Optimal Control (optimal + control)

Distribution by Scientific Domains
Distribution within Engineering

Terms modified by Optimal Control

  • optimal control policy
  • optimal control problem
  • optimal control theory

  • Selected Abstracts

    Local Government Portfolios and Regional Growth: Some Combined Dynamic CGE/Optimal Control Results

    M.S. Deepak
    A theoretical policy model is presented that combines regional dynamic CGE modeling and optimal control to explore the role of local government taxation and expenditure in enhancing regional growth. It contributes to the regional CGE literature by explicitly solving for an optimal policy and augments earlier regional optimal control models by adding endogenous optimization of producer and consumer agents in response to endogenously determined prices. Results of three policy regimes are analyzed in terms of gains in the objective function, impacts on income inequality, and sensitivity to model parameterization. [source]

    Optimal Control of Rigid-Link Manipulators by Indirect Methods

    GAMM - MITTEILUNGEN, Issue 1 2008
    Rainer Callies
    Abstract The present paper is a survey and research paper on the treatment of optimal control problems of rigid-link manipulators by indirect methods. Maximum Principle based approaches provide an excellent tool to calculate optimal reference trajectories for multi-link manipulators with high accuracy. Their major drawback was the need to explicitly formulate the complicated system of adjoint differential equations and to apply the full apparatus of optimal control theory. This is necessary in order to convert the optimal control problem into a piecewise defined, nonlinear multi-point boundary value problem. An accurate and efficient access to first- and higher-order derivatives is crucial. The approach described in this paper allows it to generate all the derivative information recursively and simultaneously with the recursive formulation of the equations of motion. Nonlinear state and control constraints are treated without any simplifications by transforming them into sequences of systems of linear equations. By these means, the modeling of the complete optimal control problem and the accompanying boundary value problem is automated to a great extent. The fast numerical solution is by the advanced multiple shooting method JANUS. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    Optimal Control of Voltage in Distribution Systems by Voltage Reference Management

    Tomonobu Senjyu Student member
    Abstract Recently, renewable energy technologies such as wind turbine generators and photovoltaic (PV) systems have been introduced as distributed generations (DGs). Connections of a large amount of distributed generations may cause voltage deviation beyond the statutory range in distribution systems. A reactive power control of DGs can be a solution of this problem, and it also has a possibility to reduce distribution loss. In this paper, we propose a control methodology of voltage profile in a distribution system using reactive power control of inverters interfaced with DGs and tap changing transformers. In the proposed method, a one-day schedule of voltage references for the control devices are determined by an optimization technique based on predicted values of load demand and PV power generation. Reactive power control of interfaced inverters is implemented within the inverter capacity without reducing active power output. The proposed method accomplishes voltage regulation within the acceptable range and reduction of distribution loss. The effectiveness of the proposed method is confirmed by simulations. Copyright © 2009 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source]

    Optimal Control of Iterative Solution Methods for Linear Systems of Equations

    Uwe Helmke
    Iterative solution methods for linear systems of equations can be regarded as discrete-time control systems, for which a stabilizing feedback control has to be found. Well known algorithms such as GMRES(m) may exhibit unstable dynamics or sensitive dependence on initial conditions, thus preventing the algorithm to converge to the desired solution. Based on linear system feedback design techniques a new algorithm is proposed that does not suffer under such shortcomings. Global convergence to the desired solution is shown for any initial state. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    Optimal Control of Selling Channels for an Online Retailer with Cost-per-Click Payments and Seasonal Products

