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Journal articles on the topic 'Control loop'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 June 2025

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1

James, M. R. "Optimal Quantum Control Theory." Annual Review of Control, Robotics, and Autonomous Systems 4, no. 1 (May 3, 2021): 343–67. http://dx.doi.org/10.1146/annurev-control-061520-010444.

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This article explains some fundamental ideas concerning the optimal control of quantum systems through the study of a relatively simple two-level system coupled to optical fields. The model for this system includes both continuous and impulsive dynamics. Topics covered include open- and closed-loop control, impulsive control, open-loop optimal control, quantum filtering, and measurement feedback optimal control.

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2

İnci, Mustafa, Tuğçe Demirdelen, and Mehmet Tümay. "Performance Analysis of Closed Loop and Open Loop Control Methods in Dynamic Voltage Restorer." International Journal of Engineering Research 4, no. 11 (November 1, 2015): 582–85. http://dx.doi.org/10.17950/ijer/v4s11/1101.

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3

Rahman, Anisur, and M. A. A. Shoukat Choudhury. "Detection of control loop interactions and prioritization of control loop maintenance." Control Engineering Practice 19, no. 7 (July 2011): 723–31. http://dx.doi.org/10.1016/j.conengprac.2011.03.007.

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4

Randeep Singh, Masataka Mochizuki, Thang Nguyen, Yuji Saito, Kazuhiko Goto, and Koichi Mashiko. "G060041 Loop Heat Pipe for Datacenter Thermal Control." Proceedings of Mechanical Engineering Congress, Japan 2012 (2012): _G060041–1—_G060041–5. http://dx.doi.org/10.1299/jsmemecj.2012._g060041-1.

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5

Nasser, Mohamed Ramli *. Haslinda Zabiri. "CONTROL STRATEGIES OF HEAT EXCHANGER." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 6, no. 2 (February 1, 2017): 43–52. https://doi.org/10.5281/zenodo.266778.

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This work consists of experimental work for heat exchanger. The approach are made for comparison purpose instead of validation of experimental data. Behaviors of heat exchanger are to be observed through these approaches under two different control systems, open loop and closed loop response. The one concern is the closed loop control system, at which the behaviors are study and clarify. However, for closed loop control system to be established, some data such as PI, and PID values must be calculated from the open loop control system. Then, behaviors are justified through some calculations using established tuning method available in literature such as IMC based PI controller and using Ziegler-Nichols formula based PID controller.

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6

Lynch, C. B., and G. A. Dumont. "Control loop performance monitoring." IEEE Transactions on Control Systems Technology 4, no. 2 (March 1996): 185–92. http://dx.doi.org/10.1109/87.486345.

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7

Zellbeck, Hans. "Closed-loop Emission Control." MTZ worldwide 78, no. 6 (May 12, 2017): 78. http://dx.doi.org/10.1007/s38313-017-0060-7.

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8

Zellbeck, Hans. "Closed Loop Emission Control." MTZ - Motortechnische Zeitschrift 78, no. 6 (May 12, 2017): 90. http://dx.doi.org/10.1007/s35146-017-0058-3.

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9

E, Govindasamy. "Converter Fed DC Motor Speed Control Open Loop and Closed Loop Control." International Journal for Research in Applied Science and Engineering Technology 7, no. 4 (April 30, 2019): 466–69. http://dx.doi.org/10.22214/ijraset.2019.4085.

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10

Kameswari, B. S. Durga, and Dola Gobinda Padhan. "Complimentary Sensitivity Function based Novel Cascade Control Structure for Automatic Generation Control." E3S Web of Conferences 87 (2019): 01012. http://dx.doi.org/10.1051/e3sconf/20198701012.

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This paper introduces a series cascade control structure for automatic generation control. The control structure consists of two loops such as Primary loop and auxiliary loop (secondary loop). The secondary loop controller is designed using internal model control (IMC) approach. The primary loop controller is a PID controller which is tuned using desired complimentary sensitivity function. The beauty of the control structure is that it effectively nullifies the disturbances entering to the secondary loop as well as primary loop. The efficacy of the proposed controller is shown by comparing the simulation results with the existing methods in the literature.

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11

Geng Wang, Geng Wang, Chunlin Guan Chunlin Guan, Hong Zhou Hong Zhou, Xiaojun Zhang Xiaojun Zhang, and Changhui Rao Changhui Rao. "Hysteresis compensation of piezoelectric actuator for open-loop control." Chinese Optics Letters 11, s2 (2013): S21202–321205. http://dx.doi.org/10.3788/col201311.s21202.

