A Critical-Siphon Approach to Fastest Deadlock Controller for S3PR

2013 ◽  
pp. 269-295 ◽  
Author(s):  
Daniel Yuh Chao
Keyword(s):  
Optimal Control ◽  
Polynomial Complexity ◽  
Dynamic Reconfiguration ◽  
Fast Computation ◽  
Reachability Graph ◽  
Computational Burden ◽  
The Family ◽  
Large Systems

The authors developed a theory to show that exactly one monitor is required for the set of siphons in the family of 2-compound siphons and how to assign its initial markings. This avoids redundant monitors and the unnecessary associated computational burden. Neither reachability graph nor minimal siphon needs to be computed to achieve polynomial complexity—essential for large systems. This chapter redevelops the theory more formally and further applies this approach to two well-known S3PR to obtain a controller full or near maximally permissive, where Weighted Control (WC) arcs are nevertheless necessary to keep the controlled model maximally permissive. However, optimal control for siphons involving WC arcs are still under research. As many as possible for simpler structures are desired to reduce WC arcs. In addition, fast computation is important for dynamic reconfiguration situations. The authors develop a single theorem to identify the condition where WC places cannot be replaced by Ordinary Control (OC) arcs, while others can be replaced.

Application of Critical-Siphon Theory to Fastest Deadlock Controller for a Class of Flexible Manufacturing Systems

2012 ◽  
Vol 605-607 ◽  
pp. 1679-1682
Author(s):  
Johannes K. Chiang ◽  
Daniel Yuh Chao
Keyword(s):  
Flexible Manufacturing ◽  
Flexible Manufacturing Systems ◽  
Manufacturing Systems ◽  
Polynomial Complexity ◽  
Reachability Graph ◽  
Computational Burden ◽  
The Family ◽  
Large Systems

We developed theory to show exactly one monitor is required for the set of siphons in the family of a 2-compound siphons and how to assign its initial markings. This avoids redundant monitors and the unnecessary associated computational burden. Neither reachability graph nor minimal siphon needs to be computed achieving polynomial complexity---essential for large systems. This paper redevelops the theory more formally and further applies this approach to two well-known S3PR to obtain a controller full or near maximally permissive.

scholarly journals On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 465
Author(s):  
Agnieszka Prusińska ◽  
Krzysztof Szkatuła ◽  
Alexey Tret’yakov
Keyword(s):  
Computational Complexity ◽  
Polynomial Complexity ◽  
Initial Point ◽  
Quadratic Functions ◽  
Problem Dimension ◽  
Piecewise Quadratic Functions ◽  
Large Systems ◽  
Systems Of Linear Inequalities ◽  
Number Of Iterations ◽  
Finite Number Of Iterations

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.

scholarly journals Analisis kestabilan dan kontrol optimal model matematika penyebaran penyakit Ebola dengan variabel kontrol berupa karantina

2021 ◽  
Vol 2 (1) ◽  
pp. 29-41
Author(s):  
Erzalina Ayu Satya Megananda ◽  
Cicik Alfiniyah ◽  
Miswanto Miswanto
Keyword(s):  
Optimal Control ◽  
Human Population ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Optimal Model ◽  
The Family ◽  
The Stability ◽  
The Cost ◽  
Two Equilibria

Ebola disease is an infectious disease caused by a virus from the genus Ebolavirus and the family Filoviridae. Ebola disease is one of the most deadly diseases for human. The purpose of the thesis is to analyze the stability of the equilibrium point and to apply the optimal control of quarantine on a mathematical model of the spread of ebola. Model without control has two equilibria, non-endemic equilibrium and endemic equilibrium. The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is asymptotically stable if R0 1 and endemic equilibrium tend to asymptotically stable if R0 1. The problem of optimal control is solved by Pontryagin’s Maximum Principle. From the numerical simulation, the result shows that control is effective enough to minimize the number of infected human population and to minimize the cost of its control.

scholarly journals Data-Driven Optimization Control for Dynamic Reconfiguration of Distribution Network

Energies ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2628 ◽  
Author(s):  
Dechang Yang ◽  
Wenlong Liao ◽  
Yusen Wang ◽  
Keqing Zeng ◽  
Qiuyue Chen ◽  
...  
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Distribution Network ◽  
Dynamic Reconfiguration ◽  
Complex Model ◽  
Data Driven ◽  
Optimal Control Strategy ◽  
Current Case ◽  
Optimization Control ◽  
Conventional Methods

