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Journal articles on the topic 'Nonlinear optimal control'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 March 2023

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1

Goncharenko, Borys, Larysa Vikhrova, and Mariia Miroshnichenko. "Optimal control of nonlinear stationary systems at infinite control time." Central Ukrainian Scientific Bulletin. Technical Sciences, no. 4(35) (2021): 88–93. http://dx.doi.org/10.32515/2664-262x.2021.4(35).88-93.

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The article presents a solution to the problem of control synthesis for dynamical systems described by linear differential equations that function in accordance with the integral-quadratic quality criterion under uncertainty. External perturbations, errors and initial conditions belong to a certain set of uncertainties. Therefore, the problem of finding the optimal control in the form of feedback on the output of the object is presented in the form of a minimum problem of optimal control under uncertainty. The problem of finding the optimal control and initial state, which maximizes the quality criterion, is considered in the framework of the optimization problem, which is solved by the method of Lagrange multipliers after the introduction of the auxiliary scalar function - Hamiltonian. The case of a stationary system on an infinite period of time is considered. The formulas that can be used for calculations are given for the first and second variations. It is proposed to solve the problem of control search in two stages: search of intermediate solution at fixed values of control and error vectors and subsequent search of final optimal control. The solution of -optimal control for infinite time taking into account the signal from the compensator output is also considered, as well as the solution of the corresponding matrix algebraic equations of Ricatti type.

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2

Fernández de la Vega, Constanza S., Richard Moore, Mariana Inés Prieto, and Diego Rial. "Optimal control problem for nonlinear optical communications systems." Journal of Differential Equations 346 (February 2023): 347–75. http://dx.doi.org/10.1016/j.jde.2022.11.050.

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3

Hassanzadeh, Iraj, Ghasem Alizadeh, Naser Pourqorban Shirjoposht, and Farzad Hashemzadeh. "A New Optimal Nonlinear Approach to Half Car Active Suspension Control." International Journal of Engineering and Technology 2, no. 1 (2010): 78–84. http://dx.doi.org/10.7763/ijet.2010.v2.104.

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4

Yang, J. N., F. X. Long, and D. Wong. "Optimal Control of Nonlinear Structures." Journal of Applied Mechanics 55, no. 4 (December 1, 1988): 931–38. http://dx.doi.org/10.1115/1.3173744.

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Three optimal control algorithms are proposed for reducing oscillations of flexible nonlinear structures subjected to general stochastic dynamic loads, such as earthquakes, waves, winds, etc. The optimal control forces are determined analytically by minimizing a time-dependent quadratic performance index, and nonlinear equations of motion are solved using the Wilson-θ numerical procedures. The optimal control algorithms developed for applications to nonlinear structures are referred to as the instantaneous optimal control algorithms, including the instantaneous optimal open-loop control algorithm, instantaneous optimal closed-loop control algorithm, and instantaneous optimal closed-open-loop control algorithm. These optimal algorithms are computationally efficient and suitable for on-line implementation of active control systems to realistic nonlinear structures. Numerical examples are worked out to demonstrate the applications of these optimal control algorithms to nonlinear structures. In particular, control of structures undergoing inelastic deformations under strong earthquake excitations are illustrated. The advantage of using combined passive/active control systems is also demonstrated.

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5

Akyurek, Alper Sinan, and Tajana Simunic Rosing. "Optimal Distributed Nonlinear Battery Control." IEEE Journal of Emerging and Selected Topics in Power Electronics 5, no. 3 (September 2017): 1045–54. http://dx.doi.org/10.1109/jestpe.2016.2645480.

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6

Kaczorek, Tadeusz. "Nonlinear and optimal control systems." Control Engineering Practice 5, no. 12 (December 1997): 1781. http://dx.doi.org/10.1016/s0967-0661(97)87397-2.

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7

Lu, Q., Y. Sun, Z. Xu, and T. Mochizuki. "Decentralized nonlinear optimal excitation control." IEEE Transactions on Power Systems 11, no. 4 (1996): 1957–62. http://dx.doi.org/10.1109/59.544670.

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8

Hualin Tan and W. J. Rugh. "Pseudolinearization and nonlinear optimal control." IEEE Transactions on Automatic Control 43, no. 3 (March 1998): 386–91. http://dx.doi.org/10.1109/9.661596.

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9

Loxton, Ryan, Qun Lin, and Kok Lay Teo. "Minimizing control variation in nonlinear optimal control." Automatica 49, no. 9 (September 2013): 2652–64. http://dx.doi.org/10.1016/j.automatica.2013.05.027.

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10

Lovíšek, Ján. "Singular perturbations in optimal control problem with application to nonlinear structural analysis." Applications of Mathematics 41, no. 4 (1996): 299–320. http://dx.doi.org/10.21136/am.1996.134328.

