Papers by Keyword: Optimal Control

Abstract: This paper is concerned with stochastic optimization in continuous time and its application in reinsurance. It deals with a model of optimization reinsurance which makes it possible to maximize the technical benefit of an insurance company and to minimize the risk for a given period. Indeed, here we discuss a stochastic optimal control problem to determine the optimal risk management strategy, the purpose of which is to identify the appropriate level of transfer rate for "quota share" reinsurance contracts, which are most appropriate to the risk profile of an insurance company. In addition, we use a resolution approach based on dynamic programming and the HJB equation in order to reach the aforementioned aim, which is finding the optimal strategy for reinsurance to adapt better for insurance company.

Abstract: The paper discusses some approaches to the development of methods of active influence on clouds, which develop in the High-Mountain geophysical institute. We considered the problems of determination in the cloud the region in which to make the particles of the reactants, concentration of these particles, the beginning and completion of seeding. Such questions should be solved on the basis of numerical modeling of clouds. The most common approach to the development of methods of active influence on clouds is a simulation of different variants of any particles of reagent in the cloud and choose the most effective one from the point of view of achieving the objectives of impact compared to a natural development of the cloud. Another approach to the development of the method of sedimentation control in the clouds is to consider this problem in the framework of optimal control theory. Despite the difficulties in implementing this approach, it is very effective and produces optimal results.

Abstract: The study is devoted to the development of an algorithm for the optimal management of the volumes of orders for various building structures and their stock in the warehouse of a construction site. The state of the warehouse is described by a first-order differential equation, the functional is compiled using Prof. Letov's method of analytical construction of optimal regulators (ACOR), the solution is carried out by the Euler-Lagrange method. Based on previous studies of the optimal number of links in the construction team, the optimal dependences of the volumes of orders and stocks on the time of installation of the panel building have been obtained. As a result, it was found that all the dependencies show a monotonous tendency to zero as they approach the end of installation, increasing the intensity of installation increases the volume of orders and reduces the concavity of the stock schedule, increasing the contribution of order quantities in the functional increases both of these parameters.

Abstract: This article presents the basis for and implementation of an approach to the development of the individualised gas carburization technology relying on optimisation of the process of carburizing surfaces of workpieces and taking into consideration working requirements. The approach is based on the hierarchical structure of carburization models, utilising the decomposition of global quality criteria and reflecting the relationship between the quality values of the hardened layer and the parameters of a technological impact on the workpiece. Taking the example of carburization of automobile gears, optimal parameters for the carburization technology are defined which minimise the duration of the process and maximise the precision of approximation to a given carbon distribution in the hardened layer within technical limitations.

Abstract: The problem of optimal control of systems disturbed by sinusoidal signals for infinite control time is considered in the paper. The control laws described in [1] is base of a modified mean-square performance index with an infinite control time. The performance index was formulated in such a way that each sinusoidal component corresponds to a separate weight matrix. This allows energy constraints on the control signals to be differentiated based on frequency. An optimal solution to the optimization problem was found. In the paper the problem of the impact of time on the identification of sinusoidal disturbance on vibration isolation system frequency characteristic. The controller was synthesized for slow-active vehicle suspension [2,3]. The model of suspension, synthesis of the controller and implementation of the system was described. The results of simulations of the designed vehicle active suspension system are presented.

Abstract: Conditions are obtained for unique solution existence of a mixed control problem without taking in account control expenses for a system that described by an initial-boundary value problem for the linearized quasi-stationary system of phase field equations. The problem is reduced to an optimal control problem for operator differential equation of first order in abstract space with degenerate operator at derivative using start and distributed controls simultaneously. The theorem on the unique solvability of this problem is applied to studying of optimal control problem for the phase field equations system.

Abstract: The optimal control problem for evolution radiative heat transfer in SP₁ approximation is considered. The problem is solved by weak form technique and Lagrange method. Numerical experiments for real materials are done.

Abstract: A boundary multiplicative control problem for a nonlinear steady-state heat transfer model accounting for heat radiation effects is considered. The aim of control consists in obtaining a prescribed temperature or radiative intensity distributions in a part of the model domain by controlling the boundary reflectivity. The solvability of this control problem is proved, and optimality conditions are derived.

Abstract: In this paper, we present a new approach for modeling the hysteresis nonlinearity of a piezo-positioning systems. Because of its nonlinear hysteresis effect, the tracking control accuracy of the precision positioning system is difficulty achieved. Hence it is desirable to take hysteresis effect into consideration for improving the trajectory performance. A model reference adaptive optimal control scheme based on online actor-critic algorithm is developed. The proposed controller can be constructed without a nonlinear hysteresis dynamic equation to compensate the hysteresis effect. Simulation results show the effectiveness of the new approach.

Abstract: This paper presents a method of controlling an anti-ship missile with the use of the linear-quadratic regulator (LQR). The equations of dynamics of the flight were linearized and written in the form of equations of state. To control the anti-ship missile, a double executive gas-dynamic (moveable nozzle of exhaust gases) and aerodynamic (moveable control surfaces) system is applied. The missile flight is considered in a three dimensional space, whereas the controlling vector is comprised of four components: two components to control the height of the flight and two components to control the direction of the flight. The results are presented in a graphic form.