scholarly journals Design of Optimal Controllers for Unknown Dynamic Systems through the Nelder–Mead Simplex Method

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 2013
Author(s):  
Hsun-Heng Tsai ◽  
Chyun-Chau Fuh ◽  
Jeng-Rong Ho ◽  
Chih-Kuang Lin
Keyword(s):  
Penalty Function ◽  
Performance Index ◽  
Simplex Method ◽  
Open Loop ◽  
The State ◽  
Time Interval ◽  
Improve Design ◽  
Optimal Controllers ◽  
Allowable Range ◽  
Termination Time

This paper presents an efficient method for designing optimal controllers. First, we established a performance index according to the system characteristics. In order to ensure that this performance index is applicable even when the state/output of the system is not within the allowable range, we added a penalty function. When we use a certain controller, if the state/output of the system remains within the allowable range within the preset time interval, the penalty function value is zero. Conversely, if the system state/output is not within the allowable range before the preset termination time, the experiment/simulation is terminated immediately, and the penalty function value is proportional to the time difference between the preset termination time and the time at which the experiment was terminated. Then, we used the Nelder–Mead simplex method to search for the optimal controller parameters. The proposed method has the following advantages: (1) the dynamic equation of the system need not be known; (2) the method can be used regardless of the stability of the open-loop system; (3) this method can be used in nonlinear systems; (4) this method can be used in systems with measurement noise; and (5) the method can improve design efficiency.

Pointwise feedback stabilization of an Euler-Bernoulli beam in observations with time delay

2019 ◽  
Vol 25 ◽  
pp. 4 ◽  
Author(s):  
Kun-Yi Yang ◽  
Jun-Min Wang
Keyword(s):  
Time Delay ◽  
Open Loop ◽  
The State ◽  
Feedback Stabilization ◽  
Loop System ◽  
Beam Equation ◽  
Time Interval ◽  
Bernoulli Beam ◽  
Exponentially Stable ◽  
Euler Bernoulli Beam

This paper considers a one-dimensional Euler-Bernoulli beam equation where two collocated actuators/sensors are presented at the internal point with pointwise feedback shear force and angle velocity at the arbitrary position ξ in the bounded domain (0,1). The boundary x = 0 is simply supported and at the other boundary x = 1 there is a shear hinge end. Both of the observation signals are subjected to a given time delay τ ( >0). Well-posedness of the open-loop system is shown to illustrate availability of the observer. An observer is then designed to estimate the state at the time interval when the observation is available, while a predictor is designed to predict the state at the time interval when the observation is not available. Pointwise output feedback controllers are introduced to guarantee the closed-loop system to be exponentially stable for the smooth initial values when ξ ∈ (0, 1) is a rational number satisfying ξ ≠ 2l∕(2m − 1) for any integers l, m. Simulation results demonstrate that the proposed feedback design effectively stabilizes the performance of the pointwise control system with time delay.

Resection of bone by sagittal saw: Investigation of effects of blade speed, feed rate, and irrigation on temperature rise

2021 ◽  
pp. 095441192199948
Author(s):  
Ehsan Shakouri ◽  
Pezhman Ghorbani ◽  
Pedram Pourheidari ◽  
Saeed Fotuhi
Keyword(s):  
Temperature Rise ◽  
Feed Rate ◽  
Saline Solution ◽  
Physiological Saline ◽  
The State ◽  
Physiological Saline Solution ◽  
Allowable Range ◽  
Dry Conditions ◽  
Saw Blade ◽  
Oscillation Rate

Heat generation during bone cutting by sagittal saw may lead to temperature rise and possible incidence of thermal necrosis. The aim of the present research is to examine the effect of saw blade oscillation rate, blade feed rate, and irrigation by physiological saline solution on the bone temperature rise during sawing in order to determine the desired conditions for reducing the extent of thermal damage. For this purpose, empirical tests of bovine femur cutting were performed in 15 states, including five levels for the blade oscillation rate (10,000–18,000 cpm with 2000 cpm intervals) and three levels for the feed rate (10–30 mm.min−1 with 10 mm.min−1 intervals) for dry conditions; and five states, including five levels for the blade oscillation rate (10,000–18,000 cpm with 2000 cpm intervals) and one level in feed rate of 20 mm.min−1 for the irrigation conditions. The results indicated that the bone temperature rise had a direct relationship with the blade oscillation rate and an inverse relationship with its feed rate. In the state of no cooling, the minimum temperature rise (Δ T = 65.45°C) occurred at the blade speed of 10,000 cpm and feed rate of 30 mm.min−1, while in the state of sawing with irrigation, the temperature rise almost did not exceed the allowable range (Δ T ≤ 10°C). The results suggested that to lower the possibility of incidence of osteonecrosis in the bone resection by sagittal saw, cooling with physiological saline solution or application of the minimum blade oscillation rate and maximum feed rate is recommended.

scholarly journals Finite-Time Boundedness for a Class of Delayed Markovian Jumping Neural Networks with Partly Unknown Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Li Liang
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Transition Probabilities ◽  
The State ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markovian Jumping ◽  
Stochastic Boundedness ◽  
Partly Unknown Transition Probabilities ◽  
Finite Time Boundedness

