• 대한산업공학회지
• /
• 제20권1호
• /
• pp.121-131
• /
• 1994

Since many infinite horizon problems have infinite sequence of data to be considered, in general, it is impossible to express the optimal strategies finitely or to calculate them in finite time. This paper considers undiscounted nonhomogeneous deterministic infinite horizon problems. For those problems, we take a basic step to solve this class of infinite horizon problems optimally by giving a sufficient condition for a finite solution.

• 대한안전경영과학회지
• /
• 제19권3호
• /
• pp.89-95
• /
• 2017

This paper presents another maintenance policy for a group of units under finite operating horizon. A group of identical units are subject to random failures. Group maintenances are performed to all units together at specified intervals, and the failed units during operation are remained idle until the next group maintenance set-up. Unlike the traditional assumption of infinite operating horizon, we adopt the assumption of the finite operating horizon which reflect the rapid industrial advance and short life cycle of modern times. The units are under operation until the end of the operating horizon. Further, the operation of units are extended to the first group maintenance time after the end of the horizon. The total cost under the proposed maintenance policy is derived. The optimal group maintenance interval and the expected number of group maintenances during the horizon are found. It is shown that the proposed policy is better than the classical group maintenance policy in terms of total cost over the operating horizon. Numerical examples are presented for illustrations.

• Journal of Communications and Networks
• /
• 제16권3호
• /
• pp.293-300
• /
• 2014

As energy harvesting communication systems emerge, there is a need for transmission schemes that dynamically adapt to the energy harvesting process. In this paper, after exhibiting a finite-horizon online throughput-maximizing scheduling problem formulation and the structure of its optimal solution within a dynamic programming formulation, a low complexity online scheduling policy is proposed. The policy exploits the existence of thresholds for choosing rate and power levels as a function of stored energy, harvest state and time until the end of the horizon. The policy, which is based on computing an expected threshold, performs close to optimal on a wide range of example energy harvest patterns. Moreover, it achieves higher throughput values for a given delay, than throughput-optimal online policies developed based on infinite-horizon formulations in recent literature. The solution is extended to include ergodic time-varying (fading) channels, and a corresponding low complexity policy is proposed and evaluated for this case as well.

• 한국전산응용수학회:학술대회논문집
• /
• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
• /
• pp.15-15
• /
• 2003

We provide some recent results of approximation algorithms for solving Markov Games and discuss their applications to problems that arise in Computer Science. We consider a receding horizon approach as an approximate solution to two-person zero-sum Markov games with an infinite horizon discounted cost criterion. We present error bounds from the optimal equilibrium value of the game when both players take “correlated” receding horizon policies that are based on exact or approximate solutions of receding finite horizon subgames. Motivated by the worst-case optimal control of queueing systems by Altman, we then analyze error bounds when the minimizer plays the (approximate) receding horizon control and the maximizer plays the worst case policy. We give two heuristic examples of the approximate receding horizon control. We extend “parallel rollout” and “hindsight optimization” into the Markov game setting within the framework of the approximate receding horizon approach and analyze their performances. From the parallel rollout approach, the minimizing player seeks to combine dynamically multiple heuristic policies in a set to improve the performances of all of the heuristic policies simultaneously under the guess that the maximizing player has chosen a fixed worst-case policy. Given $\varepsilon$>0, we give the value of the receding horizon which guarantees that the parallel rollout policy with the horizon played by the minimizer “dominates” any heuristic policy in the set by $\varepsilon$, From the hindsight optimization approach, the minimizing player makes a decision based on his expected optimal hindsight performance over a finite horizon. We finally discuss practical implementations of the receding horizon approaches via simulation and applications.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2003년도 ICCAS
• /
• pp.1896-1900
• /
• 2003

In this paper, a new type of output feedback control, called a receding horizon finite memory control (RHFMC), is proposed for stochastic discrete-time state space systems. Constraints such as linearity and finite memory structure with respect to an input and an output, and unbiasedness from the optimal state feedback control are required in advance. The proposed RHFMC is chosen to minimize an optimal criterion with these constraints. The RHFMC is obtained in an explicit closed form using the output and input information on the recent time interval. It is shown that the RHFMC consists of a receding horizon control and an FIR filter. The stability of the RHFMC is investigated for stochastic systems.

• International Journal of Reliability and Applications
• /
• 제10권1호
• /
• pp.33-42
• /
• 2009

In most of literatures of age replacement policy, the authors consider the case that a new item starts operating at time zero and is to be replaced by new one at time T. It is, however, often to purchase used items because of the limited budget. In this paper, we consider age replacement policy of a used item whose age is $t_0$. The mathematical formulas of the expected cost rate per unit time are derived for both infinite-horizon case and finite-horizon case. For each case, we show that the optimal replacement age exists and is finite and investigate the effect of the age of the used item.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2005년도 ICCAS
• /
• pp.2081-2086
• /
• 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.

• 대한안전경영과학회지
• /
• 제23권4호
• /
• pp.105-112
• /
• 2021

This paper presents a periodic replacement policy for a system subject to shocks when the system is operating for a finite random horizon. The system is subject to shocks during operation, and each shock causes downgrading of the system performance and makes it more expensive to run by the additional running cost. Shocks arrive according to a nonhomogeneous or a renewal process, and we develop periodic replacement policies under a finite random operating horizon. The optimum periodic replacement interval which minimizes the total operating cost during the horizon is found. Numerical examples are presented to demonstrate the results.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1987년도 한국자동제어학술회의논문집(한일합동학술편); 한국과학기술대학, 충남; 16-17 Oct. 1987
• /
• pp.801-806
• /
• 1987

The receding horizon tracking control for the discrete time invariant systems is presented in this paper. This control law is derived with the receding horizon concept from the standard tracking problems. Stability properties of this control law are analyzed. It is shown that there exists a finite horizon index for which the closed loop systems are always asymptotically stable. The receding horizon tracking control is a kind of predictive control and will add a new clan to many existing predictive controls, with which some comparisons are made.

• Journal of applied mathematics & informatics
• /
• 제25권1_2호
• /
• pp.231-244
• /
• 2007

In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE's). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.