    Frank Y. Chen
    The problem studied in this paper is a predigestion of the decision faced by online retailers (etailers) that advertise on publisher or comparison-shopping websites. An etailer may sell its product not only through its online and bricks-and-mortar stores, but also through the websites of one or more third parties (e.g., Yahoo.com). However, the etailer has to pay a certain amount to such third parties in an action-based payment scheme, such as a cost-per-click (CPC) scheme. Under the CPC scheme, payment is based solely on click-throughs, which means that the etailer pays only when a shopper clicks through to the product page of its website. Only a fraction of such clicks lead to actual sales. The extra cost that is associated with shoppers who first click through to the third-party websites makes them less attractive as customers than those who directly visit the etailer's online store. Moreover, the CPC rate for a prominent placement is normally set by competitive bidding, and thus varies over time. Therefore, the etailer needs to decide dynamically whether or not to list on a third-party website. The structural properties of the optimal policy are discussed, and numerical examples are given to show the revenue impact of dynamic listing control. [source]

    An Integrated Software Environment For Powertrain Feasibility Assessment Using Optimization And Optimal Control

    Ilya V. Kolmanovsky
    ABSTRACT With the increase in automotive powertrain complexity, an upfront assessment of powertrain capability in meeting its design targets is important early on in the development programs. The optimization of control policy based on powertrain simulation models can facilitate this assessment and establish limits of achievable performance for a given powertrain configuration and parameters. The paper discusses several computational optimization and user interface solutions for deploying a numerical optimal control approach in a user-friendly software environment. [source]

    Optimal flow control for Navier,Stokes equations: drag minimization

    L. Dedè
    Abstract Optimal control and shape optimization techniques have an increasing role in Fluid Dynamics problems governed by partial differential equations (PDEs). In this paper, we consider the problem of drag minimization for a body in relative motion in a fluid by controlling the velocity through the body boundary. With this aim, we handle with an optimal control approach applied to the steady incompressible Navier,Stokes equations. We use the Lagrangian functional approach and we consider the Lagrangian multiplier method for the treatment of the Dirichlet boundary conditions, which include the control function itself. Moreover, we express the drag coefficient, which is the functional to be minimized, through the variational form of the Navier,Stokes equations. In this way, we can derive, in a straightforward manner, the adjoint and sensitivity equations associated with the optimal control problem, even in the presence of Dirichlet control functions. The problem is solved numerically by an iterative optimization procedure applied to state and adjoint PDEs which we approximate by the finite element method. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Optimal control of singular systems via piecewise linear polynomial functions

    Mohsen Razzaghi
    A method for finding the optimal control of linear singular systems with a quadratic cost functional using piecewise linear polynomial functions is discussed. The state variable, state rate, and the control vector are expanded in piecewise linear polynomial functions with unknown coefficients. The relation between the coefficients of the state rate with state variable is provided and the necessary condition of optimality is derived as a linear system of algebraic equations in terms of the unknown coefficients of the state and control vectors. A numerical example is included to demonstrate the validity and the applicability of the technique. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Optimal control of a production-inventory system with both backorders and lost sales

    Saif Benjaafar
    Abstract We consider the optimal control of a production inventory-system with a single product and two customer classes where items are produced one unit at a time. Upon arrival, customer orders can be fulfilled from existing inventory, if there is any, backordered, or rejected. The two classes are differentiated by their backorder and lost sales costs. At each decision epoch, we must determine whether or not to produce an item and if so, whether to use this item to increase inventory or to reduce backlog. At each decision epoch, we must also determine whether or not to satisfy demand from a particular class (should one arise), backorder it, or reject it. In doing so, we must balance inventory holding costs against the costs of backordering and lost sales. We formulate the problem as a Markov decision process and use it to characterize the structure of the optimal policy. We show that the optimal policy can be described by three state-dependent thresholds: a production base-stock level and two order-admission levels, one for each class. The production base-stock level determines when production takes place and how to allocate items that are produced. This base-stock level also determines when orders from the class with the lower shortage costs (Class 2) are backordered and not fulfilled from inventory. The order-admission levels determine when orders should be rejected. We show that the threshold levels are monotonic (either nonincreasing or nondecreasing) in the backorder level of Class 2. We also characterize analytically the sensitivity of these thresholds to the various cost parameters. Using numerical results, we compare the performance of the optimal policy against several heuristics and show that those that do not allow for the possibility of both backordering and rejecting orders can perform poorly.© 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010 [source]