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12

Abdulrahman, Alaa Muheddin. "Conventional Control of Loop-Height in Steel Rolling Mill." Journal of Zankoy Sulaimani - Part A 11, no. 1 (January 30, 2008): 81–87. http://dx.doi.org/10.17656/jzs.10183.

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13

Zhou, Hong Cheng, and Cun Bao Chen. "Single Channel Control Simulation Used on Servo Control." Advanced Materials Research 1028 (September 2014): 191–94. http://dx.doi.org/10.4028/www.scientific.net/amr.1028.191.

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Based on analysis for characteristic of the motion configuration, the control strategy and control law used on the motion control system are presented. The controller in velocity tracking loop and location loop are respectively designed by frequency correcting method and normal control method which belongs to classical control theory. The problem of location control loop low velocity creeping is solved. A simulating experimentation demonstrates the effectiveness of the proposed approach.

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14

A, Ezhilarasi. "Inverter Fed DC Motor Speed Control for Open Loop and Closed Loop Control." International Journal for Research in Applied Science and Engineering Technology 7, no. 4 (April 30, 2019): 462–65. http://dx.doi.org/10.22214/ijraset.2019.4084.

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15

Em, Poh Ping, Khisbullah Hudha, and Hishamuddin Jamaluddin. "Automatic steering control for lanekeeping manoeuvre: outer-loop and inner-loop control design." International Journal of Advanced Mechatronic Systems 2, no. 5/6 (2010): 350. http://dx.doi.org/10.1504/ijamechs.2010.037101.

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16

Vesjolaja, Ludmila, Bjørn Glemmestad, and Bernt Lie. "Double-Loop Control Structure for Rotary Drum Granulation Loop." Processes 8, no. 11 (November 8, 2020): 1423. http://dx.doi.org/10.3390/pr8111423.

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The operation of granulation plants on an industrial scale is challenging. Periodic instability associated with the operation of the granulation loop causes the particle size distribution of the particles flowing out from the granulator to oscillate, thus making it difficult to maintain the desired product quality. To address this problem, two control strategies are proposed in this paper, including a novel approach, where product-sized particles are recycled back to maintain a stable granulation loop process. A dynamic model of the process that is based on a population balance equation is used to represent the process dynamics. Both of the control strategies utilize a double-loop control structure that is suitable for highly oscillatory systems. The simulation results show that both control strategies, including the novel approach, are able to remove the oscillating behaviour and stabilize the granulation plant loop.

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17

Lucamarini, M., G. Di Giuseppe, D. Vitali, and P. Tombesi. "Open-loop and closed-loop control of flying qubits." Journal of Physics B: Atomic, Molecular and Optical Physics 44, no. 15 (July 25, 2011): 154005. http://dx.doi.org/10.1088/0953-4075/44/15/154005.

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18

Schoute, Frits C. "Open-loop versus closed-loop control of processor loading." Performance Evaluation 11, no. 3 (September 1990): 201–8. http://dx.doi.org/10.1016/0166-5316(90)90012-8.

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19

Calvagna, Andrea, and Giuseppe Tropea. "Twofold control loop network-level congestion control." European Transactions on Telecommunications 18, no. 1 (January 2007): 81–95. http://dx.doi.org/10.1002/ett.1095.

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20

Sorrell, Ethan, Michael E. Rule, and Timothy O'Leary. "Brain–Machine Interfaces: Closed-Loop Control in an Adaptive System." Annual Review of Control, Robotics, and Autonomous Systems 4, no. 1 (May 3, 2021): 167–89. http://dx.doi.org/10.1146/annurev-control-061720-012348.

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Brain–machine interfaces (BMIs) promise to restore movement and communication in people with paralysis and ultimately allow the human brain to interact seamlessly with external devices, paving the way for a new wave of medical and consumer technology. However, neural activity can adapt and change over time, presenting a substantial challenge for reliable BMI implementation. Large-scale recordings in animal studies now allow us to study how behavioral information is distributed in multiple brain areas, and state-of-the-art interfaces now incorporate models of the brain as a feedback controller. Ongoing research aims to understand the impact of neural plasticity on BMIs and find ways to leverage learning while accommodating unexpected changes in the neural code. We review the current state of experimental and clinical BMI research, focusing on what we know about the neural code, methods for optimizing decoders for closed-loop control, and emerging strategies for addressing neural plasticity.