To improve the reliability and reduce power loss of distribution network, the dynamic reconfiguration is widely used. It is employed to find an optimal topology for each time interval while satisfying all the physical constraints. Dynamic reconfiguration is a non-deterministic polynomial problem, which is difficult to find the optimal control strategy in a short time. The conventional methods solved complex model of dynamic reconfiguration in different ways, but only local optimal solutions can be found. In this paper, a data-driven optimization control for dynamic reconfiguration of distribution network is proposed. Through two stages that include rough matching and fine matching, the historical cases which are similar to current case are chosen as candidate cases. The optimal control strategy suitable for the current case is selected according to dynamic time warping (DTW) distances which evaluate the similarity between the candidate cases and the current case. The advantage of the proposed approach is that it does not need to solve complex model of dynamic reconfiguration, and only uses historical data to obtain the optimal control strategy for the current case. The cases study shows that the optimization results and the computation time of the proposed approach are superior to conventional methods.

scholarly journals Environmental and population externalities

2009 ◽  
Vol 15 (1) ◽  
pp. 1-19 ◽  
Author(s):  
FRANK JÖST ◽  
MARTIN F. QUAAS
Keyword(s):  
Optimal Control ◽  
Population Policy ◽  
Control Model ◽  
Household Size ◽  
Economic Capital ◽  
External Effects ◽  
The Family ◽  
Different Types ◽  
Polluting Emissions ◽  
Number Of Births

ABSTRACTWe analyze the external effects that arise in the decisions of firms on polluting emissions and in the decisions of parents on the number of births in an optimal control model with three stock variables representing population, economic capital, and pollution. We distinguish two different types of households, which represent opposite ends of a spectrum of potential familial structures: ‘dynastic households’, in which the family sticks together forever and ‘micro-households’, in which children leave their parent's household immediately after birth. We show that the decision of parents on the number of births involves an externality that is qualitatively different for both types of familial structure. Hence, population policy should be different, according to the type of household. A first best result may be obtained in the case of dynastic households if an appropriate tax on the household size is applied, or, in the case of micro-households, if an appropriate tax on children is applied.

Model Predictive Control of an Electroporation Process

2010 ◽  
Author(s):  
Peinan Ge ◽  
Jingang Yi ◽  
Jianbo Li ◽  
Hao Lin
Keyword(s):  
Optimal Control ◽  
Model Predictive Control ◽  
Cell Viability ◽  
Real Time ◽  
Predictive Control ◽  
Current Practice ◽  
Electrical Pulse ◽  
Fast Computation ◽  
Electrical Field ◽  
Efficiency And Reliability

Electroporation is an elegant means to deliver molecules into the cellular cytoplasm, while simultaneously maintaining cell viability and functionality. Despite extensive research, however, electroporation methods still fall short of the desired efficiency and reliability. We present a model predictive control (MPC) design for enabling highly efficient and reliable electroporation processes. Instead of using one single electrical pulse in current practice, we consider a controlled multi-pulse electroporation based on an MPC framework. The most attractive properties of using MPC design of multi-pulse electroporation are the fast computation of optimal control solutions and the real-time tunability of the electrical field density during the process. We demonstrate the controlled electroporation process through simulation examples.

Approximate Solution for Optimal Control of Continuous-Time Switched Systems

2016 ◽  
Author(s):  
Tohid Sardarmehni ◽  
Ali Heydari
Keyword(s):  
Optimal Control ◽  
Continuous Time ◽  
Switched Systems ◽  
Online Training ◽  
Policy Iteration ◽  
Recursive Least Squares ◽  
Iteration Algorithm ◽  
Computational Burden ◽  
Time Dynamics ◽  
Policy Iteration Algorithm

Two approximate solutions for optimal control of switched systems with autonomous subsystems and continuous-time dynamics are developed. The proposed solutions consist of online training algorithms with recursive least squares training laws. The first solution is the classic policy iteration algorithm which imposes heavy computational burden (full back-up). In order to relax the computational burden in the policy iteration algorithm, the second algorithm is presented. The convergence of the proposed algorithms to the optimal solution in online training is investigated. Simulation results are presented to illustrate the effectiveness of the discussed algorithms.

Sign in / Sign up

Export Citation Format

Share Document