    Optimal control of work-in-process inventory of a two-station production line,

    A. Kokangul
    Abstract Most production lines keep a minimal level of inventory stock to save storage costs and buffer space. However, the random nature of processing, breakdown, and repair times can significantly affect the efficiency of a production line and force the stocking of work-in-process inventory. We are interested in the case when starvation and blockage are preferentially avoided. In this study, a mathematical model has been developed using asymptotic approximation and simulation that provides asymptotic results for the expected value and the variance of the stock level in a buffer as a function of time. In addition, the functional relationship between buffer capacity and the first stopping time caused by starvation or blockage has been determined. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Optimal control for linear system using genetic programming

    A. Vincent Antony Kumar
    Abstract In this paper, optimal control for a linear system with quadratic performance is obtained using genetic programming (GP). The goal is to find the optimal control with reduced calculus effort using non-traditional methods. The obtained GP solution is compared with the traditional Runge,Kutta method. To obtain optimal control, the solution of matrix Riccati differential equation is computed based on grammatical evolution. The accuracy of the solution of the GP approach to the problem is qualitatively better than traditional methods. An illustrative numerical example is presented for the proposed method. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Optimal control and design of a cold store using dynamic optimization

    Leo Lukasse
    Abstract The design of controlled processes is a combined optimal control and design problem (OCDP). Literature on solving large OCDPs is rare. This paper presents an algorithm for solving large OCDPs. For this algorithm system dynamics, objective function and their first-order derivatives must be continuous in the state, control and design parameters. The algorithm is successfully applied to the combined control and design problem of a cold store with three possible refrigeration technologies: mechanical refrigeration, ventilation and evaporative cooling. As a result, insight into cost effectiveness of the refrigeration technologies is generated. It is concluded that for this cold store in the Netherlands evaporative cooling is too expensive. Ventilation is economically viable if the cold store is to be used in January only. In case the cold store is to be operated all year then it is most economical to rely on mechanical refrigeration only and use the overcapacity during most part of the year to shift refrigeration to low-tariff hours. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Optimal control of a water reservoir with expected value,variance criteria

    Andrzej Karbowski
    Abstract The article presents how to solve a reservoir management problem, which has been formulated as a two-criteria stochastic optimal control problem. Apart from the expected value of a performance index, its variance is also considered. Three approaches are described: a method based on the Lagrange function; a method based on the ordinary moment of the second order (finite time horizon); and a method based on linear programming (infinite time horizon). In the second part of the article, they are assessed in a case study concerning a reservoir in the southern part of Poland. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Optimal control of a revenue management system with dynamic pricing facing linear demand

    Fee-Seng Chou
    Abstract This paper considers a dynamic pricing problem over a finite horizon where demand for a product is a time-varying linear function of price. It is assumed that at the start of the horizon there is a fixed amount of the product available. The decision problem is to determine the optimal price at each time period in order to maximize the total revenue generated from the sale of the product. In order to obtain structural results we formulate the decision problem as an optimal control problem and solve it using Pontryagin's principle. For those problems which are not easily solvable when formulated as an optimal control problem, we present a simple convergent algorithm based on Pontryagin's principle that involves solving a sequence of very small quadratic programming (QP) problems. We also consider the case where the initial inventory of the product is a decision variable. We then analyse the two-product version of the problem where the linear demand functions are defined in the sense of Bertrand and we again solve the problem using Pontryagin's principle. A special case of the optimal control problem is solved by transforming it into a linear complementarity problem. For the two-product problem we again present a simple algorithm that involves solving a sequence of small QP problems and also consider the case where the initial inventory levels are decision variables. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Optimal control of non-linear chemical reactors via an initial-value Hamiltonian problem

