Optimal Control Rules Research Articles

A stochastic multi-channel revenue management model with time-dependent demand

Abstract E-commerce has seen rapid growth in recent years and many firms (e.g., airline companies) sell directly to their customers through different online channels or agents (e.g., Expedia, Ctrip, Qunar, elong) by paying different proportional fees. Besides the firm's revenue management decision of dynamically allocating its limited inventory to different demand classes, it may also get a different margin for selling the same product through different channels (at the same price). This paper examines the firm's optimal channel control strategy with combining its revenue management decision. We propose a multi-period multi-channel continuous-time model with time-dependent arrival rates. The market prices are different in different periods. The firm needs to decide the protection levels for all periods and the channel control strategy in each period. By developing a stochastic (Hamiltonian) channel control system and using the Maximum Principle, the optimal channel control rules are found and a threshold channel control policy is proposed. Based on the channel control policy, we show that there exist the unique optimal protection levels for all periods.

Identification of optimal feedback control rules from micro-quadrotor and insect flight trajectories.

This paper presents "optimal identification," a framework for using experimental data to identify the optimality conditions associated with the feedback control law implemented in the measurements. The technique compares closed loop trajectory measurements against a reduced order model of the open loop dynamics, and uses linear matrix inequalities to solve an inverse optimal control problem as a convex optimization that estimates the controller optimality conditions. In this study, the optimal identification technique is applied to two examples, that of a millimeter-scale micro-quadrotor with an engineered controller on board, and the example of a population of freely flying Drosophila hydei maneuvering about forward flight. The micro-quadrotor results show that the performance indices used to design an optimal flight control law for a micro-quadrotor may be recovered from the closed loop simulated flight trajectories, and the Drosophila results indicate that the combined effect of the insect longitudinal flight control sensing and feedback acts principally to regulate pitch rate.

Approaches for periodic inventory control under random production yield and fixed setup cost

In this paper, we study a multi-period inventory control problem with random demand and stochastically proportional production yield. The model includes nonzero processing lead time as well as fixed setup cost for a replenishment order. From prior research, it is evident that the optimal control rule must have a highly complex structure so that only simple policies are reasonable candidates for practical problem solving. In this paper, we propose a periodic review (s, S) policy with simple order inflation and compare different heuristic approaches for determining the two policy parameters. Two of these approaches are taken from the literature and, partly, adjusted to fit into the periodic-review planning context. A comprehensive numerical study reveals that both methods perform insufficiently, mainly because they do not take into account the yield risk from open orders during lead time. Therefore, three new approaches for parameter determination are developed, which consider this risk but follow very different concepts in their design. Two of these approaches follow simple-to-implement ideas for parameter adjustment to demand and yield risks and can be applied as spreadsheet applications, while the third one is based on an approximation of the objective value as function of the parameters s and S, which then must be computed numerically. From the experimental study, it turns out that all three approaches have a similarly high performance, not only concerning their average but also their worst-case behavior. The numerical study also provides insights into how yield randomness affects the policy parameters and elements of total expected cost.

Application of Minimum-time Optimal Control System in Buck-Boost Bi-linear Converters

In this study, the theory of minimum-time optimal control system in buck-boost bi-linear converters is described, so that output voltage regulation is carried out within minimum time. For this purpose, the Pontryagin's Minimum Principle is applied to find optimal switching level applying minimum-time optimal control rules. The results revealed that by utilizing an optimal switching level instead of classical switching patterns, output voltage regulation will be carried out within minimum time. However, transient energy index of increased overvoltage significantly reduces in order to attain minimum time optimal control in reduced output load. The laboratory results were used in order to verify numerical simulations.

An Optimal Control Approach to HIV Immunology

This paper introduces a mathematical model which describes the dynamics of the spread of HIV in the human body. This model is comprised of a system of ordinary differential equations that involve susceptible cells, infected cells, HIV, immune cells and immune active cells. The distinguishing feature in the proposed model with respect to other models in the literature is that it takes into account cells that represent two distinct mechanisms of the immune system in the defense against HIV: the non-HIV-activated cells and the HIV-activated cells. With a view at minimizing the side effects of a treatment that employs a drug combination designed to attack the HIV at various stages of its life cycle, we introduce control variables that represent the infected patient’s medication. The optimal control rule that prescribes the medication for a given time period is obtained by means of Pontryagin’s Maximum Principle.

