scholarly journals The Solution Equivalence to General Models for the RIM Quantifier Problem

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 455
Author(s):  
Dug Hong
Keyword(s):  
Optimal Control ◽  
Maximum Entropy ◽  
Generating Functions ◽  
Minimax Problem ◽  
Minimum Variance ◽  
General Assumption ◽  
Control Technique ◽  
Modified Model ◽  
Correct Formulation ◽  
The Relationship

Hong investigated the relationship between the minimax disparity minimum variance regular increasing monotone (RIM) quantifier problems. He also proved the equivalence of their solutions to minimum variance and minimax disparity RIM quantifier problems. Hong investigated the relationship between the minimax ratio and maximum entropy RIM quantifier problems and proved the equivalence of their solutions to the maximum entropy and minimax ratio RIM quantifier problems. Liu proposed a general RIM quantifier determination model and proved it analytically by using the optimal control technique. He also gave the equivalence of solutions to the minimax problem for the RIM quantifier. Recently, Hong proposed a modified model for the general minimax RIM quantifier problem and provided correct formulation of the result of Liu. Thus, we examine the general minimum model for the RIM quantifier problem when the generating functions are Lebesgue integrable under the more general assumption of the RIM quantifier operator. We also provide a solution equivalent relationship between the general maximum model and the general minimax model for RIM quantifier problems, which is the corrected and generalized version of the equivalence of solutions to the general maximum model and the general minimax model for RIM quantifier problems of Liu’s result.

A Modified Model Referenced Adaptive Control Technique for Nonlinear Dynamic Systems

1992 ◽  
Vol 114 (2) ◽  
pp. 154-160 ◽  
Author(s):  
H. M. Sardar ◽  
M. Ahmadian
Keyword(s):  
Adaptive Control ◽  
Dynamic Systems ◽  
Process Simulation ◽  
Control Process ◽  
Nonlinear Dynamic Systems ◽  
Control Technique ◽  
Modified Model ◽  
Fundamental Understanding ◽  
Simulation Results ◽  
The Relationship

It has been shown that the model referenced adaptive control (MRAC) scheme developed by Dubowsky and DesForges (1979) is effective for controlling nonlinear systems provided that the adjusting mechanism, which modifies the control gains, is selected properly. This study presents a modified MRAC Scheme that includes a technique for effectively designing the adjusting mechanism. A fundamental understanding of the relationship between the control process and the adjusting mechanism is developed. Next, this knowledge is used to establish a systematic procedure for designing the adjusting mechanism through an optimization process. Simulation results for the UCLA arm are presented to demonstrate the effectiveness and validity of the method.

Modified Model for Static Behavior of Microcantilever Gas Sensor Adsorbed with Monolayer Molecules

2011 ◽  
Vol 415-417 ◽  
pp. 455-459
Author(s):  
Xiao Ming Wang ◽  
Fei Wang ◽  
Xue Zeng Zhao ◽  
Da Lei Jing
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Curvature Radius ◽  
Static Behavior ◽  
Neutral Layer ◽  
Modified Model ◽  
Adsorbed Molecules ◽  
Microcantilever Sensors ◽  
The Relationship ◽  
Layer Position

The modified static bending model of microcantilever with monolayer molecules has been established based on energy method, in which the change in neutral layer position caused by adsorption-induced stress has been considered. On this basis, we have analyzed the relationship between the bending curvature radius of a microcantilever with its thickness, Young’s modulus and molecule-molecule distance of adsorbed molecules when it is adsorbed with monolayer water molecules. Additionally, we have investigated the effect of change in neutral layer position on the static behavior of microcantilever sensors and have found that: 1) the bending curvature radius of microcantilever is affected by its Young’s modulus, thickness and distance of adsorbed molecules respectively; 2)the predicted error of bending curvature radius caused by the change in neutral layer position slightly increases with decreasing Young’s modulus and thickness, whereas the effect of distance between adsorbed molecules on the error is significant.

scholarly journals Production and process management: An optimal control approach

2016 ◽  
Vol 26 (3) ◽  
pp. 331-342 ◽  
Author(s):  
Haider Biswas ◽  
Ahad Ali
Keyword(s):  
Optimal Control ◽  
Process Management ◽  
Nonlinear Dynamical Systems ◽  
State Constraint ◽  
Control Technique ◽  
Optimal Control Strategy ◽  
Nonlinear Dynamical ◽  
Control Approach ◽  
Time Operation ◽  
Operation Process

Optimal control and efficient management of industrial products are the key for sustainable development in industrial and process engineering. It is well-known that proper maintenance of process performance, ensuring the quality products after a long time operation of the system, is desirable in any industry. Nonlinear dynamical systems may play crucial role to appropriately design the model and obtain optimal control strategy in production and process management. This paper deals with a mathematical model in terms of ordinary differential equations (ODEs) that describe control of production and process arising in industrial engineering. The optimal control technique in the form of maximum principle, used to control the quality products in the operation processes, is applied to analyze the model. It is shown that the introduction of state constraint can be advantageous for obtaining good products during the longer operation process. We investigate the model numerically, using some known nonlinear optimal control solvers, and we present the simulation results to illustrate the significance of introducing state constraint onto the dynamics of the model.