    V. Costanza
    Abstract The problem of designing strategies for optimal feedback control of non-linear processes, specially for regulation and set-point changing, is attacked in this paper. A novel procedure based on the Hamiltonian equations associated to a bilinear approximation of the dynamics and a quadratic cost is presented. The usual boundary-value situation for the coupled state,costate system is transformed into an initial-value problem through the solution of a generalized algebraic Riccati equation. This allows to integrate the Hamiltonian equations on-line, and to construct the feedback law by using the costate solution trajectory. Results are shown applied to a classical non-linear chemical reactor model, and compared against suboptimal bilinear-quadratic strategies based on power series expansions. Since state variables calculated from Hamiltonian equations may differ from the values of physical states, the proposed control strategy is suboptimal with respect to the original plant. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    An efficient scheme for minimax solutions of multiple linear-quadratic control

    Wan-Lung Ng
    Abstract Optimal control is one of the most important methodologies for studies of dynamic systems in many areas of sciences, engineering and economics. Minimax optimal control is a special topic in the general framework of multiple optimal control problems. Minimax optimal control can be considered as a dynamic game with multiple players under the same system. In this paper, we develop a fast search for a minimax solution of multiple linear-quadratic control problems. The algorithm improves the existing solution scheme by adjusting the multiple weighting coefficients in each iteration and also including updates for step-size control. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Optimal control for non-linear integrodifferential functional equations

    Jin-Mun Jeong
    Abstract An optimal control problem for a non-linear control system with a hemicontinuous and coercive operator is studied. The existence, uniqueness, and a variation of solutions of the system are also given. An example is presented to illustrate the theory. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Optimal control of an HIV immunology model

    Hem Raj Joshi
    Abstract A system of ordinary differential equations, which describes the interaction of HIV and T -cells in the immune system is utilized, and optimal controls representing drug treatment strategies of this model are explored. Two types of treatments are used, and existence and uniqueness results for the optimal control pair are established. The optimality system is derived and then solved numerically using an iterative method with a Runge,Kutta fourth order scheme. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Optimal control of innate immune response

    Robert F. Stengel
    Abstract Treatment of a pathogenic disease process is interpreted as the optimal control of a dynamic system. Evolution of the disease is characterized by a non-linear, fourth-order ordinary differential equation that describes concentrations of pathogens, plasma cells, and antibodies, as well as a numerical indication of patient health. Without control, the dynamic model evidences sub-clinical or clinical decay, chronic stabilization, or unrestrained lethal growth of the pathogen, depending on the initial conditions for the infection. The dynamic equations are controlled by therapeutic agents that affect the rate of change of system variables. Control histories that minimize a quadratic cost function are generated by numerical optimization over a fixed time interval, given otherwise lethal initial conditions. Tradeoffs between cost function weighting of pathogens, organ health, and use of therapeutics are evaluated. Optimal control solutions that defeat the pathogen and preserve organ health are demonstrated for four different approaches to therapy. It is shown that control theory can point the way toward new protocols for treatment and remediation of human diseases. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Optimal control of deterministic epidemics

    Horst Behncke
    Abstract Various deterministic optimal control models for SIR-epidemics are investigated in this paper. The epidemics are governed by a rather general interaction, which covers most cases studied in the literature. Vaccination, quarantine, screening or health promotion campaigns as forms of control are considered. In all cases one finds a maximum effort control on some initial time interval. In addition, uniqueness and monotonicity properties of these models are studied. The results are also extended to the infinite time-horizon situation. Copyright © 2000 John Wiley & Sons, Ltd. [source]

    Direct versus Indirect Allorecognition Pathways: On the Right Track

    G. Benichou
    Optimal control of the T cell response may rely primarily on therapeutic control of the indirect allorecognition pathway. See article by Kang et al on page 709. [source]

    Optimal control of fuel processing system using generalized linear quadratic Gaussian and loop transfer recovery method,,