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11

Esteve-Yagüe, Carlos, Borjan Geshkovski, Dario Pighin, and Enrique Zuazua. "Turnpike in Lipschitz—nonlinear optimal control." Nonlinearity 35, no. 4 (February 17, 2022): 1652–701. http://dx.doi.org/10.1088/1361-6544/ac4e61.

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Abstract We present a new proof of the turnpike property for nonlinear optimal control problems, when the running target is a steady control-state pair of the underlying system. Our strategy combines the construction of quasi-turnpike controls via controllability, and a bootstrap argument, and does not rely on analyzing the optimality system or linearization techniques. This in turn allows us to address several optimal control problems for finite-dimensional, control-affine systems with globally Lipschitz (possibly nonsmooth) nonlinearities, without any smallness conditions on the initial data or the running target. These results are motivated by applications in machine learning through deep residual neural networks, which may be fit within our setting. We show that our methodology is applicable to controlled PDEs as well, such as the semilinear wave and heat equation with a globally Lipschitz nonlinearity, once again without any smallness assumptions.

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12

Bily, Barbara. "Optimal control for 2-D nonlinear control systems." Applicationes Mathematicae 29, no. 2 (2002): 239–49. http://dx.doi.org/10.4064/am29-2-8.

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13

Sokolov, Sergey V. "Optimal Control Using Nonlinear Probabilistic Tests." Journal of Automation and Information Sciences 30, no. 4-5 (1998): 42–50. http://dx.doi.org/10.1615/jautomatinfscien.v30.i4-5.50.

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14

çimen, Tayfun. "APPROXIMATE NONLINEAR OPTIMAL SDRE TRACKING CONTROL." IFAC Proceedings Volumes 40, no. 7 (2007): 147–52. http://dx.doi.org/10.3182/20070625-5-fr-2916.00026.

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15

Papageorgiou, Nikolaos S., and Nikolaos Yannakakis. "Optimal control of nonlinear evolution equations." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 21, no. 1 (2001): 5. http://dx.doi.org/10.7151/dmdico.1016.

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16

Vinter, Richard. "Convex Duality and Nonlinear Optimal Control." SIAM Journal on Control and Optimization 31, no. 2 (March 1993): 518–38. http://dx.doi.org/10.1137/0331024.

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17

Luus, Rein. "Parametrization in nonlinear optimal control problems." Optimization 55, no. 1-2 (February 2006): 65–89. http://dx.doi.org/10.1080/02331930500530120.

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18

Tiğrek, Tûba, Soura Dasgupta, and Theodore F. Smith. "NONLINEAR OPTIMAL CONTROL OF HVAC SYSTEMS." IFAC Proceedings Volumes 35, no. 1 (2002): 149–54. http://dx.doi.org/10.3182/20020721-6-es-1901.01578.

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19

Long, C. E., P. K. Polisetty, and E. P. Gatzke. "Globally Optimal Nonlinear Model Predictive Control." IFAC Proceedings Volumes 37, no. 9 (July 2004): 83–88. http://dx.doi.org/10.1016/s1474-6670(17)31798-6.

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20

Reber, Douglas C. "Optimal control of nonlinear hereditary systems." Journal of Differential Equations 68, no. 1 (June 1987): 22–35. http://dx.doi.org/10.1016/0022-0396(87)90184-7.

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21

Hager, William W. "Multiplier Methods for Nonlinear Optimal Control." SIAM Journal on Numerical Analysis 27, no. 4 (August 1990): 1061–80. http://dx.doi.org/10.1137/0727063.

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22

Beneš, Václav E. "Nonlinear filtering and optimal quality control." Journal of Applied Mathematics and Stochastic Analysis 11, no. 3 (January 1, 1998): 225–30. http://dx.doi.org/10.1155/s1048953398000197.

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Some stochastic models of optimal decision processes in quality control problems are formulated, analyzed, and solved. It is assumed that costs, positive or negative, are assigned to various events in a simple manufacturing model, such as processing an item, producing a saleable item, discarding an item for salvage, selling a lemon, etc. and models are described by giving a sequence of events, some of which are decisions to process, to abandon, to accept, to restart, …. All the models have the rather unrealistic classical information pattern of cumulative data. The object is then to find optimal procedures for minimizing the total cost incurred, first in dealing with a single item, and second, in operating until an item first passes all the tests. The policies that appear as optimal depend on such matters as whether a conditional probability given certain data exceeds a ratio of prices, and on more complex functionals of the conditional expectations in the problem. Special sufficient classes of policies are discerned, which reduce the decision problem to finding one number.

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23

L'Afflitto, Andrea, and Wassim M. Haddad. "Optimal singular control for nonlinear semistabilisation." International Journal of Control 89, no. 6 (January 22, 2016): 1222–39. http://dx.doi.org/10.1080/00207179.2015.1126356.

