. The body is assumed to have a moving mass connected to it through elastic coupling with quadratic dissipation. In addition, the body is exposed to a small braking moment of the linear resistance of the medium. The problem of synthesizing the quasi-optimal braking of the rotations of a dynamically symmetric body in a resisting medium is investigated analytically and numerically. An approximate solution is found by the phase-averaging of the processional motion. The qualitative properties of quasi-optimal motion are analyzed and the corresponding graphs are presented.     

Transfer of a Dynamic Object onto the Surface of an Ellipsoid

Using Pontryagin’s maximum principle, the problem of the quickest transfer of a multidimensional object onto the surface of an ellipsoid is reduced to solving a scalar algebraic equation. The concentration of the endpoints of optimal trajectories in the vicinity of the points forming the boundary in the case of a degenerate ellipsoid is demonstrated. An example in which the optimal control has a jump and the Bellman function has a discontinuity when the magnitude of the initial velocity vector undergoes a small change is constructed. It is also shown that the jump in the optimal control can occur without the discontinuity of the Bellman function.     

Quasi-optimal deceleration of rotations of an asymmetric body in resistive medium

A minimum-time problem on deceleration of rotations of a free rigid body affected by a small control torque with close but not identical coefficients is studied; such a problem can be considered as a quasi-optimal control problem. In addition, the rigid body is affected by a small deceleration viscous friction torque. The body is assumed to be dynamically asymmetric. A quasi-optimal feedback control for the deceleration of rotations of the rigid body is constructed, the optimal control time, and phase trajectories are found. The quasi-stationary trajectories are analyzed.