bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical solution of the symmetric riccati equation through riccati iteration
Authors: Anderson Leonard R. , Brewer Dennis W. , Baykan A. Rasim 
Published: July 2007

AbstractThis paper presents a new method for solving the symmetric algebraic Riccati equation from optimal control. The new method employs ‘Riccati iteration’ as used for time‐scale decoupling in structural vibration problems. The rate of convergence of the algorithm is governed by the relative separation of small and large eigenvalues in the shifted Hamiltonian equations. If this ratio of eigenvalues is less than one, the algorithm is globally convergent. Riccati iteration is demonstrated for a set of 8th‐order linear‐quadratic regulator problems, and preliminary timing and accuracy comparisons are presented.
Solution algorithms for non‐linear singularly perturbed optimal control problems
Authors: Ardema Mark D. 
Published: July 2007

AbstractThe applicability and usefulness of several classical and other methods for solving the two‐point boundaryvalue problem which arises in non‐linear singularly perturbed optimal control are assessed. Specific algorithms of the Picard, Newton and averaging types are formally developed for this class of problem. The computational requirements associated with each algorithm are analysed and compared with the computational requirement of the method of matched asymptotic expansions. Approximate solutions to a linear and a non‐linear problem are obtained by each method and compared.
Optimal pulse motor control
Authors: Calise Anthony J. , Smith Stan 
Published: July 2007

AbstractThis paper considers the problem of optimal multiple‐pulse motor control. Simple pulse‐triggering algorithms are derived that are suitable for real‐time implementation in air‐launched tactical missiles. Two motor designs are addressed. The first is typical of solid radial pulse motor designs, where the number of pulses and the total impulse of each pulse is defined. The second corresponds to a liquid multipulse motor, where the thrust magnitude and total motor impulse are defined and the pulse initiation and pulse termination times are variable. Sensitivity of performance to pulse initiation time and pulse shape is discussed, and simulation results are included to demonstrate the effectiveness of the pulse‐triggering algorithms.
Optimal structural design and relaxed controls
Authors: Lurie K. A. , Cherkaev A. V. 
Published: July 2007

AbstractProblems of optimal design, particularly of the optimal distribution of various materials within the volume of a structure, require consideration of all possible mixtures, i.e. composites, which can be assembled from given components. This paper explains both the mathematical and the physical reasons for such an extended formulation, and it summarizes results which have been obtained concerning effective transport coefficients. Specifically, we describe the set G, U of effective conductivity tensors of composites which may be assembled from components in a given set U taken in prescribed proportions m. By using G, U instead of U as the set of admissible controls, one guarantees the existence of an optimal control for a large class of weakly lower‐semicontinuous functionals of solutions of various boundary‐value problems.
An integrated approach to reduced‐order control theory
Authors: Kabamba P. T. , Longman R. W. 
Published: July 2007

AbstractLinear‐Quadratic‐Gaussian (LQG) theory generally requires the use of a full‐order dynamic observer whose dimension is often prohibitive in applications so that reduced‐order controller design techniques are needed. A general formalism is presented here for the optimal design of controllers of arbitrary prescribed order with the usual quadratic cost functionals. The gradients of the cost functional are obtained in explicit form and involves Liapunov equations. A fundamental aspect of this paper is a unifying formalism; direct output feedback and reduced‐order controllers, stochastic and deterministic systems, infinite‐time and finite‐time problems and time‐invariant and time‐varying problems are considered. Optimization of sensor and actuator locations and parameter‐variation‐insensitive controller design are also considered within this framework. Examples are treated.
Optimal preventive and repair maintenance of a machine subject to failure
Authors: Gaimon Cheryl , Thompson Gerald L. 
Published: July 2007

AbstractMachine maintenance policies comprise two important activities: (a) the performance of preventive maintenance to prevent or postpone future breakdowns; and (b) the decision once a breakdown has actually occurred either to repair or to junk the machine. In this paper we study a control‐theoretic model in which both of these activities are decision variables. The optimal preventive maintenance policy is determined as an ordinary control variable, whereas the breakdown‐repair policy is determined as an impulsive control variable. A real‐time iterative procedure is presented for making the repair‐or‐junk decision at the time of each actual breakdown. Various theoretical results are presented which connect the preventive and breakdown‐repair policies.
Quantized control using differential encoding
Authors: Fischer Thomas R. , Tinnin D. Joy 
Published: July 2007

AbstractA vector generalization of differential pulse code modulation is used to provide quantization of control and measurements in a closed‐loop control system. Algorithms are developed for the adaptive quantizer and predictor. Explicit expressions are derived for the quantization and estimation errors resulting from the differential encoding. Simulation results are presented which demonstrate that even for very low bit rates the quantized control performance is very close to the performance of the unquantized optimal control solution.
A newton‐type computing technique for optimal control problems
Authors: Pillo G. Di , Grippo L. , Lampariello F. 
Published: July 2007