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21

Roca, Pablo, Thomas Duriez, Ada Cammilleri, and Guillermo Artana. "CYLINDER WAKE CLOSED-LOOP CONTROL SYSTEM." Anales AFA 23, no. 3 (September 17, 2013): 29–33. http://dx.doi.org/10.31527/analesafa.2013.23.3.29.

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22

Zhang, Jianhua, and Junghui Chen. "Neural PID Control Strategy for Networked Process Control." Mathematical Problems in Engineering 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/752489.

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A new method with a two-layer hierarchy is presented based on a neural proportional-integral-derivative (PID) iterative learning method over the communication network for the closed-loop automatic tuning of a PID controller. It can enhance the performance of the well-known simple PID feedback control loop in the local field when real networked process control applied to systems with uncertain factors, such as external disturbance or randomly delayed measurements. The proposed PID iterative learning method is implemented by backpropagation neural networks whose weights are updated via minimizing tracking error entropy of closed-loop systems. The convergence in the mean square sense is analysed for closed-loop networked control systems. To demonstrate the potential applications of the proposed strategies, a pressure-tank experiment is provided to show the usefulness and effectiveness of the proposed design method in network process control systems.

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23

Li, Kelin, Yalei Bai, and Haoyu Zhou. "Research on Quadrotor Control Based on Genetic Algorithm and Particle Swarm Optimization for PID Tuning and Fuzzy Control-Based Linear Active Disturbance Rejection Control." Electronics 13, no. 22 (November 8, 2024): 4386. http://dx.doi.org/10.3390/electronics13224386.

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The control system of a quadrotor aircraft is characterized by nonlinearity, strong coupling, and underactuation, making it susceptible to external disturbances that can affect flight performance. To address this issue, this paper proposes a novel control system based on inner–outer loop architecture. In this system, the outer loop position control adopts a PID controller optimized by Genetic Algorithm-based Particle Swarm Optimization (GA-PSO), while the inner loop attitude control employs a Linear Active Disturbance Rejection Controller (LADRC) with fuzzy algorithm-based adaptive tuning, forming a dual-loop control structure. Comparisons with traditional dual-loop cascaded PID controllers, conventional PID in the outer loop with LADRC in the inner loop, and conventional PID in the outer loop with fuzzy algorithm-based adaptive tuning in the inner loop demonstrate that the proposed control system can stably track the desired position and attitude angles under certain external disturbances, exhibiting excellent anti-disturbance capability and stability.

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24

Jin, Li Qiang, Chuan Xue Song, and Jian Hua Li. "Intelligent Velocity Control Strategy for Electric Vehicles." Applied Mechanics and Materials 80-81 (July 2011): 1180–84. http://dx.doi.org/10.4028/www.scientific.net/amm.80-81.1180.

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In conventional vehicles, the control of vehicle speed is achieved by changing the engine load through adjusting the acceleration pedal. However, in electric vehicles, this is achieved by controlling the target motor torque obtained from the look-up table in accordance with the position of acceleration pedal. This method is an open-loop control, with which the engine brake cannot be implemented during downhill trips. In this paper, a closed-loop control of vehicle speed for electric vehicles is proposed. The target vehicle speed is set by the acceleration pedal. The controller collects the real vehicle speed, whereas the PID controller, according to the error of the real and target vehicle speed, adjusts the motor torque in real time to realize the closed-loop speed control. Under such controlling, the motor torque can be changed correspondingly with the resistance, thus makes the driving performance of electric vehicles more identical to that of conventional vehicles.

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25

Ping, Em Poh, Khisbullah Hudha, and Hishamuddin Jamaluddin. "Hardware-in-the-loop simulation of automatic steering control for lanekeeping manoeuvre: outer-loop and inner-loop control design." International Journal of Vehicle Safety 5, no. 1 (2010): 35. http://dx.doi.org/10.1504/ijvs.2010.035318.

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26

Poggie, Jonathan, Carl P. Tilmann, Peter M. Flick, Joseph S. Silkey, Bradley A. Osbourne, Gregory Ervin, Dragan Maric, Siva Mangalam, and Arun Mangalam. "Closed-Loop Stall Control System." Journal of Aircraft 47, no. 5 (September 2010): 1747–55. http://dx.doi.org/10.2514/1.c000262.

