Integral Cost Function Research Articles

An inventory policy of inspection and setup cost on the integrated production-inventory system for flawed items

Almost all inventory models assume that setup cost is deterministic, and thus is not subject to control. However, in many practical situations, setup cost can be reduced at added cost, this article combines the concept of capital investment allocated to reducing the setup cost to determine an optimal integrated vendor-buyer inventory policy for flawed items in a just-in-time (JIT) manufacturing environment. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. The production process is assumed to deteriorate during processing and produces a certain number of defective items. The expected annual integrated total cost function is derived and a solution procedure is established to find out the optimal solution. Finally, the solution technique is illustrated with a numerical example available in the literature.

Guaranteed cost control for multi-inventory systems with uncertain demand

In this paper we consider the problem of controlling a multi-inventory system in the presence of uncertain demand. The demand is unknown but bounded in an assigned compact set. The control input is assumed to be also constrained in a compact set. We consider an integral cost function of the buffer levels and we face the problem of minimizing the worst-case cost. We show that the optimal cost of a suitable auxiliary problem with no uncertainties is always an upper bound for the original problem. In the special case of minimum-time control, this upper bound is tight, namely its optimal cost is equal to the worst-case cost for the original system. Furthermore, the result is constructive, since the optimal control law can be explicitly computed.

A simple integrated production policy of an imperfect item for vendor and buyer

This article develops a simple approach for determining an optimal integrated vendor–buyer inventory policy for an item with imperfect quality. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. This model is assumed to produce a certain number of defective items during the production process. Items of poor quality detected in the screening process of a lot are sold at a discounted price. The expected annual integrated total cost function is derived and a solution procedure is proposed to determine the optimal policy. Finally, a numerical example is also given to illustrate the solution procedure presented in this article.

An optimal policy for a single-vendor single-buyer integrated production–inventory problem with process unreliability consideration

This article develops a model to determine an optimal integrated vendor–buyer inventory policy for flawed items in a just-in-time manufacturing environment. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. The production process is assumed to deteriorate during processing and produces a certain number of defective items. For practical purpose, the article is concerned with the policy in which the delivery quantity to the buyer is identical at each replenishment. The expected annual integrated total cost function is derived and a solution procedure is established to find out the optimal solution. Finally, the solution technique is illustrated with a numerical example available in the literature.

Comparing Smooth Arm Movements with the Two-Thirds Power Law and the Related Segmented-Control Hypothesis

The movements of the human arm have been extensively studied for a variety of goal-directed experimental tasks. Analyses of the trajectory and velocity of the arm have led to many hypotheses for the planning strategies that the CNS might use. One family of control hypotheses, including minimum jerk, snap and their generalizations to higher orders, comprises those that favor smooth movements through the optimization of an integral cost function. The predictions of each order of this family are examined for two standard experimental tasks: point-to-point movements and the periodic tracing of figural forms, and compared both with experiment and the two-thirds power law. The aim of the analyses is to generalize previous numerical observations as well as to examine movement segmentation. It is first shown that contrary to recent statements in the literature, the only members of this family of control theories that match reaching movement experiments well are minimum jerk and snap. Then, for the case of periodic drawing, both the ellipse and cloverleaf are examined and the experimentally observed power law is derived from a first-principles approach. The results for the ellipse are particularly general, representing a unification of the two-thirds power law and smoothness hypotheses for ellipses of all reasonable eccentricities. For complex shapes it is shown that velocity profiles derived from the cost-function approach exhibit the same experimental features that were interpreted as segmented control by the CNS. Because the cost function contains no explicit segmented control, this result casts doubt on such an interpretation of the experimental data.

An integrated vendor-buyer cooperative inventory model for items with imperfect quality

This article develops a model to determine an optimal integrated vendor-buyer inventory policy for flawed items in a just-in-time (JIT) manufacturing environment. The aim is to minimize the total joint annual costs incurred by the vendor and the buyer. The proposed model extends the integrated vendor-buyer inventory model by accounting for imperfect quality items. The expected annual integrated total cost function is derived and an analytic solution procedure is proposed to determine the optimal policy. Finally, numerical examples are also given to illustrate the solution procedure presented in this article.