AbstractIn this paper we propose some Newton‐type algorithms for the numerical solution of both unconstrained and constrained discrete‐time optimal control problems. The approach followed here is based on a suitable augmented Lagrangian function whose unconstrained minimization yields the solution of the optimal control problem and the associated multipliers. We show that the Hessian matrix of the augmented Lagrangian function has a sparse structure which allows the use of an efficient decomposition scheme for the computation of the Newton's direction. In addition, consistent approximations of the Newton's direction are described. These approximations may allow a further reduction of the computational cost. Two numerical examples are reported.
Optimal control of inspiratory airflow in breathing
Authors: Hämäläinen Raimo P. , Sipilä Aarne 
Published: July 2007

AbstractThis paper describes a new optimal control model for predicting the inspiratory airflow pattern in breathing. The dynamics of the mechanical lung‐rib‐cage system is described by a linear first‐order equation. The physiological interpretation of the mathematical optimization criterion used in the model is the minimization of oxygen expenditure of the respiratory muscles together with the avoidance of movements with rapid changes in the flow rate. The optimal control analysis results in a relatively difficult two‐point boundary value problem which is solved by multiple shooting techniques. The new criterion yields better predictions for breathing at rest than previous models. The most significant improvements are that this model is able to produce asymmetric inspiratory airflow patterns and to predict the effects of changes in the operating level and the elastance coefficient of the system. A modified version of the model is suggested which would be able to predict patterns of breathing during exercise as well.
Optimal design problems for curvilinear shallow elements of structures
Authors: Banichuk N. V. , Larichev A. D. 
Published: July 2007

AbstractNew problem statements for the optimal design of thin‐wall structural elements are considered by means of optimal control theory. The distribution of initial curvature of shallow curvilinear structural elements in a non‐strain state is taken as the control function.1–3 Integral stiffness is considered as the optimized performance index. The necessary optimality condition and the partial differential equations for the adjoint variables are derived. An analysis of these relations is carried out, and the initial optimal control problem is reduced to a boundary problem of the bending of an uncurved element. Problems of optimal design of plates under transverse loads, as well as under tensile or compression forces acting in the middle surface, are studied. Analogous problems of optimal design for shallow curvilinear plates on an elastic foundation are also investigated. Some two‐dimensional analytical solutions for optimal plates under loads of different types are obtained.
Strong decision and forecast horizons in a convex production planning problem
Authors: Teng Jinn‐Tsair , Thompson Gerald L. , Sethi Suresh P. 
Published: July 2007

AbstractWe consider a production‐inventory planning problem with time‐varying demands, convex production costs and a warehouse capacity constraint. It is solved by use of the Lagrangian form of the maximum principle. The possible existence of strong decision and forecast horizons is demonstrated. When they exist, they permit the breaking up of the whole problem into a set of smaller problems which can be solved independently because optimal decisions up to a strong decision horizon are completely independent of demand data beyond the next forecast horizon. A forward branch and bound algorithm is developed to determine such horizons and to solve the whole problem.
Advertising decisions in oligopoly: An industry equilibrium analysis
Authors: Rao Ram C. 
Published: July 2007

AbstractThis paper determines the stationary level of advertising in which firms in an oligopoly invest. These levels are outcomes of an industry equilibrium which corresponds to a Nash solution to the set of maximizing problems that firms face. The existence of an equilibrium is established for two alternative specifications of the dynamics of advertising. Stability, and therefore observability, of stationary states is examined.
Feasibility of disturbance‐accommodating control in steering of a large tanker
Authors: Mears Barry C. , Reid Robert E. 
Published: July 2007

AbstractThe feasibility of applying disturbance‐accommodating control (DAC) techniques to the problem of steering control of a large tanker in a seaway is examined. A performance criterion representative of propulsion losses related to steering is used as a basis for the design of course‐keeping controllers. The development of disturbance state models to take advantage of the short‐term regularity of the seaway within a DAC framework is presented. Comparisons are made between the performance resulting from the DAC approach and previous LQG approaches to the problem using computer simulation results. On this basis, it is shown that controller design within a DAC framework may be a viable alternative to existing Kalman filter estimation/control schemes used in autopilot design.
Some experiences with the application of multivariable adaptive control in chemical and electromechanical plants
Authors: Hahn V. , Röck H. , Schmid Chr. , Wiemer P. 
Published: July 2007

AbstractBased on a new unified theory, multivariable adaptive generalized minimum variance and model reference adaptive control are applied to three different types of processes. The improvement of control quality in a foil coating process using adaptive control is significant. Reduced energy costs can be really achieved on distillation columns as shown on a production column. The tuning of a multivariable controller for a turbogenerator can be done automatically and yields satisfactory disturbance rejection. The examples illustrate that adaptive control using these techniques has reached a high degree of maturity, making it a powerful tool for the control engineer.
Implicit dual control for general stochastic systems
Authors: Bayard David S. , Eslami Mansour 
Published: July 2007