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27

Struys, Michel M. R. F., Tom De Smet, and Eric P. Mortier. "Closed-loop control of anaesthesia." Current Opinion in Anaesthesiology 15, no. 4 (August 2002): 421–25. http://dx.doi.org/10.1097/00001503-200208000-00003.

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28

Kenny, G. N. C., W. McFadzean, H. Mantzaridis, and A. C. Fisher. "CLOSED-LOOP CONTROL OF ANESTHESIA." Anesthesiology 77, Supplement (September 1992): A328. http://dx.doi.org/10.1097/00000542-199209001-00328.

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29

Alekseev, A. S., S. V. Zamyatin, and V. A. Rudnicki. "Multi-loop control system design." Bulletin of the Polish Academy of Sciences: Technical Sciences 60, no. 3 (December 1, 2012): 627–30. http://dx.doi.org/10.2478/v10175-012-0074-x.

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Abstract The approach based on a special case of the Laplace transform, which allows to design multi-loop system is considered. The tuning regulators program on the base of this approach is developed. The numerical example is shown.

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30

Kribus, Abraham, Irina Vishnevetsky, Amnon Yogev, and Tatiana Rubinov. "Closed loop control of heliostats." Energy 29, no. 5-6 (April 2004): 905–13. http://dx.doi.org/10.1016/s0360-5442(03)00195-6.

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31

Hägglund, T. "A control-loop performance monitor." Control Engineering Practice 3, no. 11 (November 1995): 1543–51. http://dx.doi.org/10.1016/0967-0661(95)00164-p.

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32

Perez, R. B., P. J. Otaduy, and M. Abdalla. "Nonlinear closed-loop control theory." Annals of Nuclear Energy 19, no. 3 (March 1992): 123–43. http://dx.doi.org/10.1016/s0306-4549(06)80010-1.

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33

Huang, Hong-Yi, Shiun-Dian Jan, and Ruei-Iun Pu. "All digital pulsewidth control loop." International Journal of Electronics 100, no. 3 (March 2013): 337–54. http://dx.doi.org/10.1080/00207217.2012.713010.

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34

Van Herpe, Tom, Bart De Moor, and Greet Van den Berghe. "Towards closed-loop glycaemic control." Best Practice & Research Clinical Anaesthesiology 23, no. 1 (March 2009): 69–80. http://dx.doi.org/10.1016/j.bpa.2008.07.003.

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35

Dumont, Guy A., and J. Mark Ansermino. "Closed-Loop Control of Anesthesia." Anesthesia & Analgesia 117, no. 5 (November 2013): 1130–38. http://dx.doi.org/10.1213/ane.0b013e3182973687.

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36

Nævdal, Geir, D. Roald Brouwer, and Jan-Dirk Jansen. "Waterflooding using closed-loop control." Computational Geosciences 10, no. 1 (April 28, 2006): 37–60. http://dx.doi.org/10.1007/s10596-005-9010-6.

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37

Laudan, Timo, and Axel Mauritz. "Integrated Project Control Loop Concept." INCOSE International Symposium 16, no. 1 (July 2006): 1733–48. http://dx.doi.org/10.1002/j.2334-5837.2006.tb02847.x.

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38

Harris, Thomas J. "Assessment of control loop performance." Canadian Journal of Chemical Engineering 67, no. 5 (October 1989): 856–61. http://dx.doi.org/10.1002/cjce.5450670519.

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39

Wang, Li, Fan Zhang, and Yali Xue. "A comparative study of single-loop control and multi-loop control of gas turbine." IFAC-PapersOnLine 55, no. 9 (2022): 525–30. http://dx.doi.org/10.1016/j.ifacol.2022.07.091.

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40

Hu, Fa Huan, Xiao Tong Qiu, and Jun Tang. "Application of Fuzzy PI Control to Speed Control System of Brushless DC Motor." Advanced Materials Research 516-517 (May 2012): 1575–79. http://dx.doi.org/10.4028/www.scientific.net/amr.516-517.1575.

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Basing on analysis the principle and mathematical model of the brushless DC motor, the paper proposes a control model on the basis of speed loop and current loop, fuzzy PI control model is adopted in the speed loop, and traditional PID control model is used in the current loop. It is showed that when the load or parameters vary, comparing to traditional PID control model, the fuzzy PI control model gets less fluctuation and better robustness.