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24

Papageorgiou, N. S. "Optimal control of nonlinear evolution inclusions." Journal of Optimization Theory and Applications 67, no. 2 (November 1990): 321–54. http://dx.doi.org/10.1007/bf00940479.

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25

Trigub, M. V. "Optimal control over nonlinear stochastic systems." Ukrainian Mathematical Journal 51, no. 4 (April 1999): 592–603. http://dx.doi.org/10.1007/bf02591761.

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26

Stolz, Claude. "Optimal control approach in nonlinear mechanics." Comptes Rendus Mécanique 336, no. 1-2 (January 2008): 238–44. http://dx.doi.org/10.1016/j.crme.2007.11.015.

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27

Papageorgiou, Nikolaos S. "Optimal control of nonlinear evolution equations." Publicationes Mathematicae Debrecen 41, no. 1-2 (January 1, 1992): 41–51. http://dx.doi.org/10.5486/pmd.1992.1148.

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28

Murray, J. M. "Simple nonlinear dual control problems." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 27, no. 2 (October 1985): 131–44. http://dx.doi.org/10.1017/s0334270000004835.

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AbstractIn this paper we consider a simple, nonlinear optimal control problem with sufficient convexity to enable us to formulate its dual problem. Both primal and dual problems will include constraints on both the states and controls. The constraints in one problem may cause the “optimal” dual states to be discontinuous. However, we will look at conditions under which the presence of constraints does not force discontinuities and the optimal states and costates are absolutely continuous.

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29

Haddad, Wassim M., Vijaya-Sekhar Chellaboina, and Jerry L. Fausz. "Optimal nonlinear disturbance rejection control for nonlinear cascade systems." International Journal of Control 68, no. 5 (January 1997): 997–1018. http://dx.doi.org/10.1080/002071797223172.

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30

Orivuori, Juha, and Kai Zenger. "1B23 Active control of vibrations in a rolling process by nonlinear optimal controller." Proceedings of the Symposium on the Motion and Vibration Control 2010 (2010): _1B23–1_—_1B23–15_. http://dx.doi.org/10.1299/jsmemovic.2010._1b23-1_.

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31

Zong, Xi Ju, Xin Gong Cheng, and Yong Zhang. "Sub-Optimal Control for Nonlinear Heat Equations." Applied Mechanics and Materials 217-219 (November 2012): 2488–91. http://dx.doi.org/10.4028/www.scientific.net/amm.217-219.2488.

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This paper presents a successive approximation approach (SAA) designing optimal controllers for a class of nonlinear heat equations with a quadratic performance index. By using the SAA, the optimal control problem for nonlinear heat equations is transformed into a sequence of nonhomogeneous linear differential Riccati operator equations. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoin vector sequence. By using the finite-step iteration of the nonlinear compensation sequence, we can obtain a suboptimal control law.

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32

Yildirim, Kenan, and Ismail Kucuk. "A nonlinear plate control without linearization." Open Mathematics 15, no. 1 (March 8, 2017): 179–86. http://dx.doi.org/10.1515/math-2017-0011.

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Abstract In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

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33

Young, G. E., and R. J. Chang. "Optimal Control of Stochastic Parametrically and Externally Excited Nonlinear Control Systems." Journal of Dynamic Systems, Measurement, and Control 110, no. 2 (June 1, 1988): 114–19. http://dx.doi.org/10.1115/1.3152660.

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A sub-optimal nonlinear controller which is synthesized by using the external linearization approach is applied to the optimal control of stochastic parametrically and externally excited nonlinear systems with complete state information. Algebraic necessary conditions are derived for the minimization of the quadratic cost function through the concepts of equivalent external excitation. The concepts and applications of the statistical linearization approach for the externally excited nonlinear systems are extended to the nonlinear systems subjected to both stochastic parametric and external excitations. Two examples which include a first-order nonlinear and a second-order Duffing type stochastic system are used to illustrate the performance of the present design. The applications of the statistical linearization approach to the optimal control of a stochastic parametrically and externally excited Duffing type system is illustrated and compared with the present approach by using Monte Carlo simulation.

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34

Yang, J. N., Z. Li, and S. Vongchavalitkul. "Generalization of Optimal Control Theory: Linear and Nonlinear Control." Journal of Engineering Mechanics 120, no. 2 (February 1994): 266–83. http://dx.doi.org/10.1061/(asce)0733-9399(1994)120:2(266).

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35

Chen, Wen-Hua, Donald J. Ballance, and Peter J. Gawthrop. "Optimal control of nonlinear systems: a predictive control approach." Automatica 39, no. 4 (April 2003): 633–41. http://dx.doi.org/10.1016/s0005-1098(02)00272-8.

