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1

Garcia, G., S. Tarbouriech, R. Suarez, and J. Alvarez-Ramirez. "Nonlinear bounded control for norm-bounded uncertain systems." IEEE Transactions on Automatic Control 44, no. 6 (1999): 1254–58. http://dx.doi.org/10.1109/9.769385.

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2

Novikov, D. A. "Bounded Rationality and Control." Automation and Remote Control 83, no. 6 (2022): 990–1009. http://dx.doi.org/10.1134/s0005117922060145.

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3

Новиков, Дмитрий Александрович, and Dmitriy Novikov. "Bounded Rationality and Control." Mathematical Game Theory and Applications 14, no. 1 (2023): 49–84. http://dx.doi.org/10.17076/mgta_2022_1_44.

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The rationality constraint condition is formulated, which states that when solving control, computing and communication problems ($C^3$) together, real-time requirements may not make it possible to find the optimal solution (control action), forcing the use of almost optimal solutions (the best found with the existing restrictions on the search procedure). This condition connects and demonstrates the unity and deep interconnection of such concepts common in management and optimization as: necessary diversity, limited rationality, analytical complexity, heuristics, records in real-time optimization. In relation to the problem of institutional management of organizational and technical systems, a number of examples of solving problems of minimizing error or complexity, as well as searching for: critical bandwidth of the communication channel, critical computing rate and the maximum number of controlled subsystems are given.
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4

Lu, Ping. "Tracking Control of Nonlinear Systems with Bounded Controls and Control Rates." IFAC Proceedings Volumes 29, no. 1 (1996): 2307–12. http://dx.doi.org/10.1016/s1474-6670(17)58017-9.

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5

Lu, Ping. "Tracking control of nonlinear systems with bounded controls and control rates." Automatica 33, no. 6 (1997): 1199–202. http://dx.doi.org/10.1016/s0005-1098(97)00033-2.

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6

Liu, Baishun. "Constructive General Bounded Integral Control." Intelligent Control and Automation 05, no. 03 (2014): 146–55. http://dx.doi.org/10.4236/ica.2014.53017.

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7

Hirschorn, Ronald. "Lower Bounded Control-Lyapunov Functions." Communications in Information and Systems 8, no. 4 (2008): 399–412. http://dx.doi.org/10.4310/cis.2008.v8.n4.a3.

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8

Hokayem, P., D. Chatterjee, F. A. Ramponi, and J. Lygeros. "Stable Networked Control Systems With Bounded Control Authority." IEEE Transactions on Automatic Control 57, no. 12 (2012): 3153–57. http://dx.doi.org/10.1109/tac.2012.2195934.

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9

Rohloff, Kurt. "Bounded Sensor Failure Tolerant Supervisory Control." IFAC Proceedings Volumes 45, no. 29 (2012): 272–77. http://dx.doi.org/10.3182/20121003-3-mx-4033.00045.

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10

Deka, Shankar A., Dusan M. Stipanovic, and Thenkurussi Kesavadas. "Stable Bilateral Teleoperation With Bounded Control." IEEE Transactions on Control Systems Technology 27, no. 6 (2019): 2351–60. http://dx.doi.org/10.1109/tcst.2018.2871874.

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11

Chuang, C. H., D. N. Wu, and Q. Wang. "LQR for State-Bounded Structural Control." Journal of Dynamic Systems, Measurement, and Control 118, no. 1 (1996): 113–19. http://dx.doi.org/10.1115/1.2801130.

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In order to prevent structural damages, it is more important to bound the vibration amplitude than to reduce the vibration energy. However, in the performance index for linear quadratic regulator (LQR), the instantaneous amplitude of vibration is not minimized. An ordinary LQR may have an unacceptable amplitude at some time instant but still have a good performance. In this paper, we have developed an LQR with adjustable gains to guarantee bounds on the vibration amplitude. For scalar systems, the weighting for control is switched between two values which give a low-gain control when the amplitude is inside the bound and a high-gain control when the amplitude is going to violate the given bound. For multivariable systems, by assuming a matching condition, a similar controller structure has been obtained. This controller is favored for application since the main structure of a common LQR is not changed; the additional high-gain control is required only if the vibration amplitude fails to stay inside the bound. We have applied this controller to a five-story building with active tendon controllers. The results show that the largest oscillation at the first story stays within a given bound when the building is subject to earthquake excitation.
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12

Khlebnikov, M. V., and P. S. Shcherbakov. "Optimal feedback design under bounded control." Automation and Remote Control 75, no. 2 (2014): 320–32. http://dx.doi.org/10.1134/s0005117914020118.