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41

Alagöz, Barış Baykant, Furkan Nur Deniz, and Cemal Keleş. "REVISITING BODE’S IDEAL LOOPS: INTEGRAL SQUARE ERROR OPTIMALITY OF BODE’S IDEAL LOOPS AND BODE’S IDEAL LOOP INVERSE CONTROLLER DESIGN." Mühendislik Bilimleri ve Tasarım Dergisi 13, no. 1 (March 20, 2025): 202–20. https://doi.org/10.21923/jesd.1452157.

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Bode’s ideal loop models have been utilized in control system designs to obtain performance robustness for the Direct Current (DC) gain variations. However, effects of crossover frequency and fractional order on control optimality of Bode's ideal loop reference models have not been sufficiently discussed, and it may raise a question of whether a control system design based on Bode’s ideal loop reference model is optimal. In this regard, this study revisits Bode’s ideal loops to investigate Integral Square Error (ISE) optimality of Bode’s ideal loops. For this purpose, the ISE optimality of Bode’s ideal loop is theoretically investigated by using Parseval’s theorem, and an ISE optimality condition is suggested in terms of crossover frequency and fractional order. Then, a generic controller family, which achieves an exact matching with the characteristics of the ISE optimal Bode’s ideal loop, was implemented for inverse fractional-order control of a class of minimum phase fractional order plant models. The authors present a numerical experiment on an ISE optimal Bode’s ideal loop inverse (OBILI) controller, and the ISE optimality and performance robustness of the designed control system were investigated for closed-loop control of a heat furnace system model via Monte Carlo simulations.

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42

Amalia, Norma, Eka Setia Nugraha, and Muntaqo Alfin Amanaf. "Open Loop and Closed Loop Power Control Analysis on LTE." JURNAL INFOTEL 10, no. 4 (November 30, 2018): 195. http://dx.doi.org/10.20895/infotel.v10i4.399.

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LTE downlink is using Orthogonal Frequency Division Multiple Access (OFDMA) multiple access system which have high invulnerability from multipath problem. One of the weakness of OFDM system is the high level from Peak to Average Power Ratio (PAPR) that was required higher level transmit power for maintaining the Bit Error Rate (BER) requirement. Using uplink scheme with Single Carrier FDMA (SC-FDMA) which is OFDMA modification, will be offered better level of PAPR than its conventional OFDM. The main problem of using OFDMA is the high level of PAPR, while using SC-FDMA the problem is intra-cell interference. Intra-cell or inter-cell interference is the common problem that can reduce the LTE performance. Minimizing received power for each users (UE) which is still at acceptable tolerance parameter, can be used for reducing the interference problem to another UE. Power control is the appropriate solution for minimizing the interference level. In this paper will be analyzed the power control using open loop and closed loop scheme at LTE network. The simulation result show that without power control schemes, the transmit power of UE is 23 dBm. While, after applying power control scheme, the transmit power is 18.8 dBm at ?=0.4 of open loop condition and 9.05 dBm at closed loop condition. Using this transmit power value as the UE power can improve the SINR performance. The SINR average value without power control scheme is only 20.38 dB which is lower than using open loop scheme is achieved 22.44 dB and 24.02 dB at closed loop scheme.

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43

Kogan, Konstantin. "Production control under uncertainty: Closed-loop versus open-loop approach." IIE Transactions 41, no. 10 (August 17, 2009): 905–15. http://dx.doi.org/10.1080/07408170902973944.

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44

Chao-Hwa Yang, D. Y. Chen, C. Jamerson, and Yan Pei Wu. "Stabilizing magamp control loop by using an inner-loop compensation." IEEE Transactions on Power Electronics 6, no. 3 (July 1991): 419–29. http://dx.doi.org/10.1109/63.85910.

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45

Gabasov, R., F. M. Kirillova, and N. V. Balashevich. "OPEN-LOOP AND CLOSED-LOOP OPTIMIZATION OF LINEAR CONTROL SYSTEMS." Asian Journal of Control 2, no. 3 (October 22, 2008): 155–68. http://dx.doi.org/10.1111/j.1934-6093.2000.tb00154.x.

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46

Zakaria, Diky, Dewi Indriati Hadi Putri, Muhammad Rizalul Wahid, Rezka Bunaiya Prayudha, Fauzie Salman, Alimudinsyah Alrasyid, Muhammad Bilal Hamzah, Agung Satria Pamungkas, and Dany Syauqi Nazhif. "Simple Control System Training for Students and Teachers of Vocational School in Purwakarta." REKA ELKOMIKA: Jurnal Pengabdian kepada Masyarakat 4, no. 3 (November 1, 2023): 255–62. http://dx.doi.org/10.26760/rekaelkomika.v4i3.255-262.

