Markov跳变系统滚动时域有限记忆控制

针对离散时间Markov跳变系统,提出滚动时域有限记忆控制的方法.在一段有限滤波时域上,利用系统输入与输出变量的线性组合构造一段有限控制时域上的输出反馈控制器.首先,不考虑跳变系统均方可镇定,基于最优控制的方法,获得以迭代计算形式给出的控制器,并使其在无偏条件下能优化二次型性能指标.其次,进一步考虑在成本衰减条件下确定终端加权矩阵,并以它作为边界条件计算得到最优控制律,调节系统均方稳定.为便于求解,成本衰减条件以线性矩阵不等式的形式给出.仿真实例验证了所提方法的可行性和有效性.     

A unified approach to portfolio optimization with linear transaction costs

In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume of trade. We also discuss some methods for solving numerically the problem within our unified framework.     

Primal-dual methods for the computation of trading regions under proportional transaction costs

Portfolio optimization problems on a finite time horizon under proportional transaction costs are considered. The objective is to maximize the expected utility of the terminal wealth. The ensuing non-smooth time-dependent Hamilton–Jacobi–Bellman equation is solved by regularization and the application of a semi-smooth Newton method. Discretization in space is carried out by finite differences or finite elements. Computational results for one and two risky assets are provided.     

Capital renewal as a real option

We consider the timing of replacement of obsolete subsystems within an extensive, complex infrastructure. Such replacement action, known as capital renewal, must balance uncertainty about future profitability against uncertainty about future renewal costs. Treating renewal investments as real options, we derive an optimal solution to the infinite horizon version of this problem and determine the total present value of an institution’s capital renewal options. We investigate the sensitivity of the infinite horizon solution to variations in key problem parameters and highlight the system scenarios in which timely renewal activity is most profitable. For finite horizon renewal planning, we show that our solution performs better than a policy of constant periodic renewals if more than two renewal cycles are completed.     

Optimal Quarantine Programmes for Controlling an Epidemic Spread

An optimal control problem is formulated with a simple epidemic model in which the control of the epidemic is effected by varying the scale of the quarantine program in a way which minimizes a discounted linear cost over an infinite horizon. An important function of the problem parameters is identified. It is shown that if this function has a value of less than or equal to one, then the optimal policy is not to quarantine at all. While if this functions assume a value in excess of one, then the optimal policy is not to quarantine at all if the initial fraction of infectives is sufficiently high; otherwise, it is optimal to have a full scale quarantine program. Slight modification in these policies are required for the finite horizon version of the problem.     

Receding Horizon Robust Control for Nonlinear Systems Based on Linear Differential Inclusion of Neural Networks

In this paper, we present a new receding horizon neural robust control scheme for a class of nonlinear systems based on the linear differential inclusion (LDI) representation of neural networks. First, we propose a linear matrix inequality (LMI) condition on the terminal weighting matrix for a receding horizon neural robust control scheme. This condition guarantees the nonincreasing monotonicity of the saddle point value of the finite horizon dynamic game. We then propose a receding horizon neural robust control scheme for nonlinear systems, which ensures the infinite horizon robust performance and the internal stability of closed-loop systems. Since the proposed control scheme can effectively deal with input and state constraints in an optimization problem, it does not cause the instability problem or give the poor performance associated with the existing neural robust control schemes.     

The Repair Limit Replacement Method

In the repair limit replacement method when an item requires repair it is first inspected and the repair cost is estimated. Repair is only then undertaken if the estimated cost is less than the "repair limit". Dynamic programming methods are used in this paper as a general approach to the problem of determining optimum repair limits. Two problems are formulated and the cases of finite and infinite planning horizons and discounted and undiscounted costs are discussed. Methods are given for allowing for equipment availability and for the introduction of new types of equipment. An improved general formulation for finite time horizon, stochastic, dynamic programming problems is developed.     