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13

Dimentberg, M. F., and A. S. Bratus'. "Bounded parametric control of random vibrations." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 456, no. 2002 (2000): 2351–63. http://dx.doi.org/10.1098/rspa.2000.0615.

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14

Min, Sun. "Singular control problems in bounded intervals." Stochastics 21, no. 4 (1987): 303–44. http://dx.doi.org/10.1080/17442508708833462.

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15

Carlsson, Gunnar, and Boris Goldfarb. "Bounded G-theory with fibred control." Journal of Pure and Applied Algebra 223, no. 12 (2019): 5360–95. http://dx.doi.org/10.1016/j.jpaa.2019.04.003.

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16

EVANS, M. E. "Bounded control and discrete-time controllability†." International Journal of Systems Science 17, no. 6 (1986): 943–51. http://dx.doi.org/10.1080/00207728608926859.

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17

Soldatos, A. G., and M. Corless. "Stabilizing uncertain systems with bounded control." Dynamics and Control 1, no. 3 (1991): 227–38. http://dx.doi.org/10.1007/bf02169679.

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18

Chen, Yun, Anke Xue, Renquan Lu, Shaosheng Zhou, and Hongbo Zou. "Passive Control for Bilinear Stochastic Systems with Bounded Control." IFAC Proceedings Volumes 47, no. 3 (2014): 11183–88. http://dx.doi.org/10.3182/20140824-6-za-1003.01861.

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19

Balaguer, P. "Similar model reference adaptive control with bounded control effort." International Journal of Adaptive Control and Signal Processing 25, no. 7 (2011): 577–92. http://dx.doi.org/10.1002/acs.1222.

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20

Hokayem, Peter, Eugenio Cinquemani, Debasish Chatterjee, Federico Ramponi, and John Lygeros. "Stochastic receding horizon control with output feedback and bounded controls." Automatica 48, no. 1 (2012): 77–88. http://dx.doi.org/10.1016/j.automatica.2011.09.048.

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21

López-Araujo, Daniela, Antonio Loría, and Arturo Zavala-Río. "Adaptive tracking control of Euler-Lagrange systems with bounded controls." International Journal of Adaptive Control and Signal Processing 31, no. 3 (2016): 299–313. http://dx.doi.org/10.1002/acs.2697.

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22

Arunsawatwon, Suchin, and Tadchanon Chuman. "Stability of Control Systems with Multiple Sector-Bounded Nonlinearities for Inputs Having Bounded Magnitude and Bounded Slope." Engineering Journal 27, no. 5 (2023): 69–81. http://dx.doi.org/10.4186/ej.2023.27.5.69.

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23

Tsypkin, Ya Z. "Robust Internal Model Control." Journal of Dynamic Systems, Measurement, and Control 115, no. 2B (1993): 419–25. http://dx.doi.org/10.1115/1.2899082.

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This paper discusses the method of control systems design for dynamic plants under bounded uncertainty. The structure of these systems coincides with the structure of systems with an internal model. But the choice of an internal model and a controller depends on the demand of the bounded decrease of system sensitivity to the change of plant characteristics and external action and on the demand of modal control. The absorption principle is used for the synthesis of a controller of such robust modal control systems. The realization conditions of robust systems of modal control are stated.
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24

Motta, Monica, and Caterina Sartori. "Minimum Time with Bounded Energy, Minimum Energy with Bounded Time." SIAM Journal on Control and Optimization 42, no. 3 (2003): 789–809. http://dx.doi.org/10.1137/s0363012902385284.

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25

Rincon, Alejandro, and Fabiola Angulo. "Adaptive Control for Nonlinear Systems with Time-Varying Control Gain." Journal of Control Science and Engineering 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/269346.