This paper is concerned with the problem of finite-time boundedness for a class of delayed Markovian jumping neural networks with partly unknown transition probabilities. By introducing the appropriate stochastic Lyapunov-Krasovskii functional and the concept of stochastically finite-time stochastic boundedness for Markovian jumping neural networks, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a prespecified finite-time interval. Finally, numerical examples are given to illustrate the effectiveness and reduced conservativeness of the proposed results.

scholarly journals A escola invade as ruas: passeatas cívicas dos grupos escolares sergipanos. Civismo e patriotismo no espaço urbano

2017 ◽  
Vol 1 (1) ◽  
pp. 229
Author(s):  
Degenal De Jesus da Silva
Keyword(s):  
Urban Space ◽  
The State ◽  
Time Interval ◽  
Norbert Elias ◽  
First Republic ◽  
New Look

Este artigo apresenta a pesquisa sobre as festas cívicas realizadas nas ruas de Sergipe, entre 1923 e 1930. Nesse intervalo temporal, aconteceu algo inusitado, e os historiadores sergipanos não se debruçaram a estudar: o declínio das comemorações republicanas nas ruas. Este estudo ganha relevância, principalmente, porque se sucedeu no governo de Graccho Cardoso a presidente do estado, considerado pela historiografia sergipana como um governante desenvolvimentista, especialmente, na área da educação. Assim, o objetivo é examinar o percurso das festividades, tentando perceber os indícios deixados nas fontes sobre as formas de participação de indivíduos e instituições envolvidos nesses momentos de celebração; e, as representações utilizadas naquele momento histórico. Para tanto, utilizamos diversos documentos para que pudéssemos cruzar as informações, com o intuito de podermos lançar um novo olhar sobre esse período. Dessa forma, utilizamos os conceitos de Representações, de Roger Chartier; de indivíduos, de Norbert Elias; e do paradigma indiciário, de Carlo Ginzburg.The school invade streets: parades civic of the sergipeans groups school. Civility and patriotism in urban space. Article search civic parties in Sergipe held in the streets, between 1923-1930. In this time interval, there was something unusual, and that the Sergipeans historians pored studying: the decline of republican celebrations in the streets. This study becomes relevant, especially because this fact began under President Cardoso Graccho the President of the State, considered by sergipana historiography as a developmentalist - and especially in education. The objective is to examine the course of the festivities, trying to understand the clues left in the sources of the forms of participation; individuals and institutions involved in these moments of celebration; and the representations used in that historic moment. Therefore, we use various documents so that we could cross the information, In order that we can launch a new look at this period. Thus, we used the concepts: Representations of Roger Chartier; individuals of Norbert Elias and the indiciary paradigm of Carlo Ginzburg. Keywords: Civic Parties; First Republic; Representations.

scholarly journals UNDERSTANDING ASSAM’S SUSTAINABILITY ISSUES

2021 ◽  
pp. 90-96
Author(s):  
Pratyush Paras Sarma ◽  
Sagarmoy Phukan
Keyword(s):  
Sustainable Development ◽  
Citizen Science ◽  
Performance Index ◽  
Sustainable Development Goals ◽  
The State ◽  
The Other ◽  
Development Goals ◽  
The Government

Assam was the first state in India to have undertaken the Global Sustainable Development Goals (SDGs) as a long-term guiding strategy for development. At the end of five years, before the state election, evaluating the work on SDGs in Assam is essential to follow up on the commitment of the government. But before we start evaluating the SDGs it is important to understand the development road Assam has taken over the last 100-150 years and why we must make a new turn. This study has tried to understand certain loopholes which have hampered the progress of SDGs in Assam along with how much Assam has been able to address its sustainability issues and how we can progress. We have reviewed the performance of the state based upon the official performance index released by NITI Aayog, Government of India. Our review of the index reflects that Assam has performed relatively poorer than the other states of the country. However, the ethnic culture of the region was deeply rooted in nature which the state can now adopt and harness to achieve its SDGs. KEYWORDS: Sustainable Development Goals; Assam Election; Indigenous Knowledge; Citizen Science; Polycentric Governance

scholarly journals Combined assimilation of streamflow and snow water equivalent for mid-term ensemble streamflow forecasts in snow-dominated regions

2016 ◽  
Author(s):  
Jean M. Bergeron ◽  
Mélanie Trudel ◽  
Robert Leconte
Keyword(s):  
Data Assimilation ◽  
State Vector ◽  
Snow Water Equivalent ◽  
Synthetic Data ◽  
Hydrologic Model ◽  
Open Loop ◽  
The State ◽  
Wide Range ◽  
Snow Water ◽  
The Impact