    Huan-Liang Tsai
    Abstract This paper proposes an optimal control system that consists of both feedforward and state-feedback controllers designed using a generalized linear quadratic Gaussian and loop transfer recovery (GLQG/LTR) method for a fuel processing system (FPS). This FPS uses natural gas as fuel and reacts with atmospheric air through a catalytic partial oxidation (CPO) response. The control objective is focused on the regulatory performance of the output vector in response to a desired stack current command in the face of load variation. The proposed method provides another degree of freedom in the optimal control design and gives the compensated system a prescribed degree of stability. Finally, the numerical simulations of compensated FPS reveal that the proposed method displays better performance and robustness properties in both time-domain and frequency-domain responses than those obtained by the traditional LQ Method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source]

    Predictive instantaneous optimal control of elastic structures during earthquakes

    Kevin K. F. Wong
    Abstract A predictive instantaneous optimal control (PIOC) algorithm is proposed for controlling the seismic responses of elastic structures. This algorithm compensates for the time delay that happens in practical control applications by predicting the structural response over a period that equals the time delay, and by substituting the predicted response in the instantaneous optimal control (IOC) algorithm. The unique feature of this proposed PIOC algorithm is that it is simple and at the same time compensates for the time delay very effectively. Numerical examples of single degree of freedom structures are presented to compare the performance of PIOC and IOC systems for various time delay magnitudes. Results show that a time delay always causes degradation of control efficiency, but PIOC can greatly reduce this degradation compared to IOC. The effects of the structure's natural periods and the choice of control gains on the degradation induced by the time delay are also analyzed. Results show that shorter natural periods and larger control gains are both more sensitive and more serious to the degradation of control efficiency. Finally, a practical application of PIOC is performed on a six-story moment-resisting steel frame. It is demonstrated that PIOC contributes significantly to maintain stability in multiple degree of freedom structures, and at the same time PIOC has a satisfactory control performance. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    Experiments on stabilizing receding horizon control of a direct drive manipulator

    Yasunori Kawai
    Abstract In this paper, the application of receding horizon control to a two-link direct drive robot arm is demonstrated. Instead of terminal constraints, a terminal cost on receding horizon control is used to guarantee stability, because of the computational demand. The key idea of this paper is to apply receding horizon control with a terminal cost derived from the energy function of the robot system. The energy function is defined as the control Lyapunov function by considering inverse optimality. In experimental results, stability and performance are compared with respect to the horizon length by applying receding horizon control and inverse optimal control to the robot arm. © 2008 Wiley Periodicals, Inc. Electron Comm Jpn, 91(5): 33,40, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10113 [source]

    Optimal capacitors on-line operation on distribution networks by an integrated control system based on local neurocontrollers

    I. Arces
    This work proposes a contribution to the problem of an optimal control of switched capacitor banks installed in radial distribution networks, by studying the possibility of adopting an integrated control strategy based on the use of neural local controllers able to manage the status of every compensation bank. In order to analyse the feasibility of this solution, the kind of control proposed was implemented in a particular study case, which allowed to compare the performance of a set of local neurocontrollers with the results of a centralized optimisation procedure, for different conditions of load and network configuration. [source]

    Lie Theory for Quantum Control

    GAMM - MITTEILUNGEN, Issue 1 2008
    G. Dirr
    Abstract One of the main theoretical challenges in quantum computing is the design of explicit schemes that enable one to effectively factorize a given final unitary operator into a product of basic unitary operators. As this is equivalent to a constructive controllability task on a Lie group of special unitary operators, one faces interesting classes of bilinear optimal control problems for which efficient numerical solution algorithms are sought for. In this paper we give a review on recent Lie-theoretical developments in finite-dimensional quantum control that play a key role for solving such factorization problems on a compact Lie group. After a brief introduction to basic terms and concepts from quantum mechanics, we address the fundamental control theoretic issues for bilinear control systems and survey standard techniques fromLie theory relevant for quantum control. Questions of controllability, accessibility and time optimal control of spin systems are in the center of our interest. Some remarks on computational aspects are included as well. The idea is to enable the potential reader to understand the problems in clear mathematical terms, to assess the current state of the art and get an overview on recent developments in quantum control-an emerging interdisciplinary field between physics, control and computation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    Reverse computation of forced convection heat transfer for optimal control of thermal boundary conditions

