A Note on Avoidance Control

1981 ◽  
Vol 103 (1) ◽  
pp. 69-70 ◽  
Author(s):  
B. R. Barmish ◽  
W. E. Schmitendorf ◽  
G. Leitmann
Keyword(s):  
State Space ◽  
Existence Theorem ◽  
The State ◽  
Avoidance Control

This note points out some technical difficulties which can arise when attempting to determine the existence of a control which guarantees avoidance of a given set in the state space. It is concluded that the hypotheses of the existence theorem in [1] require strengthening.

Guaranteed Avoidance Control and Holding Control

1982 ◽  
Vol 104 (2) ◽  
pp. 166-172 ◽  
Author(s):  
W. E. Schmitendorf ◽  
B. R. Barmish ◽  
B. S. Elenbogen
Keyword(s):  
Control Problem ◽  
State Space ◽  
The State ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Avoidance Control ◽  
Avoidance Problem

This paper considers the problem of steering the state of a system, in the presence of disturbances, so that it avoids a specified subset of the state space. This subset is called the avoidance set and the problem is called the avoidance control problem. An avoidance control is a control which guarantees that the system does not enter the avoidance set regardless of the disturbance. A necessary condition and a sufficient condition for the existence of an avoidance control are given when the disturbance is subject to magnitude constraints. Closely related to the avoidance problem is the holding problem which is concerned with guaranteeing that the state of the system remains within a specified set. We also reinterpret our conditions for the existence of an avoidance control within the context of the holding problem.

Modeling of CCLP in koryo extract production

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ji Chol ◽  
Ri Jun Il
Keyword(s):  
Process Control ◽  
Medical Care ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Space Model ◽  
Effective Components ◽  
Counter Current

Abstract The modeling of counter-current leaching plant (CCLP) in Koryo Extract Production is presented in this paper. Koryo medicine is a natural physic to be used for a diet and the medical care. The counter-current leaching method is mainly used for producing Koryo medicine. The purpose of the modeling in the previous works is to indicate the concentration distributions, and not to describe the model for the process control. In literature, there are no nearly the papers for modeling CCLP and especially not the presence of papers that have described the issue for extracting the effective components from the Koryo medicinal materials. First, this paper presents that CCLP can be shown like the equivalent process consisting of two tanks, where there is a shaking apparatus, respectively. It allows leachate to flow between two tanks. Then, this paper presents the principle model for CCLP and the state space model on based it. The accuracy of the model has been verified from experiments made at CCLP in the Koryo Extract Production at the Gang Gyi Koryo Manufacture Factory.

Cylindrically Anisotropic Tubes Containing a Line Dislocation

2006 ◽  
Author(s):  
Chung-Hao Wang
Keyword(s):  
State Space ◽  
Dislocation Line ◽  
Longitudinal Axis ◽  
The State ◽  
Fourier Series Expansion ◽  
General Solutions ◽  
Mixed Dislocation ◽  
Line Dislocation ◽  
Space Formulation ◽  
Cylindrically Anisotropic

An analytical solution of the problem of a cylindrically anisotropic tube which contains a line dislocation is presented in this study. The state space formulation in conjunction with the eigenstrain theory is proved to be a feasible and systematic methodology to analyze a tube with the existence of dislocations. The state space formulation which expediently groups the displacements and the cylindrical surface traction can construct a governing differential matrix equation. By using Fourier series expansion and the well developed theory of matrix algebra, the asymmetrical solutions are not only explicit but also compact in form. The dislocation considered in this study is a kind of mixed dislocation which is the combination of edge dislocations and a screw dislocation and the dislocation line is parallel to the longitudinal axis of the tube. The degeneracy of the eigen relation and the technique to determine the inverse of a singular matrix are thoroughly discussed, so that the general solutions can be applied to the case of isotropic tubes, which is one of the novel features of this research. The results of isotropic problems, which are belong to the general solutions, are compared with the well-established expressions in the literature. The satisfied correspondences of these comparisons indicate the validness of this study. A cylindrically orthotropic tube is also investigated as an example and the numerical results for the displacements and tangential stress on the outer surface are displayed. The effects on surface stresses due to the existence of a dislocation appear to have a characteristic of localized phenomenon.

scholarly journals Novel domain expansion methods to improve the computational efficiency of the Chemical Master Equation solution for large biological networks