Information Fusion Based Decoupling Control for Multivariable Nonlinear System

A decoupling control method based on information fusion estimation for a nonlinear system is presented in the paper. For each main channel and its coupled channels of the system, according to the information fusion theorem, the estimation of the system future state is obtained by fusing the information of the desired output trajectory of the system. Furthermore, approximate optimal control rule is obtained by fusing the system future state information and the control energy soft constraint information. Then an information fusion based decoupling control (IFBDC) system is established for the nonlinear coupled multiple-input multiple-output systems. This system cannot only control every channel to track reference signals, but also control any channel to be decoupled with other channels. Finally, a robot manipulator system is given to investigate the effectiveness of the decoupling control strategy, analyze its key parameters, and analyze the computational cost. The simulation results show that the IFBDC method is characterized by adjustable decoupling degree and high control quality.

Research on the optimal power management strategy for a hybrid electric bus

The power management strategy for a hybrid electric vehicle uses expert knowledge and experience to determine the control rules and thresholds, but it is difficult to obtain good performance. This paper presents a dynamic programming algorithm based on a powertrain system to find the optimal solution in the specific speed cycle, but this method cannot be applied to a real-time control system. Therefore, the optimal control rules and thresholds are extracted for the rule-based strategy; the simulation results show that the refined strategy can reduce the fuel consumption by about 14.41% compared with that obtained by the original logic rule control algorithm in the Chinese urban driving cycle. An online neural network energy controller based on the dynamic programming results is provided by choosing a reasonable network structure and control parameters to improve the control precision; the numerical simulation results show that the neural network controller improves the vehicle fuel economy by 15.05%, which is closer to the dynamic programming algorithm simulation result. This control algorithm not only can be used in real-time control and reduces the computational complexity but also allows new design ideas to be proposed for the control algorithm and the vehicle fuel consumption to be reduced.

An optimal vibration control strategy for a vehicle's active suspension based on improved cultural algorithm

This research is conducted such that the bodywork vertical vibration acceleration of a quarter car model is selected as a control objective and Fuzzy-PID control strategy based on improved cultural algorithm is proposed for vibration reduce. Cultural algorithm and niche algorithm are mixed together to design Fuzzy-PID controller and optimize control rules, which can accelerate optimization speed and has a good global optimal performance. The numerical results show that the active suspension, with Fuzzy-PID control strategy in which control rules are optimized by improved cultural algorithm, can significantly suppress the bodywork vertical vibration acceleration, and the ride comfort is improved. All the simulation analyses can give the support for the optimal control scheme.

Nonlinear Optimal Control of Continuously Variable Transmission Powertrain

Optimization of gear ratio with the objectives of fuel consumption reduction and vehicle longitudinal performance improvement has been the subject of many studies for years. Finding a strategy for changing gears with specific control objectives, especially in the design of vehicles equipped with Continuously Variable Transition system (CVT), which has advantage of arbitrary selection of gear ratio, has been the aim of some recent researches. Optimal control theory has rarely been used in the previous control approaches applied to such systems due to the limitations in the use of fast computational systems. The aim of this study is to design the aforementioned gear ratio change strategy and related control rules on the basis of optimal control. A driver model is also designed for the simulation of driving cycle using MATLAB Simulink Toolbar. Results of implementing optimal control rules in vehicle longitudinal movement simulation with the aim of fuel consumption reduction are finally represented. The presented method has the remarkable advantage of considerable fuel consumption reduction in comparison to other proposed approaches for gear ratio change strategies.