AbstractA new implicit dual technique is presented for stochastic adaptive control synthesis. In this technique, denoted as the method of utility costs (MOUC), a new control policy is derived from a known starting control policy by using a single iteration in time‐varying policy space. An important result is that the new control policy yields a corresponding improvement in adaptive performance relative to the known starting policy. Since the starting policy can be chosen arbitrarily, the new policy has potentially superior performance relative to any existing design. Unlike other implicit dual designs, the MOUC can be applied to systems having constrained inputs, discontinuities, discrete valued disturbances, as well as in situations where the variances of the associated process statistics are large. A numerical example is given in which a controller is synthesized to provide improved performance relative to the Open‐Loop Feedback policy of Dreyfus.
Equilibria and threats in a fishery management game
Authors: Hämäläinen R. P. , Haurie A. , Kaitala V. 
Published: July 2007

AbstractA two‐country fishery management game is considered in the realm of the theory of non‐co‐operative and co‐operative differential games. Conditions which guarantee global asymptotic stability of the open‐loop equilibrium trajectories are given and applied to a class of harvest games. Co‐operative solutions of the two‐country fishery management games are examined for the case of Kalaï‐Smorodinsky bargaining schemes. We show that the use of retaliation threats can transform a co‐operative solution into an equilibrium memory strategy. Two numerical examples present an analysis of threat effectiveness. The ‘turnpike’ property, or global asymptotic stability of optimally controlled systems, is an important part of the computational approach used.
Optimal proportional plus integral control for regulator and tracking problems
Authors: Wong Kin P. , Seborg Dale E. 
Published: July 2007

AbstractTwo new design methods are proposed for optimal PI control which give fast recovery from load disturbances without producing large overshoots associated with set‐point changes. Unlike existing methods, such as set‐point filtering or any other scheme that essentially detunes the controller for set‐point changes, the proposed methods do not increase the rise time significantly in order to reduce overshoot. The first method resets the integral term in the control law when the new set point is reached. The second method is a modified model‐following approach that does not increase the overall dimension of the system. Two numerical examples demonstrate that the proposed methods are superior to alternatives such as set‐point filtering and conventional model following.
Optimal parametrized design of thermal diffusers for communication satellites
Authors: Delfour M. C. , Payre G. , Zolesio J.‐P. 
Published: July 2007

AbstractThe object of this paper is to present recent developments in the design of mass‐optimized thermal diffusers with a priori specifications on the input power flux and a bound on the output power flux. This problem arises in connection with the use of high power solid state devices (HPSSD's) in future Canadian communication satellites. Delfour, Payre and Zolésio1,2 have obtained results on the optimal design using the techniques of shape optimal design.3‐8 In this paper, we also consider suboptimal designs (e.g. doublers) and compare them with the optimal one. A similar problem has been studied by Destuynder.9 However, the present design differs in that we have a constraint on the normal derivative on a piece of the boundary surface instead of a constraint on the maximum temperature in the domain or body of the diffuser.
Optimal feedback control of power systems governed by non‐linear dynamics
Authors: Biswas S. K. , Ahmed N. U. 
Published: July 2007

AbstractLinear‐quadratic regulator theory is commonly used in feedback optimization problems for power system stabilization. In this paper an extension of Gamkrelidze's maximum principle, which applies directly to non‐linear systems, is used to find an optimal feedback control law from a given practically implementable class of parametrized control structures. An algorithm for finding the optimal set of parameters is presented. The results obtained, using the optimal feedback control law determined by the given algorithm, indicate a substantial improvement of the transient performance of the system.
A primal‐dual method for linear‐quadratic gaussian control problems with quadratic constraints
Authors: Toivonen H. T. 
Published: July 2007

AbstractLinear‐quadratic Gaussian control with quadratic state and input constraints is studied. A primal‐dual method is considered in which the solution of a dual maximization problem is found by solving a sequence of unconstrained linear‐quadratic Gaussian control problems. Second derivatives are derived for the dual problem and Newton‐type methods are applied to its solution. Non‐negativity constraints on the Lagrange multipliers of the primal problem lead to corresponding constraints in the dual problem, and for these both an active set strategy and a method based on quadratic subproblems are considered. A numerical example is presented to illustrate the performance of the numerical algorithms.
Direct solution to an optimal control problem of econometric systems
Authors: Kabe D. G. , Rao U. L. Gouranga 
Published: July 2007