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Rahul Kosarwal ◽  
Don Kulasiri ◽  
Sandhya Samarasinghe
Keyword(s):  
Master Equation ◽  
State Space ◽  
Performance Management ◽  
Numerical Solutions ◽  
De Novo ◽  
Exact Analytical Solution ◽  
Chemical Master Equation ◽  
The State ◽  
Biochemical System ◽  
Biochemical Systems

Abstract Background Numerical solutions of the chemical master equation (CME) are important for understanding the stochasticity of biochemical systems. However, solving CMEs is a formidable task. This task is complicated due to the nonlinear nature of the reactions and the size of the networks which result in different realizations. Most importantly, the exponential growth of the size of the state-space, with respect to the number of different species in the system makes this a challenging assignment. When the biochemical system has a large number of variables, the CME solution becomes intractable. We introduce the intelligent state projection (ISP) method to use in the stochastic analysis of these systems. For any biochemical reaction network, it is important to capture more than one moment: this allows one to describe the system’s dynamic behaviour. ISP is based on a state-space search and the data structure standards of artificial intelligence (AI). It can be used to explore and update the states of a biochemical system. To support the expansion in ISP, we also develop a Bayesian likelihood node projection (BLNP) function to predict the likelihood of the states. Results To demonstrate the acceptability and effectiveness of our method, we apply the ISP method to several biological models discussed in prior literature. The results of our computational experiments reveal that the ISP method is effective both in terms of the speed and accuracy of the expansion, and the accuracy of the solution. This method also provides a better understanding of the state-space of the system in terms of blueprint patterns. Conclusions The ISP is the de-novo method which addresses both accuracy and performance problems for CME solutions. It systematically expands the projection space based on predefined inputs. This ensures accuracy in the approximation and an exact analytical solution for the time of interest. The ISP was more effective both in predicting the behavior of the state-space of the system and in performance management, which is a vital step towards modeling large biochemical systems.

A State-Space Approach to the Synthesis of Random Vertical and Crosslevel Rail Irregularities

1990 ◽  
Vol 112 (1) ◽  
pp. 83-87 ◽  
Author(s):  
R. H. Fries ◽  
B. M. Coffey
Keyword(s):  
Numerical Simulation ◽  
White Noise ◽  
State Space ◽  
Spectral Characteristics ◽  
The State ◽  
Second Derivatives ◽  
Time Histories ◽  
Sample Interval ◽  
Rail Irregularities ◽  
Derivatives Of

Solution of rail vehicle dynamics models by means of numerical simulation has become more prevalent and more sophisticated in recent years. At the same time, analysts and designers are increasingly interested in the response of vehicles to random rail irregularities. The work described in this paper provides a convenient method to generate random vertical and crosslevel irregularities when their time histories are required as inputs to a numerical simulation. The solution begins with mathematical models of vertical and crosslevel power spectral densities (PSDs) representing PSDs of track classes 4, 5, and 6. The method implements state-space models of shape filters whose frequency response magnitude squared matches the desired PSDs. The shape filters give time histories possessing the proper spectral content when driven by white noise inputs. The state equations are solved directly under the assumption that the white noise inputs are constant between time steps. Thus, the state transition matrix and the forcing matrix are obtained in closed form. Some simulations require not only vertical and crosslevel alignments, but also the first and occasionally the second derivatives of these signals. To accommodate these requirements, the first and second derivatives of the signals are also generated. The responses of the random vertical and crosslevel generators depend upon vehicle speed, sample interval, and track class. They possess the desired PSDs over wide ranges of speed and sample interval. The paper includes a comparison between synthetic and measured spectral characteristics of class 4 track. The agreement is very good.

REMARKS ON SYMMETRIES OF GENERALIZED ROTOR SPACE

2004 ◽  
Vol 13 (01) ◽  
pp. 37-45 ◽  
Author(s):  
A. GÓŹDŹ ◽  
M. MIŚKIEWICZ ◽  
A. OLSZEWSKI
Keyword(s):  
State Space ◽  
The State ◽  
Methods Of Analysis ◽  
Quantum Rotors

We propose methods of analysis of the symmetries of the rotor space. A few examples of the point symmetries and their consequences for the state space of the quantum rotors are shortly considered.

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