• International Journal of Control, Automation, and Systems
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• v.2 no.1
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• pp.15-22
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• 2004

Some recent advances in stability and optimality for the nonlinear receding horizon control (NRHC) or the nonlinear model predictive control (NMPC) are assessed. The NRHCs with terminal conditions are surveyed in terms of a terminal state equality constraint, a terminal cost, and a terminal constraint set. Other NRHCs without terminal conditions are surveyed in terms of a control Lyapunov function (CLF) and cost monotonicity. Additional approaches such as output feedback, fuzzy, and neural network are introduced. This paper excludes the results for linear receding horizon controls and concentrates only on the analytical results of NRHCs, not including applications of NRHCs. Stability and optimality are focused on rather than robustness.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2081-2086
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• 2005

This paper proposes the receding horizon $H_{\infty}$ predictive control (RHHPC) for systems with a state-delay. We first proposes a new cost function for a finite horizon dynamic game problem. The proposed cost function includes two terminal weighting terns, each of which is parameterized by a positive definite matrix, called a terminal weighting matrix. Secondly, we derive the RHHPC from the solution to the finite dynamic game problem. Thirdly, we propose an LMI condition under which the saddle point value satisfies the well-known nonincreasing monotonicity. Finally, we shows the asymptotic stability and $H_{\infty}$-norm boundedness of the closed-loop system controlled by the proposed RHHPC. Through a numerical example, we show that the proposed RHHC is stabilizing and satisfies the infinite horizon $H_{\infty}$-norm bound.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.749-754
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• 1999

The cost is known to be proportional to the size of sample. We consider a cost function of the form Cost=c1np+c2npmq where c1, c2 p, and q are all positive constants. This cost function is to be used in finding an optimal allocation in two-stage cluster sampling. The optimal allocations of n and m gives the properties of uniqueness under some conditions and of monotonicity with p>0 when q=1.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.460-465
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• 2004

In this paper, we present some properties on receding horizon $H_{\infty}$ control for nonlinear discrete-time systems. First, we propose the nonlinear inequality condition on the terminal cost for nonlinear discrete-time systems. Under this condition, noninceasing monotonicity of the saddle point value of the finite horizon dynamic game is shown to be guaranteed. We show that the derived condition on the terminal cost ensures the closed-loop internal stability. The proposed receding horizon $H_{\infty}$ control guarantees the infinite horizon $H_{\infty}$ norm bound of the closed-loop systems. Also, using this cost monotonicity condition, we can guarantee the asymptotic infinite horizon optimality of the receding horizon value function. With the additional condition, the global result and the input-to-state stable property of the receding horizon value function are also given. Finally, we derive the stability margin for the saddle point value based receding horizon controller. The proposed result has a larger stability region than the existing inverse optimality based results.

• Environmental and Resource Economics Review
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• v.19 no.3
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• pp.633-658
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• 2010

In this paper, we estimate the Translog cost function in Korean manufacturing, using capital (K), labor (L), material (M), electricity (E), fuel (F) data over the period from 1970 to 2005. Especially, this paper investigates the impact of imposing concavity in the estimation of a Translog cost function. Although the value of log-likelihood is somewhat reduced in a concavity imposed function rather than a function which is not, a concavity imposed function satisfies regularity conditions (monotonicity, positivity, concavity) at all data points. We also calculate price elasticities using a concavity imposed Translog cost function. Electricity complements capital so electricity demand increases as capital demand increases. Meanwhile, electricity substitutes labor, fuel, and material. These results show that Korean manufacturing experienced a structural change of increase in electricity demand.

• Journal of the Korean Operations Research and Management Science Society
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• v.30 no.2
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• pp.117-129
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• 2005

This paper considers a make-to-order inventory-production system in which customer orders are admitted only when the number of outstanding customer orders is below a value committed by the system. We deal with general distributions for the customer order Inter-arrival, production, and replenishment lead time processes. Monotonicities of the optimal average cost with respect to these distribution parameters are established using sample path coupling arguments. When distributions are given as an exponential one, we implement a sensitivity analysis on the optimal inventory policy and show that it has monotonicities with respect to system costs using dynamic programming.

• Journal of the Korean Operations Research and Management Science Society
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• v.29 no.3
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• pp.111-127
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• 2004

We consider a supply chain model with a make-to-order production facility and a single supplier. The model we treat here is a special case of a two-echelon inventory model. Unlike classical two-echelon systems, the demand process at the supplier is affected by production process at the production facility as well as customer order arrival process. In this paper, we address that how the demand variability impacts on the optimal replenishment policy. To this end, we incorporate Erlang and phase-type demand distributions into the model. Formulating the model as a Markov decision problem, we investigate the structure of the optimal replenishment policy. We also implement a sensitivity analysis on the optimal policy and establish its monotonicity with respect to system cost parameters.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.3
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• pp.295-300
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• 2008

In this paper, a new looper controller is proposed to minimize the tension variation of a strip in the hot strip finishing mill. The proposed control technology is based on a receding horizon control (RHC) to satisfy the constraints on the control input/state variables. The finite terminal weighting matrix is used instead of the terminal equality constraint. The closed loop stability of the RHC for the looper system is analyzed to guarantee the monotonicity of the optimal cost. Furthermore, the RHC is combined with a 4SID(Subspace-based State Space System Identification) model identifier to improve the robustness for the parameter variation and the disturbance of an actuator. As a result, it is shown through a computer simulation that the proposed control scheme satisfies the given constraints on the control inputs and states: roll speed, looper current, unit tension, and looper angle. The control scheme also diminishes the tension variation for the parameter variation and the disturbance as well.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.7
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• pp.1019-1023
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• 2012

This paper considers a model predictive control problem of discrete-time constrained systems with time-varying delay. For this problem, a delay dependent state feedback control approach is used to achieve asymptotic stabilization of systems with input constraints. Based on Lyapunov stability theory, a new stability condition is obtained via linear matrix inequality formulation to find cost monotonicity condition of the model predictive control algorithm which guarantee the closed loop stability. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our results.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2006.11a
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• pp.127-132
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• 2006

Quantization in video coding plays an important role in controlling the bit-rate of compressed video bit-streams. It has been used as an important control means to adjust the amount of bit-streams to at]owed bandwidth of delivery networks and storage. Due to the dependent nature of video coding, dependent quantization has been proposed and applied for MPEG-2 video coding to better maintain the quality of reconstructed frame for given constraints of target bit-rate. Since Scalable Video Coding (SVC) being currently standardized exhibits highly dependent coding nature not only between frames but also lower and higher scalability layers where the dependent quantization can be effectively applied, in this paper, we propose a dependent quantization scheme for SVC and compare its performance in visual qualities and bit-rates with the current JSVM reference software for SVC. The proposed technique exploits the frame dependences within each GOP of SVC scalability layers to formulate dependent quantization. We utilize Lagrange optimization, which is widely accepted in R-D (rate-distortion) based optimization, and construct trellis graph to find the optimal cost path in the trellis by minimizing the R-D cost. The optimal cost path in the trellis graph is the optimal set of quantization parameters (QP) for frames within a GOP. In order to reduce the complexity, we employ pruning procedure using monotonicity property in the trellis optimization and cut the frame dependency into one GOP to decrease dependency depth. The optimal Lagrange multiplier that is used for SVC is equal to H.264/AVC which is also used in the mode prediction of the JSVM reference software. The experimental result shows that the dependent quantization outperforms the current JSVM reference software encoder which actually takes a linear increasing QP in temporal scalability layers. The superiority of the dependent quantization is achieved up to 1.25 dB increment in PSNR values and 20% bits saving for the enhancement layer of SVC.