GUARANTEED COST CONTROL FOR MULTI-INVENTORY SYSTEMS WITH UNCERTAIN DEMAND

In this paper we consider the problem of controlling a multi–inventory system in the presence of uncertain demand. The demand is unknown but bounded in an assigned compact set. The control input is assumed to be also constrained in a compact set. We consider an integral cost function of the buffer level and we face the problem of minimizing the worst case cost. We show that the optimal cost of a suitably constructed auxiliary problem with no uncertainties is always an upper bound for the original problem. In the special case of minimum–time control, this upper bound is tight, namely its optimal cost is equal to the worst case cost for the original system. Furthermore the result is constructive, since the optimal control law can be explicitly computed.

INPUT DESIGN: A METHOD FOR ACHIEVING PERSISTENCY OF EXCITATION IN NONLINEAR PARMETRIZED SYSTEMS

In this work sufficient time-varying conditions were established for assuring local persistent excitation for identification of a large class of nonlinearly parametrized model structures under integral cost functionals of arbitrary degree. The conditions are algebraic in nature. They can be set up off-line in a symbolic form and evaluated on-line. The potential benefit of these conditions mainly reclines in the design of excitations for nonlinear system identification. A simple method for optimal input design is presented. Examples illustrate the features of the approach.

Minimax controller design for a class of uncertain linear systems

This paper considers the design of minimax controllers for a class of linear systems. The system is perturbed by a known initial condition on the state and by a disturbance process constrainted by an L 2 norm bound. Structured undertainty is represented by perturbation feedback through L 2-induced norm bounded operators. The performance is measured by an integral quadratic cost function. The resultant controllers minimise the worst-case cost for all admissible distrubances and for all admissible systems. The design involves the optimal solution of a parametric algebraic Riccati equation. A new proof of minimax optimality is given using standard methods for linear systems. The multivariable optimisation problem is shown to be convex and the set of feasible parameter values is shown to be compact. Thus, the design procedure is computationally tractable.

A new composite adaptive speed controller for induction motor based on feedback linearization

A new adaptive control technique is proposed to control the speed of the induction motor in this paper. First, the rotor flux is estimated with the simplified rotor flux observer on the rotor reference frame and the feedback linearization theory is used to decouple the rotor speed and the flux amplitude. Then, a new composite adaptive control algorithm based on an integral cost function is designed to control the speed of the induction motor. The overall speed control system is verified to be stable and robust to the parameter variations and external disturbances. Experimental results are provided to demonstrate the effectiveness of the presented approach. The good speed tracking and load regulating responses can be obtained by the proposed controller.

Composite adaptive position controller for induction motor using feedback linearisation

A new adaptive control technique is proposed to control the position of the induction motor. First, the rotor flux is estimated with the simplified rotor flux observer on the rotor reference frame and the feedback linearisation theory is used to decouple the rotor position and the flux amplitude. Then, a new composite adaptive control algorithm based on an integral cost function is designed to control the position of the induction motor. The overall position control system is verified to be stable and robust to the parameter variations and external disturbances. Experimental results are provided to demonstrate the effectiveness of the presented approach. The good position tracking and load regulating responses can be obtained by the proposed controller.