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We propose a scheme for nonlinear plants with time-varying control gain and time-varying plant coefficients, on the basis of a plant model consisting of a Brunovsky-type model with polynomials as approximators. We develop an adaptive robust control scheme for this plant, under the following assumptions: (i) the plant terms involve time-varying but bounded coefficients, being its upper bound unknown; (ii) the control gain is unknown, not necessarily bounded, and only its signum is known. To achieve robustness, we use a combination of robustifying control inputs and dead zone-type update laws. We apply this methodology to the speed control of a permanent magnet synchronous motor (PMSM), and we achieve proper tracking results.
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26

Baranovskii, Evgenii S., and Mikhail A. Artemov. "Existence of Optimal Control for a Nonlinear-Viscous Fluid Model." International Journal of Differential Equations 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/9428128.

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We consider the optimal control problem for a mathematical model describing steady flows of a nonlinear-viscous incompressible fluid in a bounded three-dimensional (or a two-dimensional) domain with impermeable solid walls. The control parameter is the surface force at a given part of the flow domain boundary. For a given bounded set of admissible controls, we construct generalized (weak) solutions that minimize a given cost functional.
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27

Wang, Yougang, Jing Zhang, and Huaiqin Wu. "Distributed Adaptive Mittag–Leffler Formation Control for Second-Order Fractional Multi-Agent Systems via Event-Triggered Control Strategy." Fractal and Fractional 6, no. 7 (2022): 380. http://dx.doi.org/10.3390/fractalfract6070380.

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This brief investigates the Mittag–Leffler formation bounded control problem for second-order fractional multi-agent systems (FMASs), where the dynamical nodes of followers are modeled to satisfy quadratic (QUAD) condition. Firstly, under the undirected communication topology, for the considered second-order nonlinear FMASs, a distributed event-triggered control scheme (ETCS) is designed to realize the global Mittag–Leffler bounded formation control goal. Secondly, by introducing adaptive weights into triggering condition and control protocol, an adaptive event-triggered formation protocol is presented to achieve the global Mittag–Leffler bounded formation. Thirdly, a five-step algorithm is provided to describe protocol execution steps. Finally, two simulation examples are given to verify the effectiveness of the proposed schemes.
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28

Xu, Jin, and Ye Guo Sun. "Finite-Time Control of Networked Control Systems with Bounded Packet Dropout." Advanced Materials Research 629 (December 2012): 840–44. http://dx.doi.org/10.4028/www.scientific.net/amr.629.840.

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In this paper, the finite-time boundedness and stabilization problems of a class of networked control systems (NCSs) with bounded packet dropout are investigated. The main results provided in the paper are sufficient conditions for finite-time boundedness and stability via state feedback. An iterative approach is proposed to model NCSs with bounded packet dropout as jump liner systems (JLSs). Based on Lyapunov stability theory and JLSs theory, the sufficient conditions for finite-time boundedness and stabilization of the underlying systems are derived via liner matrix inequalities (LMIs) formulation. Moreover, both sensor-to-controller and controller-to-actuator packet dropouts are considered simultaneously. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.
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29

Gurko, Alexander G., and Igor F. Eryemenko. "Control of Discrete System under Bounded Disturbances." Journal of Automation and Information Sciences 43, no. 11 (2011): 18–29. http://dx.doi.org/10.1615/jautomatinfscien.v43.i11.30.

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30

Hernandez-Mejia, Gustavo, Xin Du, Alma Y. Alanis, and Esteban A. Hernandez-Vargas. "Bounded input impulsive control for scheduling therapies." Journal of Process Control 102 (June 2021): 34–43. http://dx.doi.org/10.1016/j.jprocont.2021.03.003.

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31

Van Vu, Dung, Minh Hoang Trinh, Phuoc Doan Nguyen, and Hyo-Sung Ahn. "Distance-Based Formation Control With Bounded Disturbances." IEEE Control Systems Letters 5, no. 2 (2021): 451–56. http://dx.doi.org/10.1109/lcsys.2020.3003418.

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32

Hovd, Morten. "FEASIBLE MODEL PREDICTIVE CONTROL WITH BOUNDED DISTURBANCES." IFAC Proceedings Volumes 39, no. 2 (2006): 117–22. http://dx.doi.org/10.3182/20060402-4-br-2902.00117.