    Kazunari Momose
    Abstract A reverse computation based on adjoint formulation of forced convection heat transfer is proposed to obtain the optimal thermal boundary conditions for heat transfer characteristics; for example, a total heat transfer rate or a temperature at a specific location. In the reverse analysis via adjoint formulation, the heat flow is reversed in both time and space. Thus, using the numerical solution of the adjoint problem, we can inversely predict the boundary condition effects on the heat transfer characteristics. As a result, we can obtain the optimal thermal boundary conditions in both time and space to control the heat transfer at any given time. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(3): 161,174, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20002 [source]

    Method to improve the mitigative effectiveness of a series of check dams against debris flows

    Rabindra Osti
    Abstract The advance of technology has led to more competent countermeasures, but lives and properties still continue to suffer from water-induced disasters, such as floods, landslides, and debris flows. To increase the effectiveness of counter systems, improved methods of planning and designing such systems are prerequisite. This paper describes briefly a methodological approach for predicting debris flow characteristics, and proposes techniques for evaluating and improving the mitigative effectiveness of check dams against debris flows in steep mountain torrents. Additionally, a non-dimensional parameter, namely potential storage volume, is introduced to generalize the evaluation processes. As an example, the 1999 debris-flow event in the San Julian River, Venezuela, is chosen for discussion. The paper also proposes a method of evaluating the control function of a series of check dams as well as the criteria for the selection of their sizes, numbers and locations. It is hoped that this work will help to determine which combinations of check dams will fit best together for the optimal control of debris flows and available resources in any river basin. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Optimization of Train Speed Profile for Minimum Energy Consumption

    Masafumi Miyatake Member
    Abstract The optimal operation of railway systems minimizing total energy consumption is discussed in this paper. Firstly, some measures of finding energy-saving train speed profiles are outlined. After the characteristics that should be considered in optimizing train operation are clarified, complete optimization based on optimal control theory is reviewed. Their basic formulations are summarized taking into account most of the difficult characteristics peculiar to railway systems. Three methods of solving the formulation, dynamic programming (DP), gradient method, and sequential quadratic programming (SQP), are introduced. The last two methods can also control the state of charge (SOC) of the energy storage devices. By showing some numerical results of simulations, the significance of solving not only optimal speed profiles but also optimal SOC profiles of energy storage are emphasized, because the numerical results are beyond the conventional qualitative studies. Future scope for applying the methods to real-time optimal control is also mentioned. Copyright © 2010 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source]

    Optimal design and optimal control of structures undergoing finite rotations and elastic deformations

    A. Ibrahimbegovic
    Abstract In this work, we deal with the optimal design and optimal control of structures undergoing large rotations and large elastic deformations. In other words, we show how to find the corresponding initial configuration through optimal design or the corresponding set of multiple load parameters through optimal control, in order to recover a desired deformed configuration or some desirable features of the deformed configuration as specified more precisely by the objective or cost function. The model problem chosen to illustrate the proposed optimal design and optimal control methodologies is the one of geometrically exact beam. First, we present a non-standard formulation of the optimal design and optimal control problems, relying on the method of Lagrange multipliers in order to make the mechanics state variables independent from either design or control variables and thus provide the most general basis for developing the best possible solution procedure. Two different solution procedures are then explored, one based on the diffuse approximation of response function and gradient method and the other one based on genetic algorithm. A number of numerical examples are given in order to illustrate both the advantages and potential drawbacks of each of the presented procedures. Copyright © 2004 John Wiley & Sons, Ltd. [source]