2203 Inverse treatment planning for intensity modulated radiation therapy: CDVH Treatment prescription with integral cost function

2203 Inverse treatment planning for intensity modulated radiation therapy: CDVH Treatment prescription with integral cost function

Two-arm manipulation tasks with friction-assisted grasping

—The main objective of this paper is to study human dual-arm manipulation tasks and to develop a computational model that predicts the trajectories and force distribution for the coordination of two arms moving an object between two given positions and orientations in a horizontal plane. Our ultimate goal is to understand the dynamics of human dual-arm coordination in order to develop better robot control algorithms. We propose a computational model based on the hypothesis proposed by Uno et al. that suggests that human movements minimize the integral of the norm of the rate of change of actuator torques. We compare the experimental trajectories and force distributions with those obtained from the computational model. The observed trajectories show a significant degree of repeatability across trials and across subjects. We show that the computational model predicts the trajectories and the distribution of forces (torques) for a certain class of trajectories. However, the trajectories in the sagittal and frontal plane are characterized by asymmetric features that are hard to model using any integral cost function. Finally, we show that the computational model can be used to generate smooth trajectories and actuator forces for cooperating robots and discuss the advantages of such an approach to motion planning.

Optimal Trajectories of Open-Chain Mechanical Systems: An Explicit Optimality Equation with a Multiple Shooting Solution*

ABSTRACT This paper addresses the problem of finding optimal trajectories of multi-degree-of-freedom open-chain systems, while minimizing integral cost function-als. The contributions of this paper are (i) explicit optimality equations in terms of inertia matrix and potential energy of the system, (ii) compatibility conditions on the terminal conditions of the system that are consistent with the cost functional, (iii) a robust computational procedure for solving the two-point boundary value problem using the multiple shooting method, and (iv) integrated software for dynamic optimization and simulation of open-chain systems.

Convergence of optimal solutions in control problems for hyperbolic equations

A sequence of optimal control problems for systems governed by linear hyperbolic equations with the nonhomogeneous Neumann boundary conditions is considered. The integral cost functionals and the differential operators in the equations depend on the param

Asymptotic behavior of optimal solutions to control problems for systems described by differential inclusions corresponding to partial differential equations

In the paper, we consider differential inclusions related to PDEs of parabolic type and some control problems with integral cost functionals associated to them. Given a sequence of such problems, we investigate first the asymptotic behavior of solution sets (mild solutions or more precisely selection-trajectory pairs) for differential inclusions, and we get some semicontinuity or continuity results (Kuratowski convergence of solution sets). Then, we prove the Γ-convergence of cost functionals, related to the above Kuratowski convergence of solution sets. Finally, applying the Buttazzo-Dal Maso abstract scheme, based on the sequential Γ-convergence, we obtain results concerning the asymptotic behavior (hence, also stability results) for optimal solutions to control problems as well as the convergence of minimal values.

Regularity Properties of Optimal Controls

A class of optimal control problems is considered, involving integral cost functions and linear dynamics. Broad, verifiable hypotheses (HE) are known under which the problems have solutions. These must be supplemented for standard optimality conditions, in the form of a Maximum Principle, to apply. New regularity properties of optimal controls, when merely hypotheses (HE) are in force, are established. A byproduct is a Maximum Principle governing optimal controls under such circumstances, where the ostate function is possibly unbounded. Criteria for minimizing controls to be essentially bounded are also deduced.

Optimality of extremals for linear systems with quadratic costs

In this paper we consider linear control systems on R n with integral quadratic cost functionals and investigate optimality properties of extremals. In this context, extremals are curves which satisfy the Pontryagin maximum principle. We extend the Jacobi necessary condition from the calculus of variations to the optimal control setting and describe a relationship between optimality of extremals and the existence of a solution for a certain Riccati differential equation.

An existence theorem for optimal control with nonstandard cost functionals

An existence theorem for optimal control is obtained for a general nonstandard cost functional of fractional type in this work. As an application of our result we can derive an existence theorem for optimal control given by M. B. Subrahamanyam for a cost functional, which is a ratio of two given integral cost functionals.

Das Poincarésche Randsteuerproblem bei elliptischen Differentialgleichungen zweiter Ordnung

There are considered the Poincaré boundary control problem for elliptic differential equations of second order and a mixed Riemann-Hilbert control problem with generalized analytic functions, where the control occurs non-linearly in the coefficients of the boundary condition or the differential equation too. Existence theorems are proved for these problems with integral cost functions, constraints and additional conditions.