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33

Shoureshi, R., M. J. Corless, and M. D. Roesler. "Control of Industrial Manipulators With Bounded Uncertainties." Journal of Dynamic Systems, Measurement, and Control 109, no. 1 (1987): 53–59. http://dx.doi.org/10.1115/1.3143820.

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Present on-line control schemes for robotic manipulators require high computing power to perform real-time estimation and adaptation and/or an exact model of the manipulator. These requirements result in impractical control schemes for real industrial manipulators. This paper presents a new robust tracking control technique for industrial manipulators in the presence of various uncertainties. It does not require an exact model of the manipulator and it compensates for uncertainties in the system dynamics, such as friction, and uncertain inputs including load variations. The controller consists of two portions: one for the nominal part of the system, and the other portion for uncertainties compensation. This control scheme is simulated for a General Electric P50 robot and the results are presented.
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34

Prieur, Christophe, Sophie Tarbouriech, and Joao M. Gomes da Silva. "Wave Equation With Cone-Bounded Control Laws." IEEE Transactions on Automatic Control 61, no. 11 (2016): 3452–63. http://dx.doi.org/10.1109/tac.2016.2519759.

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35

Yang, Jung-Min. "Fault-Tolerant Corrective Control With Bounded Delays." IEEE Transactions on Automatic Control 62, no. 4 (2017): 1992–98. http://dx.doi.org/10.1109/tac.2016.2584788.

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36

Sayed, A. H., V. H. Nascimento, and S. Chandrasekaran. "Estimation and control with bounded data uncertainties." Linear Algebra and its Applications 284, no. 1-3 (1998): 259–306. http://dx.doi.org/10.1016/s0024-3795(98)10129-5.

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37

Bolonkin, A. A., and N. S. Khot. "Optimal bounded control design for vibration suppression." Acta Astronautica 38, no. 10 (1996): 803–13. http://dx.doi.org/10.1016/s0094-5765(96)00079-3.

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38

Tsiotras, Panagiotis, and Jihao Luo. "Control of underactuated spacecraft with bounded inputs." Automatica 36, no. 8 (2000): 1153–69. http://dx.doi.org/10.1016/s0005-1098(00)00025-x.

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39

Huang, Shoudong, M. R. James, and Z. P. Jiang. "-bounded robust control of nonlinear cascade systems." Systems & Control Letters 54, no. 3 (2005): 215–24. http://dx.doi.org/10.1016/j.sysconle.2004.08.008.

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40

Wu, Wei. "Nonlinear Bounded Control of a Nonisothermal CSTR." Industrial & Engineering Chemistry Research 39, no. 10 (2000): 3789–98. http://dx.doi.org/10.1021/ie990186e.

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41

Ntumy, Emmanuel A., and Sergey V. Utyuzhnikov. "Active sound control in 3D bounded regions." Wave Motion 51, no. 2 (2014): 284–95. http://dx.doi.org/10.1016/j.wavemoti.2013.08.004.

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42

Karatzas, Ioannis, and Daniel Ocone. "A leavable bounded-velocity stochastic control problem." Stochastic Processes and their Applications 99, no. 1 (2002): 31–51. http://dx.doi.org/10.1016/s0304-4149(01)00157-0.

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43

Koike, Shigeaki, and Hiroaki Morimoto. "Variational Inequalities for Leavable Bounded-Velocity Control." Applied Mathematics and Optimization 48, no. 1 (2003): 1–20. http://dx.doi.org/10.1007/s00245-003-0763-9.

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44

Medhin, N. G. "Bounded state problem for hereditary control problems." Journal of Optimization Theory and Applications 79, no. 1 (1993): 87–103. http://dx.doi.org/10.1007/bf00941888.

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45

Iourtchenko, D. V., J. L. Menaldi, and A. S. Bratus. "On the LQG theory with bounded control." Nonlinear Differential Equations and Applications NoDEA 17, no. 5 (2010): 527–34. http://dx.doi.org/10.1007/s00030-010-0066-1.