Alternate approaches to solving the Holt et al. model and to performing sensitivity analysis

The staircase structure of the recurrence relations for the Holt et al. model can be used to develop simple and efficient computational approaches for obtaining the optimal solution. The computational approaches are noniterative. We deal with finite planning horizon cases in which one or more terminal boundary conditions are not specified. The computation time varies linearly with the number of periods in the planning horizon. A framework is also developed for sensitivity analysis on the terminal values and for generation of alternate production plans. The alternate plans provide considerable flexibility to the decision maker because they can be evaluated in the context of (a) constraints not included in the model, (b) plant capacity, (c) actual costs, and (d) implications beyond the planning horizon. The results should be of interest for real world applications as well as for research because the Holt et al. model continues to be used as a benchmark to evaluate the performance of other aggregate production planning models.     

Portfolio Optimization in a Semi-Markov Modulated Market

We address a portfolio optimization problem in a semi-Markov modulated market. We study both the terminal expected utility optimization on finite time horizon and the risk-sensitive portfolio optimization on finite and infinite time horizon. We obtain optimal portfolios in relevant cases. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem. This work was supported in part by a DST project: SR/S4/MS: 379/06; also supported in part by a grant from UGC via DSA-SAP Phase IV, and in part by a CSIR Fellowship.     

Dynamic cost allocation for economic lot sizing games

We consider a cooperative game defined by an economic lot sizing problem with concave ordering costs over a finite time horizon, in which each player faces demand for a single product in each period and coalitions can pool orders. We show how to compute a dynamic cost allocation in the strong sequential core of this game, i.e. an allocation over time that exactly distributes costs and is stable against coalitional defections at every period of the time horizon.     

Optimal inventory policies with two modes of freight transportation

Theoretical inventory models with constant demand rate and two transportation modes are analyzed in this paper. The transportation options are truckloads with fixed costs, a package delivery carrier with a constant cost per unit, or using a combination of both modes simultaneously. Exact algorithms for computing the optimal policies are derived for single stage models over both an infinite and a finite planning horizon.     

On the Selection of One Feedback Nash Equilibrium in Discounted Linear-Quadratic Games

We study a selection method for a Nash feedback equilibrium of a one-dimensional linear-quadratic nonzero-sum game over an infinite horizon. By introducing a change in the time variable, one obtains an associated game over a finite horizon T > 0 and with free terminal state. This associated game admits a unique solution which converges to a particular Nash feedback equilibrium of the original problem as the horizon T goes to infinity.     

On the control of a generalized storage model

A finite-capacity storage model is considered. The random inputs (negative inputs represent demands) are of various types, determined by a Markov chain, and occur at discrete times. Under suitable assumptions on the costs involved, including a penalty cost for unmet demand, an optimal control policy is determined for the releases from the storage facility, when operated over a finite horizon. Stationary control policies for the unbounded horizon are also determined and conditions for their optimality are discussed. Finally, a few simple examples are considered.The author would like to acknowledge the constructive comments of the referee, which led to an improved exposition of the present paper.     

Economies of scale,competitiveness, and trade patterns within the European community: Clarendon Press,Oxford, 1983, 193 pages, £20.00

We consider two queues in series with input to each queue, which can be controlled by accepting or rejecting arriving customers. The objective is to maximize the discounted or average expected net benefit over a finite or infinite horizon, where net benefit is composed of (random) rewards for entering customers minus holding costs assessed against the customers at each queue. Provided that it costs more to hold a customer at the first queue than at the second, we show that an optimal policy is monotonic in the following senses: Adding a customer to either queue makes it less likely that we will accept a new customer into either queue; moreover moving a customer from the first queue to the second makes it more (less) likely that we will accept a new customer into the first (second) queue. Our model has policy implications for flow control in communication systems, industrial job shops, and traffic-flow systems. We comment on the relation between the control policies implied by our model and those proposed in the communicationa literature.     

Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem

This paper concerns optimal investment problem of a CRRA investor who faces proportional transaction costs and finite time horizon. From the angle of stochastic control, it is a singular control problem, whose value function is governed by a time-dependent HJB equation with gradient constraints. We reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. This enables us to make use of the well-developed theory of obstacle problem to attack the problem. The C2,1 regularity of the value function is proven and the behaviors of the free boundaries are completely characterized.     