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36

Chen, Wen-Hua, Donald J. Ballance, and Peter J. Gawthrop. "Nonlinear generalised predictive control and optimal dynamical inversion control." IFAC Proceedings Volumes 32, no. 2 (July 1999): 2540–45. http://dx.doi.org/10.1016/s1474-6670(17)56432-0.

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37

Liu, Can-Chang, Chuan-Bo Ren, Lu Liu, and Hai Yun. "Optimal Control of Nonlinear Resonances for Vehicle Suspension Using Linear and Nonlinear Control." Journal of Low Frequency Noise, Vibration and Active Control 32, no. 4 (December 2013): 335–45. http://dx.doi.org/10.1260/0263-0923.32.4.335.

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38

Chen, Xian Li, and Xin Tao Liu. "The Optimal Nonlinear PI Composed Control of Nonlinear Uncertain System." Applied Mechanics and Materials 668-669 (October 2014): 549–52. http://dx.doi.org/10.4028/www.scientific.net/amm.668-669.549.

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An improved cooperative method to control a nonlinear uncertain system is raised in this paper. First, the optimal control law is introduced to attain the desired dynamics of the linear part of original system. Then, a nonlinear PI controller is used to remove the influence of uncertain unit. It is proved by simulation that this method is effective to control this special system and is easy to be carried in applications.

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39

Badakhshan, K. P., and A. V. Kamyad. "Numerical solution of nonlinear optimal control problems using nonlinear programming." Applied Mathematics and Computation 187, no. 2 (April 2007): 1511–19. http://dx.doi.org/10.1016/j.amc.2006.09.074.

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40

Ju, Eun-Young, and Jin-Mun Jeong. "Optimal Control Problems for Nonlinear Variational Evolution Inequalities." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/724190.

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We deal with optimal control problems governed by semilinear parabolic type equations and in particular described by variational inequalities. We will also characterize the optimal controls by giving necessary conditions for optimality by proving the Gâteaux differentiability of solution mapping on control variables.

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41

Sjöberg, Johan, and Torkel Glad. "Rational Approximation of Nonlinear Optimal Control Problems." IFAC Proceedings Volumes 41, no. 2 (2008): 11340–45. http://dx.doi.org/10.3182/20080706-5-kr-1001.01921.

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42

Ruderman, Michael. "Convergent dynamics of optimal nonlinear damping control." IFAC-PapersOnLine 54, no. 17 (2021): 141–44. http://dx.doi.org/10.1016/j.ifacol.2021.11.039.

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43

Robinett, Rush D., Gordon G. Parker, Hanspeter Schaub, and John L. Junkins. "Lyapunov Optimal Saturated Control for Nonlinear Systems." Journal of Guidance, Control, and Dynamics 20, no. 6 (November 1997): 1083–88. http://dx.doi.org/10.2514/2.4189.

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44

Zhu, W. Q., Z. G. Ying, Y. Q. Ni, and J. M. Ko. "Optimal Nonlinear Stochastic Control of Hysteretic Systems." Journal of Engineering Mechanics 126, no. 10 (October 2000): 1027–32. http://dx.doi.org/10.1061/(asce)0733-9399(2000)126:10(1027).

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45

Albuquerque, Flavio G. de, and John W. Labadie. "Optimal Nonlinear Predictive Control for Canal Operations." Journal of Irrigation and Drainage Engineering 123, no. 1 (January 1997): 45–54. http://dx.doi.org/10.1061/(asce)0733-9437(1997)123:1(45).

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46

Jacewicz, E., and A. Nowakowski. "Stability of approximations in optimal nonlinear control." Optimization 34, no. 2 (January 1995): 173–84. http://dx.doi.org/10.1080/02331939508844103.

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47

Danbury, R. N. "Near time-optimal control of nonlinear servomechanisms." IEE Proceedings - Control Theory and Applications 141, no. 3 (May 1, 1994): 145–53. http://dx.doi.org/10.1049/ip-cta:19949970.

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48

Stojanovic, Srdjan. "Optimal Damping Control and Nonlinear Elliptic Systems." SIAM Journal on Control and Optimization 29, no. 3 (May 1991): 594–608. http://dx.doi.org/10.1137/0329033.

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49

Kaisare, Niket S., Jong Min Lee, and Jay H. Lee. "SIMULATION-BASED OPTIMIZATION FOR NONLINEAR OPTIMAL CONTROL." IFAC Proceedings Volumes 35, no. 1 (2002): 387–92. http://dx.doi.org/10.3182/20020721-6-es-1901.00633.

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50

Rigatos, G., N. Zervos, P. Siano, M. Abbaszadeh, P. Wira, and B. Onose. "Nonlinear optimal control for DC industrial microgrids." Cyber-Physical Systems 5, no. 4 (July 29, 2019): 231–53. http://dx.doi.org/10.1080/23335777.2019.1640796.

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