Solution of the Synthesis Problem of Boundary Optimal Control of a Rod Cooling Process with a Heat Conductive Viscosity

The problem of synthesis of the boundary optimal control of the cooling process of media with heat conductive viscosity is investigated. In addition to the distributed parameters, the concentrated parameters act on the system. This is due to the fact that the temperature of the external environment is unknown and varies according to a given law. As a result, the process is described by a system of partial differential equations and ordinary differential equations. In this case, heat transfer occurs at the right end of the rod. This complicates the obtaining of a solution of this boundary-value problem in an explicit form. But it is possible to establish the existence and uniqueness of the solution of the corresponding boundary-value problem for concrete admissible controls.The criterion of quality is a quadratic functional and it is required to build control in the form of feedback. First by the Fourier method, the problem under consideration is formulated in an infinite-dimensional phase space. As a result, the problem of synthesis of optimal control in a functional space is obtained. To solve this problem, the dynamic programming method is used. To do this, let's introduce the Bellman functional and obtain the Bellman equation, which this functional satisfies. The solution of this equation allows to find the control parameter in the form of a functional defined on the set of the state function. Further, by introducing the corresponding functions, feedback control is constructed for the original problem. Unlike program control, this allows to influence the behavior of the system at any time, that is, to ensure the self-regulation of the process. However, let's note that the difficulties in solving this problem are connected with the justification of the proposed method. This is established by the investigation of a closed system

Change in the room temperature magnetic property of ZnO upon Mn doping

We present in this paper the changes in the room temperature magnetic property of ZnO on Mn doping prepared using solvo-thermal process. The zero field cooled (ZFC) and field cooled (FC) magnetisation of undoped ZnO showed bifurcation and magnetic hysteresis at room temperature. Upon Mn doping the magnetic hysteresis at room temperature and the bifurcation in ZFC-FC magnetization vanishes. The results seem to indicate that undoped ZnO is ferromagnetic while on the other hand the Mn doped ZnO is not a ferromagnetic system. We observe that on addition of Mn atoms the system shows antiferromagnetism with very giant magnetic moments.Comment: 5 figure