Abstract. The potential of data assimilation for hydrologic predictions has been demonstrated in many research studies. Watersheds over which multiple observation types are available can potentially further benefit from data assimilation by having multiple updated states from which hydrologic predictions can be generated. However, the magnitude and time span of the impact of the assimilation of an observation varies according not only to its type, but also to the variables included in the state vector. This study examines the impact of multivariate synthetic data assimilation using the Ensemble Kalman Filter (EnKF) into the spatially distributed hydrologic model CEQUEAU for the mountainous Nechako River located in British-Columbia, Canada. Synthetic data includes daily snow cover area (SCA), daily measurements of snow water equivalent (SWE) at three different locations and daily streamflow data at the watershed outlet. Results show a large variability of the continuous rank probability skill score over a wide range of prediction horizons (days to weeks) depending on the state vector configuration and the type of observations assimilated. Overall, the variables most closely linearly linked to the observations are the ones worth considering adding to the state vector. The performance of the assimilation of basin-wide SCA, which does not have a decent proxy among potential state variables, does not surpass the open loop for any of the simulated variables. However, the assimilation of streamflow offers major improvements steadily throughout the year, but mainly over the short-term (up to 5 days) forecast horizons, while the impact of the assimilation of SWE gains more importance during the snowmelt period over the mid-term (up to 50 days) forecast horizon compared with open loop. The combined assimilation of streamflow and SWE performs better than its individual counterparts, offering improvements over all forecast horizons considered and throughout the whole year, including the critical period of snowmelt. This highlights the potential benefit of using multivariate data assimilation for streamflow predictions in snow-dominated regions.

Contracts and Information Structure in a Supply Chain with Operations and Marketing Interaction

2016 ◽  
Vol 18 (04) ◽  
pp. 1650014 ◽  
Author(s):  
Fouad El Ouardighi ◽  
Gary Erickson ◽  
Dieter Grass ◽  
Steffen Jørgensen
Keyword(s):  
Supply Chain ◽  
Information Structure ◽  
Wholesale Price ◽  
Revenue Sharing ◽  
Open Loop ◽  
The State ◽  
Current State ◽  
Marketing Activities ◽  
Purchase Rate ◽  
The Impact

The objective of the paper is to study how wholesale price and revenue sharing contracts affect operations and marketing decisions in a supply chain under different dynamic informational structures. We suggest a differential game model of a supply chain consisting of a manufacturer and a single retailer that agree on the contract parameters at the outset of the game. The model includes key operational and marketing activities related to a single product in the supply chain. The manufacturer sets a production rate and the rate of advertising efforts while the retailer chooses a purchase rate and the consumer price. The state of the game is summarized in the firms’ backlogs and the manufacturer’s advertising goodwill. Depending on whether the supply chain members have and share state information, they may either make decisions contingent on the current state of the game (feedback Nash strategy), or precommit to a plan of action during the whole game (open-loop Nash strategy). Given a contract type, the impact of the availability of information regarding the state of the game on the firms’ decisions and payoffs is investigated. It is shown that double marginalization can be better mitigated if the supply chain members adopt a contingent strategy under a wholesale price contract and a commitment strategy under a revenue sharing contract.

One-Player Differential Games

2017 ◽  
Author(s):  
João P. Hespanha
Keyword(s):  
Dynamical System ◽  
Differential Games ◽  
Continuous Time ◽  
Information Structure ◽  
Dynamic Games ◽  
State Feedback ◽  
Open Loop ◽  
Linear Quadratic ◽  
Time Dynamic ◽  
Termination Time

This chapter focuses on one-player continuous time dynamic games, that is, the optimal control of a continuous time dynamical system. It begins by considering a one-player continuous time differential game in which the (only) player wants to minimize either using an open-loop policy or a state-feedback policy. It then discusses continuous time cost-to-go, with the following conclusion: regardless of the information structure considered (open loop, state feedback, or other), it is not possible to obtain a cost lower than cost-to-go. It also explores continuous time dynamic programming, linear quadratic dynamic games, and differential games with variable termination time before concluding with a practice exercise and the corresponding solution.

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

2020 ◽  
Vol 42 (10) ◽  
pp. 1871-1881 ◽  
Author(s):  
Morteza Motahhari ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Linear Matrix ◽  
Time Interval ◽  
State Variables ◽  
L2 Gain

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

Modeling and Control of a Rotary Crane

1985 ◽  
Vol 107 (3) ◽  
pp. 200-206 ◽  
Author(s):  
Y. Sakawa ◽  
A. Nakazumi
Keyword(s):  
Feedback Control ◽  
Equilibrium State ◽  
Open Loop ◽  
The State ◽  
Control Input ◽  
Loop Control ◽  
Modeling And Control ◽  
Control Scheme ◽  
Rotary Crane ◽  
And Control

In this paper we first derive a dynamical model for the control of a rotary crane, which makes three kinds of motion (rotation, load hoisting, and boom hoisting) simultaneously. The goal is to transfer a load to a desired place in such a way that at the end of transfer the swing of the load decays as quickly as possible. We first apply an open-loop control input to the system such that the state of the system can be transferred to a neighborhood of the equilibrium state. Then we apply a feedback control signal so that the state of the system approaches the equilibrium state as quickly as possible. The results of computer simulation prove that the open-loop plus feedback control scheme works well.

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