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Everyday life depends on control systems. If a system has a good control system, it will give you the results we want. Through the control system, we can change things like temperature, speed, pressure, level, and other physical numbers to the way you want them to be. There are two kinds of control system: open loop control and closed loop control. The open loop control system is the easiest to use because the person controls the system without getting any feedback. While the closed loop control system will get feedback from the system output so that the system will automatically reach the desired state. Teachers and children at vocational school in Purwakarta get to try out open loop and closed loop control system applications during this community service project. This is important so that teachers and students can get the experience in control system application.

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47

Li, Da, Jian Zhang, Yifei Zhuang, Cheng Zhen, and Jiawei Zhang. "Simulation application of support vector machine feedforward control in gas turbine load control." Journal of Physics: Conference Series 2835, no. 1 (August 1, 2024): 012073. http://dx.doi.org/10.1088/1742-6596/2835/1/012073.

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Abstract To address the challenges of excessive overshoot, prolonged settling time, and complex PID parameter tuning in gas turbine load control, this study investigates a gas turbine load control system utilizing support vector machine feedforward control. Firstly, the load control loop is decomposed, and the existing model structure is integrated with the load control section. Subsequently, the gas turbine load loop is modeled based on field test data. Following this, a gas turbine load control system incorporating a support vector machine feedforward loop is constructed in the MATLAB/Simulink environment. Finally, the entire loop undergoes simulation experiments. The simulation results demonstrate that the system exhibits rapid response to load step changes, enhances the stability of the load control loop, and effectively fulfills the requirements of grid-source coordination in modern power systems.

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48

Fang, Qian, Yong Zhou, Shangjun Ma, Chao Zhang, Ye Wang, and Haibin Huangfu. "Electromechanical Actuator Servo Control Technology Based on Active Disturbance Rejection Control." Electronics 12, no. 8 (April 19, 2023): 1934. http://dx.doi.org/10.3390/electronics12081934.

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Electromechanical actuators (EMA) are becoming more and more widely used. As the core technology of EMA, servo control technology determines their performance. In this paper, an active disturbance rejection control (ADRC) method with an improved extended state observer (ESO) is proposed to design a cascade controller of EMA based on permanent magnet synchronous motor (PMSM). The mathematical model of PMSM in a two-phase rotating coordinate system is established, then it is decoupled by an id=0 current control method to realize the vector control of the motor. In a three closed-loop vector control system, a PID controller including current loop, speed loop and position loop is designed. To solve the problems caused by measurement noise, the filter link and system are modeled as a whole, and an improved ESO is constructed. On this basis, an ADRC controller of the speed loop and position loop of PMSM is designed and simulated based on Simulink. Based on the physical test platform, a load step test and load disturbance test of ADRC are completed. The results show that, in comparison to the PID method, the ADRC method shortens the response time by 25% on average, and reduces the overshoot by 60% on average. So, it can be concluded that ADRC has good static and dynamic performance, which has a good guiding role for engineering practice.

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49

Glizer, Valery Y., and Vladimir Turetsky. "One Class of Stackelberg Linear–Quadratic Differential Games with Cheap Control of a Leader: Asymptotic Analysis of an Open-Loop Solution." Axioms 13, no. 11 (November 18, 2024): 801. http://dx.doi.org/10.3390/axioms13110801.

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We consider a two-player finite horizon linear–quadratic Stackelberg differential game. For this game, we study the case where the control cost of a leader in the cost functionals of both players is small, which means that the game under consideration is a cheap control game. We look for open-loop optimal players’ controls of this game. Using the game’s solvability conditions, the obtaining such controls is reduced to the solution to a proper boundary-value problem. Due to the smallness of the leader’s control cost, this boundary-value problem is singularly perturbed. Asymptotic behavior of the solution to this problem is analyzed. Based on this analysis, the asymptotic behavior of the open-loop optimal players’ controls and the optimal values of the cost functionals is studied. Using these results, asymptotically suboptimal players’ controls are designed. An illustrative example is presented.

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Devie, Sylvain, Pierre-Philippe Robet, Yannick Aoustin, and Maxime Gautier. "Impedance Control Using a Cascaded Loop Force Control." IEEE Robotics and Automation Letters 3, no. 3 (July 2018): 1537–43. http://dx.doi.org/10.1109/lra.2018.2801472.

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