Admissible Controls in a Nonlinear Time-Optimal Problem with Phase Constraints

The paper is devoted to constructing admissible controls in a problem of optimal control by a nonlinear dynamic system under constraints on the current phase state. The dynamic system under consideration describes the controlled motion of a carrier rocket from the launching point to the time when the carrier rocket enters a given elliptic earth orbit. A problem consists in designing a program control for the carrier rocket that provides the maximal value of the payload mass led to the given orbit and the fulfillment of a number of additional restrictions on the current phase state of the dynamic system at the atmospheric part of the trajectory. The restrictions considered are due to the need to take into account the values of the dynamic velocity pressure, the attack angle and slip angle when the carrier moves in dense layers of the atmosphere. Such a problem is equivalent to a nonlinear time-optimal problem with phase constraints for carrier rockets of some classes. The algorithm for constructing admissible controls ensuring the fulfillment of additional phase constraints is suggested. The methodological basis of this algorithm is the application of some predictive control. This control is constructed in the problem without taking into account the constraints above. For a deterministic model of the atmosphere, such a predictive control is used to predict the values of a part of the phase state of the dynamic system at the next time. The prediction results are applied in the procedure of desired control construction. This procedure essentially takes into account specific features of the additional constraints. The results of numerical modeling are presented. © 2018Russian Academy of Medical Science

Numerical investigation of a nonlinear time-optimal problem

The questions of constructing admissible controls in a problem of optimal control of a nonlinear dynamic system under constraints on its current phase state are discussed. The dynamic system under consideration describes the controlled motion of a carrier rocket from the launching point to the time when the carrier rocket enters a given elliptic earth orbit. The problem consists in designing a program control for the carrier rocket that provides the maximal value of the payload mass led to the given orbit and the fulfillment of a number of additional restrictions on the current phase state of the dynamic system. The additional restrictions are due to the need to take into account the values of the dynamic velocity pressure, the attack and slip angles when the carrier rocket moves in dense layers of the atmosphere. In addition it is required to provide the fall of detachable parts of the rocket into specified regions on the earth surface. For carrier rockets of some classes, such a problem is equivalent to a nonlinear time-optimal problem with phase constraints. Two algorithms for constructing admissible controls ensuring the fulfillment of additional phase constraints are suggested. The numerical analysis of these algorithms is performed. The methodological basis of one algorithm is the application of some predictive control, which is constructed without taking into account the constraints above. Another algorithm is based on special control modes. The results of numerical modeling are presented. © 2018 Udmurt State University.All Rights Reserved

The Accidental Terrorist: Okhrana Connections to the Extreme-Right and the Attempt to Assassinate Sergei Witte in 1907

This article represents a case study in the relationship between the tsarist secret police (commonly known as the Okhrana in the West and okhranka in Russia) and acts of political terror perpetrated by the extreme-right in late imperial Russia. This specific case concerns the tangled web of conspiracy, propaganda and controversy that surrounded the attempted assassination of former-Chairman of the Council of Ministers, Sergei Witte, in 1907