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46

Ying, Z. G., Y. Q. Ni, and J. M. Ko. "A bounded stochastic optimal semi-active control." Journal of Sound and Vibration 304, no. 3-5 (2007): 948–56. http://dx.doi.org/10.1016/j.jsv.2007.03.003.

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47

Lozano-Leal, R., and J. Collado. "Adaptive control for systems with bounded disturbances." IEEE Transactions on Automatic Control 34, no. 2 (1989): 225–28. http://dx.doi.org/10.1109/9.21107.

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48

INDRAWAN, B., T. KOBORI, M. SAKAMOTO, N. KOSHIKA, and S. OHRUI. "EXPERIMENTAL VERIFICATION OF BOUNDED-FORCE CONTROL METHOD." Earthquake Engineering & Structural Dynamics 25, no. 2 (1996): 179–93. http://dx.doi.org/10.1002/(sici)1096-9845(199602)25:2<179::aid-eqe545>3.0.co;2-n.

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49

Slotine, Jean-Jacques E., and Mark W. Spong. "Robust robot control with bounded input torques." Journal of Robotic Systems 2, no. 4 (1985): 329–52. http://dx.doi.org/10.1002/rob.4620020402.

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50

Conrado, Giovanna Kobus, Amir Kafshdar Goharshady, and Chun Kit Lam. "The Bounded Pathwidth of Control-Flow Graphs." Proceedings of the ACM on Programming Languages 7, OOPSLA2 (2023): 292–317. http://dx.doi.org/10.1145/3622807.

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Pathwidth and treewidth are standard and well-studied graph sparsity parameters which intuitively model the degree to which a given graph resembles a path or a tree, respectively. It is well-known that the control-flow graphs of structured goto-free programs have a tree-like shape and bounded treewidth. This fact has been exploited to design considerably more efficient algorithms for a wide variety of static analysis and compiler optimization problems, such as register allocation, µ-calculus model-checking and parity games, data-flow analysis, cache management, and liftetime-optimal redundancy elimination. However, there is no bound in the literature for the pathwidth of programs, except the general inequality that the pathwidth of a graph is at most O (lg n ) times its treewidth, where n is the number of vertices of the graph. In this work, we prove that control-flow graphs of structured programs have bounded pathwidth and provide a linear-time algorithm to obtain a path decomposition of small width. Specifically, we establish a bound of 2 · d on the pathwidth of programs with nesting depth d . Since real-world programs have small nesting depth, they also have bounded pathwidth. This is significant for a number of reasons: (i) ‍pathwidth is a strictly stronger parameter than treewidth, i.e. ‍any graph family with bounded pathwidth has bounded treewidth, but the converse does not hold; (ii) ‍any algorithm that is designed with treewidth in mind can be applied to bounded-pathwidth graphs with no change; (iii) ‍there are problems that are fixed-parameter tractable with respect to pathwidth but not treewidth; (iv) ‍verification algorithms that are designed based on treewidth would become significantly faster when using pathwidth as the parameter; and (v) ‍it is easier to design algorithms based on bounded pathwidth since one does not have to consider the often-challenging case of merge nodes in treewidth-based dynamic programming. Thus, we invite the static analysis and compiler optimization communities to adopt pathwidth as their parameter of choice instead of, or in addition to, treewidth. Intuitively, control-flow graphs are not only tree-like, but also path-like and one can obtain simpler and more scalable algorithms by relying on path-likeness instead of tree-likeness. As a motivating example, we provide a simpler and more efficient algorithm for spill-free register allocation using bounded pathwidth instead of treewidth. Our algorithm reduces the runtime from O ( n · r 2 · tw · r + 2 · r ) to O ( n · pw · r pw · r + r + 1 ), where n is the number of lines of code, r is the number of registers, pw is the pathwidth of the control-flow graph and tw is its treewidth. We provide extensive experimental results showing that our approach is applicable to a wide variety of real-world embedded benchmarks from SDCC and obtains runtime improvements of 2-3 orders of magnitude. This is because the pathwidth is equal to the treewidth, or one more, in the overwhelming majority of real-world CFGs and thus our algorithm provides an exponential runtime improvement. As such, the benefits of using pathwidth are not limited to the theoretical side and simplicity in algorithm design, but are also apparent in practice.
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