Network Simulation Method for the evaluation of perturbed supply chains on a finite horizon

Due to lead times and other delays in a chain, the Net Present Value (NPV) can be easily estimated if Laplace transforms in MRP models are employed. This leads to the estimation of NPV on an infinite horizon. However, for the simultaneous perturbations of several parameters in a supply chain and activities running on the finite horizon, NPV could be overestimated. Therefore, we suggest the parallel use of the Network Simulation Method (NSM) with the MRP theory to reduce these overestimations. This paper aims to present the NSM to evaluate supply chains on a finite horizon when stochastic behaviour of time delays and other perturbations of parameters are also essential, which is typical for food and drug supply chains. The circuit simulator NGSPICE, which was previously used by certain authors in thermodynamics, also evaluates the financial consequences of simultaneous perturbations in a finite chain. This approach holds better for the stochastic processes of simultaneous perturbations, compared to our results achieved using MRP theory without these corrections. As presented in the numerical example, the shorter the horizon and lower the interest rate, the more important it is to use the correction factors obtained from the NGSPICE simulator.

     

Joint pricing and inventory control with a Markovian demand model

We consider the joint pricing and inventory control problem for a single product over a finite horizon and with periodic review. The demand distribution in each period is determined by an exogenous Markov chain. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. The surplus costs as well as fixed and variable costs are state dependent. We show the existence of an optimal (s, S, p)-type feedback policy for the additive demand model. We extend the model to the case of emergency orders. We compute the optimal policy for a class of Markovian demand and illustrate the benefits of dynamic pricing over fixed pricing through numerical examples. The results indicate that it is more beneficial to implement dynamic pricing in a Markovian demand environment with a high fixed ordering cost or with high demand variability.     

A multi-period order selection problem in flexible manufacturing systems

We consider a multi-period order selection problem in flexible manufacturing systems, which is the problem of selecting orders to be produced in each period during the upcoming planning horizon with the objective of minimising earliness and tardiness costs and subcontracting costs. The earliness and tardiness costs are incurred if an order is not finished on time, while subcontracting cost is incurred if an order is not selected within the planning horizon (and must be subcontracted) due to processing time capacity or tool magazine capacity. This problem is formulated as a 0–1 integer program which can be transformed into a generalised assignment problem. To solve the problem, a heuristic algorithm is developed using a Lagrangian relaxation technique. Effectiveness of the algorithm is tested on randomly generated problems and results are reported.     

Markov Decision Processes on Borel Spaces with Total Cost and Random Horizon

This paper deals with Markov Decision Processes (MDPs) on Borel spaces with possibly unbounded costs. The criterion to be optimized is the expected total cost with a random horizon of infinite support. In this paper, it is observed that this performance criterion is equivalent to the expected total discounted cost with an infinite horizon and a varying-time discount factor. Then, the optimal value function and the optimal policy are characterized through some suitable versions of the Dynamic Programming Equation. Moreover, it is proved that the optimal value function of the optimal control problem with a random horizon can be bounded from above by the optimal value function of a discounted optimal control problem with a fixed discount factor. In this case, the discount factor is defined in an adequate way by the parameters introduced for the study of the optimal control problem with a random horizon. To illustrate the theory developed, a version of the Linear-Quadratic model with a random horizon and a Logarithm Consumption-Investment model are presented.     

Joint replacement in an operational planning phase

We consider the problem of combining replacements of multiple components in an operational planning phase. Within an infinite or finite time horizon, decisions concerning replacement of components are made at discrete time epochs. The optimal solution of this problem is limited to only a small number of components. We present a heuristic rolling horizon approach that decomposes the problem; at each decision epoch an initial plan is made that addresses components separately, and subsequently a deviation from this plan is allowed to enable joint replacement. This approach provides insight into why certain actions are taken. The time needed to determine an action at a certain epoch is only quadratic in the number of components. After dealing with harmonisation and horizon effects, our approach yields average costs less than 1% above the minimum value.