Computers and infrared spectroscopy: evolution and revolution

1991 ◽  
Vol 69 (11) ◽  
pp. 1781-1785 ◽  
Author(s):  
D. J. Moffatt ◽  
J. K. Kauppinen ◽  
H. H. Mantsch
Keyword(s):  
Fourier Transform ◽  
Infrared Spectroscopy ◽  
Key Words ◽  
Maximum Entropy ◽  
Input Data ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
History Of ◽  
The Fourier Transform ◽  
The Relationship

A brief history of the relationship between computer and infrared spectroscopist is given with emphasis on the use of the Fourier transform. Subsequently, an algorithm is developed that may be used to devise an objective Fourier self-deconvolution procedure which depends only on the input data and is not subject to the biases that are often introduced in such subjective techniques. Key words: deconvolution, Fourier transform, maximum entropy method.

A Modified Monte-Carlo Potts Model for Dynamic Recrystallization

2015 ◽  
Vol 1096 ◽  
pp. 280-287 ◽  
Author(s):  
Jian Fu ◽  
Bi You Peng ◽  
Bin Xie ◽  
Yi Gen Ye
Keyword(s):  
Monte Carlo ◽  
Dynamic Recrystallization ◽  
Potts Model ◽  
Metallic Materials ◽  
Stored Energy ◽  
Modified Model ◽  
Grain Sizes ◽  
Basic Characteristics ◽  
Evolution Modeling ◽  
The Relationship

In order to improve the microstructure evolution modeling of dynamic recrystallization (DRX) in agreement with physical experiment, a modified Monte-Carlo (MC) Potts model for simulating DRX process was proposed in this paper under the consideration of the inhomogeneous stored energy distribution related to grain sizes, the nucleation criteria related to critical dislocation density, the site energy change related to grain preferred-growth, the combination of macroscopic thermo-mechanical parameters and microscopic material parameters, and the relationship between MC calculation steps and real DRX time. The results show that the modified model can better simulate the basic characteristics of dynamic recrystallization of metallic materials during forging, which the recrystallized grains nucleate mainly in the deformed regions with high stored energy and preferentially grow up by merging adjacent deformed grains with high stored energy.

Advanced modeling and optimal control of a cart-double pendulum system

2019 ◽  
Author(s):  
◽  
Cecil Jr. Shy
Keyword(s):  
Optimal Control ◽  
Lagrange Equation ◽  
Control Technique ◽  
Tuning Parameter ◽  
Microgravity Environment ◽  
Double Pendulum ◽  
Overhead Crane ◽  
Material Transport ◽  
Pendulum System ◽  
Industry Standards

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The Overhead Crane has evolved in scope since its inception in the late 1800's. Its early use as a hoist for material transport is now proceeded by new found applications, such as in the Active Response Gravity Offload System (ARGOS) at the NASA Johnson Space Center. ARGOS is an astronaut training facility designed to simulate reduced gravity environments such as Lunar, Martian, or microgravity. By industry standards, it is essentially a repurposed Overhead Crane; in academia it can be conceptualized as a cart-double pendulum system. Anti-sway control of cart-pendulum systems has been heavily researched; however, these methods are not typically designed for space simulation. The goal of this research is to design a controller that provides both energy and error minimization for the cart-pendulum, so that its payload moves as if it were floating freely in a microgravity environment (according to Newton's 1st law). The Euler-Lagrange equation is used to model the system and an optimal control technique called the [alpha]-shift is used to control the system. Most treatments on optimal linear control do not include the [alpha]-shift, but its addition allows one to stabilize the system faster and provides an extra tuning parameter while maintaining the simplicity of the solution. Numerical experiments show that the [alpha]-shift method significantly improves the cart-pendulum's ability to control its payload; especially for payloads in the cart-double-pendulum case.

scholarly journals Portfolio Optimization with Asset-Liability Ratio Regulation Constraints

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
De-Lei Sheng ◽  
Peilong Shen
Keyword(s):  
High Speed ◽  
Asset Price ◽  
Investment Strategy ◽  
Minimum Variance ◽  
Control Technique ◽  
Duality Method ◽  
Lagrange Duality ◽  
Short Period ◽  
High Investment ◽  
Hamilton Jacobi Bellman

This paper considers both a top regulation bound and a bottom regulation bound imposed on the asset-liability ratio at the regulatory time T to reduce risks of abnormal high-speed growth of asset price within a short period of time (or high investment leverage), and to mitigate risks of low assets’ return (or a sharp fall). Applying the stochastic optimal control technique, a Hamilton–Jacobi–Bellman (HJB) equation is derived. Then, the effective investment strategy and the minimum variance are obtained explicitly by using the Lagrange duality method. Moreover, some numerical examples are provided to verify the effectiveness of our results.

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