“logMSY” and optimal harvesting control rules: New tools for the implementation of the European Common Fisheries Policy

The reform of the European Common Fisheries Policy (CFP) aims to restores and maintains fish resources at levels which can produce the maximum sustainable yield (MSY) not later than 2015. In this paper we show why if MSY is used as reference point, optimal management may entail pulse fishing. This means that current management of the European fisheries is based on metrics that may generate solutions that would not be accepted as feasible due to the large social costs implied. We discuss why changes in the metrics used to define the reference point (the logMSY) and/or optimal harvesting control rules that stabilize the employment and the biomass around the optimal stationary values are two possible solutions of this paradox. The European Union should take into account all these considerations for the CFP reform proposals.

Endogenous Fishery Management in a Stochastic Model: Why Do Fishery Agencies Use TACs Along with Fishing Periods?

This paper seeks to explain the circumstances under which using total allowable catch (TAC) as an instrument to manage a fishery along with fishing periods may be of interest from a regulatory point of view. The deterministic analysis by Homans and Wilen (J Environ Econ Manag 32:1–21, 1997) and Anderson (Ann Oper Res 94:231–257, 2000) is thus extended to a stochastic scenario where the resource cannot be measured accurately. The resulting model is solved numerically to find the optimal control rules in the Iberian sardine stock. Three relevant conclusions can be highlighted from simulations: first, the greater the uncertainty regarding the state of the stock, the lower the probability of the fishery being closed before the end of the fishing period. Second, the use of TACs as a management instrument in fisheries that are already regulated by fishing periods leads to: (i) an increase in the optimal season length and harvests, especially for medium and high numbers of licences; (ii) improved biological and economic variables when the fleet is large; and (iii) extinction risk for the resource being eliminated. Third, the regulator would rather select the number of licences than restrict the season length.

News Shocks and Optimal Simple Rules

Summary This paper evaluates the performance of optimal simple policy rules in the presence of news shocks. It is shown that the inclusion of forward-looking elements enhances the performance of simple optimized interest rate rules when agents learn about future disturbances in advance. We provide a rationale for this result by demonstrating that, if shocks are news shocks, the optimal unrestricted control rule under commitment contains as a basic principle a forward-looking element.

Computations of optimal cylinder flow control in weakly conductive fluids

A nonlinear adjoint-based optimal control approach of cylinder wake by electromagnetic force has been investigated numerically in the paper. A cost functional representing the balance of the regulated quantities with different weights and interaction parameter N (Lorentz force) has been constituted, where the regulated quantities related with flow and force are taken as targets of regulation and the Lorentz force, (as interaction parameter N), is taken as a control input. Based on the cost functional and Navier–Stokes equations, the corresponding adjoint equations have been derived and the sensitivity of the cost functional is found to be a simple function of the adjoint stream function in the adjoint field. For the different regulations, the forms of optimal control rules are similar while the adjoint equations are different. The receding-horizon predictive control setting is employed to discuss the optimal control problems. Under the action of optimal N( t), the flow separation is suppressed fully, so that the oscillations of drag and lift are suppressed and the total drag coefficient decreases dramatically. For the different regulations, the control effects have some differences due to the different values of optimal inputs corresponding to the different adjoint flow fields.

A distributed on-off amplify-and-forward protocol for the fading parallel relay channel

A single source-destination pair communicating via a layer of two parallel relay nodes under slow fading is considered. The bit error rate (BER) performance of Alamouti-Coded Amplify-and-Forward (ACAF) transmission protocol under different power control strategies is investigated. The optimal power control rule is analytically derived and two distributed approximations to this rule are proposed. The optimal rule reveals an interesting fact: The transmission of each relay is on-off in nature. Simulation results show that our proposed distributed approximations improve the BER performance significantly.

Optimal control strategy for greenhouse lettuce: Incorporating supplemental lighting

Lettuce constitutes an important part of greenhouse production and much research has been devoted to investigating appropriate control strategies for that crop. In particular, recent studies have been concerned with avoiding high nitrate content of the harvested crop. This paper supplements previous studies by developing optimal control rules for the application of artificial light (when justified). It utilizes an existing lettuce model, Nicolet, in conjunction with a simple greenhouse model, to explore the control possibilities for hydroponic greenhouses where plant spacing is constant and marketing is limited by quota. Optimal control theory is used to solve the problem. It is shown that the optimal policy for the control of temperature and nitrate supply is unaffected by adding light control. Supplemental lighting starts when the crop coverage of the ground reaches a certain level and then increases continuously up to the installed capacity, if justified. Numerical simulations are used to illustrate this behaviour.