AbstractA direct solution is proposed to an optimal control problem of linear econometric systems with a quadratic welfare loss function when there are linear equality constraints on the control variables. The direct solution proposed here eliminates the problem of non‐uniqueness of the optimal solution, which is present when this optimal control problem is solved using the recursive algorithm proposed by Chow,1 Pindyck2 and Tan.3 If a unique solution to the optimal control problem exists, then the direct solution and the recursive solution coincide.
Exact penalty function approach to constrained optimal control problems
Authors: Xing A. Q. , Chen Z. H. , Wang C. L. , Yao Y. Y. 
Published: July 2007

AbstractGiven the well known concept that optimal control problems may be solved either by the maximum principle or by the dynamic programming technique which employs many numerical algorithms, this paper attempts to show that the exact penalty function method may be used to transform a constrained optimal control problem into an unconstrained optimal control problem. Under certain conditions the constrained optimal control problem is shown to be equivalent to an unconstrained optimal control problem, which can be easily solved by a numerical technique.
A real‐time solution for preventive and repair maintenance
Authors: Gaimon Cheryl , Thompson Gerald L. 
Published: July 2007

AbstractA deterministic approach to a single‐machine maintenance problem is presented which is solved forward in real‐time. The importance of real‐time solutions is particularly evident in new manufacturing environments, where fast decisions reflecting the most current information are vital to obtain high utilization of expensive equipment and to avoid bottlenecks in the production process. A sequential decision‐making process in introduced. First, the model presented is solved at the initial time when the machine is purchased. Then, each time a breakdown occurs, the model is solved again using the updated breakdown information. The initial solution contains the optimal preventive maintenance policy and the optimal resale time of the machine assuming it remains functional. At each breakdown time, the optimal breakdown‐repair policy is obtained indicating whether a repair should be made or whether the broken machine should be junked. If a repair is made, then the optimal preventive maintenance policy and resale time of the machine are derived. It is shown that if a breakdown occurs following the interval in which preventive maintenance is optimally applied, then a repair is not advocated and the machine is junked. In addition, a method for deriving the future expected times of machine failures is presented. Therefore, in addition to the optimal decisions corresponding to the realized behaviour to the machine, optimal policies are derived which consider its future expected performance.
Optimal advertising and pricing for a three‐stage time‐lagged monopolistic diffusion model incorporating income
Authors: Jedidi Kamel , Eliashberg Jehoshua , Desarbo Wayne S. 
Published: July 2007

AbstractA three‐stage time‐lagged diffusion model that incorporates consumers' income, advertising and price effects is proposed. The derivation of the model synthesizes and relies upon a number of important arguments made in the diffusion and economic literature. Optimal control theory is used to derive normative advertising and pricing strategic implications for a monopolist introducing a new durable product.
R & D Spending and product pricing
Authors: Erickson Gary M. 
Published: July 2007

AbstractAn optimal control model is developed that combines cost reduction through R & D with pricing. Price and R & D spending level are control variables and unit cost is a state variable. Analysis of the model reveals that if a firm has a positive discount rate, optimal R & D spending on cost reduction may grow to a peak before eventually declining. If the firm has a zero discount rate, optimal R & D spending declines monotonically across time. Optimal price declines monotonically in either case, in a direct relationship with unit cost.
Mixed h2 and h∞ optimal robust control design
Authors: Sparks Andrew G. , Yeh Hsi‐Han , Banda Siva S. 
Published: July 2007

AbstractThis paper introduces a design methodology for a dynamic compensator that simultaneously minimizes the upper bound of a quadratic performance index and the H∞‐norm of a disturbance transfer function matrix of a multiple‐input/multiple‐output system whose model contains parameter uncertainty in the state and input matrices. The real parameter uncertainty is modelled as additional measurement outputs and as additional weights on the existing noise inputs and measurement outputs of the system. The compensator equations are derived by taking the dual of a system with parameter variation in the state and output matrices, for which the compensator equations have previously been derived, and then taking the dual of the compensator equations. An algorithm for applying this theory is given and an example is shown.
Robust quadratic optimization of systems with large parameter variations
Authors: Eslami Mansour 
Published: July 2007

AbstractIn this paper, two new algorithms to synthesize robust controllers which tolerate large parameter variations in the system are presented. The new analytical procedure that has led to the establishment of these algorithms can be easily used to solve similar perturbational problems when small‐sensitivity measures are used. These algorithms are applied to a numerical example to show the system performance under these design methodologies and to compare the final outcomes of these algorithms.
Optimal temperature control of jacket‐cooled fermentation reactors
Authors: Gee Douglas A. , Ramirez W. Fred 
Published: July 2007

AbstractFor systems such as jacketed vessels with significant dead time, cooling jacket dynamics and unpredictable but measurable load disturbances, advanced control concepts need to be used in order to achieve quality regulatory control. In the current work, optimal regulatory control theory has been applied to this problem. An optimal control algorithm is used to effectively control a batch fermentation reactor. The algorithm is easily implementable and very effective. It is capable of responding to both measurable and unmeasurable process disturbances.