• East Asian mathematical journal
• /
• v.27 no.1
• /
• pp.91-100
• /
• 2011

It is important to find an optimal strategy which maximize the surplus of the insurance company at the maturity time T. The purpose of this paper is to give an explicit expression for the optimal reinsurance and investment strategy, under the CEV model, which maximizes the expected exponential utility of the final value of the surplus at T. To do this optimization problem, the corresponding Hamilton-Jacobi-Bellman equation will be transformed a linear partial differential equation by applying a Legendre transform.

• Journal of applied mathematics & informatics
• /
• v.30 no.5_6
• /
• pp.699-717
• /
• 2012

In this paper, we deal with the robust mixed $H_2/H_{\infty}$ guaranteed-cost control problem involving uncertain neutral stochastic distributed delay systems. More precisely, the aim of this problem is to design a robust mixed $H_2/H_{\infty}$ guaranteed-cost controller such that the close-loop system is stochastic mean-square exponentially stable, and an $H_2$ performance measure upper bound is guaranteed, for a prescribed $H_{\infty}$ attenuation level ${\gamma}$. Therefore, the fast convergence can be fulfilled and the proposed controller is more appealing in engineering practice. Based on the Lyapunov-Krasovskii functional theory, new delay-dependent sufficient criteria are proposed to guarantee the existence of a desired robust mixed $H_2/H_{\infty}$ guaranteed cost controller, which are derived in terms of linear matrix inequalities(LMIs). Furthermore, the design problem of the optimal robust mixed $H_2/H_{\infty}$ guaranteed cost controller, which minimized an $H_2$ performance measure upper bound, is transformed into a convex optimization problem with LMIs constraints. Finally, two simulation examples illustrate the design procedure and verify the expected control performance.

• Structural Engineering and Mechanics
• /
• v.25 no.1
• /
• pp.21-37
• /
• 2007

In this study a stochastic approach for linear viscous dampers design adopted for seismic protection of buildings is developed. Devices optimal placement into the main structure and their mechanical parameters are attained by means of a reliability-based optimum design criterion, in which an objective function (O.F.) is minimized, subject to a stochastic constraint. The seismic input is modelled by a non stationary modulated Kanai Tajimi filtered stochastic process. Building is represented by means of a plane shear type frame model. The selected criterion for the optimization searches the minimum of the O.F., here assumed to be the cost of the seismic protection, i.e., assumed proportional to the sum of added dampings of each device. The stochastic constraint limits a suitable approximated measure of the structure failure probability, here associated to the maximum interstorey drift crossing over a given threshold limit, related, according with modern Technical Codes, to the required damage control.

• Structural Engineering and Mechanics
• /
• v.81 no.1
• /
• pp.51-57
• /
• 2022

The problem of optimal stochastic GA control of the system with uncertain parameters and unsure noise covariates is studied. First, without knowing the explicit form of the dynamic system, the open-loop determinism problem with path optimization is solved. Next, Gaussian linear quadratic controllers (LQG) are designed for linear systems that depend on the nominal path. A robust genetic neural network (NN) fuzzy controller is synthesized, which consists of a Kalman filter and an optimal controller to assure the asymptotic stability of the discrete control system. A simulation is performed to prove the suitability and performance of the recommended algorithm. The results indicated that the recommended method is a feasible method to improve the performance of active tuned mass damper (ATMD) shear buildings under random earthquake disturbances.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.27 no.6
• /
• pp.313-320
• /
• 2015

In this paper, a method to obtain the probability distribution of room temperature and cooling load is presented, when the internal heat generation is applied to the system as a disturbance in the air conditioning system with slab cooling storage. The probability distribution of room temperature and the cooling load due to the disturbance were examined in one room of an office building. When considering only the electric power consumption as a probability component, it was found that the effect on room temperature and cooling load is small, because the probability component of the measured electric power consumption in the building is small. On the other hand, when considering the stochastic fluctuations of electric power consumption together with the heat generated by human bodies, the mean value of the cooling load was about 2,300 W and the ratio of the standard deviations was 19% (10 o'clock in second day). It was revealed that the stochastic effects of internal heat generation acting on the air conditioning system with slab cooling storage are not small.