Optimal Exchange Rate Policy Under Unknown Pass-through and Learning With Applications to Korea

The purpose of this analysis is to explore optimal monetary and exchange rate policy in continuous time when there is uncertainty in the exchange rate pass-through mechanism. Selecting official reserves as an operating target, optimal feedback control rules are derived using MATLAB Simulink under a stochastic linear-quadratic Gaussian specification with a Kalman observer approach to learning the differing pass-through expectations. The model is estimated using discrete time Korean data, which is transformed into the continuous time model where simulations are applied to the Korean economy.

ACS algorithm-based adaptive fuzzy PID controller and its application to CIP-I intelligent leg

Based on the ant colony system (ACS) algorithm and fuzzy logic control, a new design method for optimal fuzzy PID controller was proposed. In this method, the ACS algorithm was used to optimize the input/output scaling factors of fuzzy PID controller to generate the optimal fuzzy control rules and optimal real-time control action on a given controlled object. The designed controller, called the Fuzzy-ACS PID controller, was used to control the CIP-I intelligent leg. The simulation experiments demonstrate that this controller has good control performance. Compared with other three optimal PID controllers designed respectively by using the differential evolution algorithm, the real-coded genetic algorithm, and the simulated annealing, it was verified that the Fuzzy-ACS PID controller has better control performance. Furthermore, the simulation results also verify that the proposed ACS algorithm has quick convergence speed, small solution variation, good dynamic convergence behavior, and high computation efficiency in searching for the optimal input/output scaling factors.

Generator Bidding in Oligopolistic Electricity Markets Using Optimal Control: Fundamentals and Application

In this paper, optimal control is applied to study generator bidding in an oligopolistic electricity market. The repeated bidding process in (hourly-based) real-time electricity markets is modeled as a dynamic feedback system; an optimal control problem is then formulated to explore individual generator's long-term/multiperiod optimization behavior. Particularly in our formulation, the periodic property of the system demand is considered. Several lemmas are included for concerning system stability. Based on the necessary conditions for optimality from the Pontryagin maximum principle, a sweeping method is proposed, and an optimal state-feedback control rule is then obtained via backward induction. Numerical results suggest that the generator who unilaterally applies optimal control for generation decisions will obtain more profits. A sensitivity analysis is also performed, identifying these market factors that affect the performance of optimal control

Optimal Monetary Policy in a Regime-Switching Economy: The Response to Abrupt Shifts in Exchange Rate Dynamics

This paper examines the trade-offs that a central bank faces when the exchange rate can experience sustained deviations from fundamentals and occasionally collapse. The economy is modelled as switching randomly between different regimes according to time-invariant transition probabilities. We compute both the optimal regime-switching control rule for this economy and optimised linear Taylor rules, in the two cases where the transition probabilities are known with certainty and where they are uncertain. The simple algorithms used in the computation are also of independent interest as tools for the study of monetary policy under general forms of (asymmetric) additive and multiplicative uncertainty. An interesting finding is that policies based on robust (minmax) values of the transition probabilities are usually more conservative.

Optimal monetary policy in a regime-switching economy: The response to abrupt shifts in exchange rate dynamics

This paper examines the trade-offs that a central bank faces when the exchange rate can experience sustained deviations from fundamentals and occasionally collapse. The economy is modelled as switching randomly between different regimes according to time-invariant transition probabilities. We compute both the optimal regime-switching control rule for this economy and optimised linear Taylor rules, in the two cases where the transition probabilities are known with certainty and where they are uncertain. The simple algorithms used in the computation are also of independent interest as tools for the study of monetary policy under general forms of (asymmetric) additive and multiplicative uncertainty. An interesting finding is that policies based on robust (minmax) values of the transition probabilities are usually more conservative.