Spectral theory for the failure of linear control in a nonlinear stochastic system [PDF]
Physical Review E, 2002 We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur in systems described by linearly stable but strongly nonnormal evolution operators. In spatially extended systems
Roman O. Grigoriev, Andreas Handel
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Discussion: “A Résumé of the Development and Literature of Nonlinear Control-System Theory” (Higgins, T. J., 1957, Trans. ASME, 79, pp. 445–449) [PDF]
, 1957 James D. Horgan
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Nonlinear control theory and chaotic dynamical systems [PDF]
Proceedings of the IEEE 1991 National Aerospace and Electronics Conference NAECON 1991, 2002 The author treats the role of multiparameters in the existence of solutions of highly coupled nonlinear dynamical systems and numerical computation of solutions. An attempt is made to develop methods applicable to control of highly coupled nonlinear dynamical systems containing multiparameters which may have a chaotic behavior.
Julian R. Jones
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Control theory for nonlinear fractional dispersive systems
, 2022 We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical theorems in the fractional setting (representation of the solution through the Gramian type matrix, Kalman's principle,
Jolić, Maja +2 more
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Switching control for incremental stabilization of nonlinear systems via contraction theory [PDF]
2016 European Control Conference (ECC), 2016 In this paper we present a switching control strategy to incrementally stabilize a class of nonlinear dynamical systems. Exploiting recent results on contraction analysis of switched Filippov systems derived using regularization, sufficient conditions are presented to prove incremental stability of the closed-loop system.
Di Bernardo M., Fiore D.
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Linear Theory for Control of Nonlinear Stochastic Systems [PDF]
Physical Review Letters, 2005 We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of non-linear control problems that can be formulated as a path integral and where the noise plays the role of temperature.
Hilbert J. Kappen
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A bang-bang optimal control for a nonlinear system modeling the Gate Control Theory of Pain [PDF]
Discrete and Continuous Dynamical Systems - S12 ...
Diaz, Gregorio, Diaz, Jesus Ildefonso
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Guarantees for data-driven control of nonlinear systems using semidefinite programming: A survey [PDF]
Annual Reviews in Control, 2023 This survey presents recent research on determining control-theoretic properties and designing controllers with rigorous guarantees and for nonlinear systems for which no mathematical models but measured trajectories are available.
Tim Martin +2 more
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A general theory of nonlinear estimation problems in control systems
Journal of Mathematical Analysis and Applications, 1964 A. V. Balakrishnan
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Mathematical Theories and Applications for Nonlinear Control Systems
Mathematical Problems in Engineering, 2019 Xue-Jun Xie +3 more
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