• Journal of the Korea Society for Simulation
• /
• v.12 no.3
• /
• pp.31-40
• /
• 2003

This paper studies an optimal policy for a certain class of (s, S) inventory control systems, where the demands are characterized by the renewal arrival process. To minimize the average cost over a simulation period, we apply a stochastic optimization algorithm which uses the gradients of parameters, s and S. We obtain the gradients of objective function with respect to ordering amount S and reorder point s via a combined perturbation method. This method uses the infinitesimal perturbation analysis and the smoothed perturbation analysis alternatively according to occurrences of ordering event changes. The optimal estimates of s and S from our simulation results are quite accurate. We consider that this may be due to the estimated gradients of little noise from the regenerative system simulation, and their effect on search procedure when we apply the stochastic optimization algorithm. The directions for future study stemming from this research pertain to extension to the more general inventory system with regard to demand distribution, backlogging policy, lead time, and inter-arrival times of demands. Another direction involves the efficiency of stochastic optimization algorithm related to searching procedure for an improving point of (s, S).

• Journal of Institute of Control, Robotics and Systems
• /
• v.20 no.2
• /
• pp.170-174
• /
• 2014

In this paper, an unknown input estimation method via the optimal FIR smoother is proposed for linear discrete-time systems. The unknown inputs are represented by random walk processes and treated as auxiliary states in augmented state space models. In order to estimate augmented states which include unknown inputs, the optimal FIR smoother is applied to the augmented state space model. Since the optimal FIR smoother is unbiased and independent of any a priori information of the augmented state, the estimates of each unknown input are independent of the initial state and of other unknown inputs. Moreover, the proposed method can be applied to stochastic singular systems, since the optimal FIR smoother is derived without the assumption that the system matrix is nonsingular. A numerical example is given to show the performance of the proposed estimation method.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.23 no.12
• /
• pp.836-842
• /
• 2011

It has been shown that the air-conditioning system with slab cooling storage is effective in cutting peak load and utilizing nighttime electric power. The stochastic properties of internal heat generation which has great influence on the cooling load are examined in this paper. Based on the measured cooling load and electric power consumption in an office building with slab cooling storage, stochastic time series models to simulate these random processes are investigated. Furthermore, a calculated result by an optimal control method of thermal analysis taking into account the internal heat is compared with the measured cooling load.

• Journal of the Korean Society of Safety
• /
• v.27 no.2
• /
• pp.57-64
• /
• 2012

For the vibration control of earthquake-excited buildings, an optimal design method of integrated control system considering soil-structure interaction is studied in this paper. Interaction between soils and the base of the building is simply modeled as lumped parameters and equations of motion are derived. The equations of motion are transformed into the state space equations and the probabilistic excitations such as Kanai-Tajumi power spectral density function is introduced. Then an optimization problem is formulated as finding hybrid or integrated control systems which minimizes the stochastic responses of the building structure for given constraints. In order to investigate the feasibility of the optimization method, an example design and numerical simulations are performed with tenstory building. Finally, numerical results are compared with a conventional design case that soil-structure interaction is not considered.

• Earthquakes and Structures
• /
• v.1 no.1
• /
• pp.43-67
• /
• 2010

A gradient-based evolutionary optimization methodology is presented for finding the optimal design of both the added dampers and their supporting members to minimize an objective function of a linear multi-storey structure subjected to the critical ground acceleration. The objective function is taken as the sum of the stochastic interstorey drifts. A frequency-dependent viscoelastic damper and the supporting member are treated as a vibration control device. Due to the added stiffness by the supplemental viscoelastic damper, the variable critical excitation needs to be updated simultaneously within the evolutionary phase of the optimal damper placement. Two different models of the entire damper unit are investigated. The first model is a detailed model referred to as "the 3N model" where the relative displacement in each component (i.e., the spring and the dashpot) of the damper unit is defined. The second model is a simpler model referred to as "the N model" where the entire damper unit is converted into an equivalent frequency-dependent Kelvin-Voigt model. Numerical analyses for 3 and 10-storey building models are conducted to investigate the characters of the optimal design using these models and to examine the validity of the proposed technique.