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Keywords = stochastic antiresonance

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11 pages, 315 KB  
Article
Mixed Control Strategy for a Class of Sector-Bounded Nonlinear Systems
by Adrian-Mihail Stoica and Isaac Yaesh
Entropy 2025, 27(3), 261; https://doi.org/10.3390/e27030261 - 1 Mar 2025
Cited by 1 | Viewed by 1189
Abstract
Here, mixed-strategy-based control of systems with sector-bounded nonlinearities is considered. The suggested control strategy applies a stochastic state feedback, where the control gain includes a white noise component in addition to the deterministic part. While each of the control signal components can sometimes [...] Read more.
Here, mixed-strategy-based control of systems with sector-bounded nonlinearities is considered. The suggested control strategy applies a stochastic state feedback, where the control gain includes a white noise component in addition to the deterministic part. While each of the control signal components can sometimes accomplish the control task independently, the combination may have some merits. This is especially true when both the mean value and the variance of the control signal need to be quantified separately. Systems that apply deterministic state-feedback control are abundant, whereas the application of state-multiplicative noise as a mean of control is more limited. Nevertheless, Stochastic Anti Resonance (SAR) with state-multiplicative noise based control, are encountered in diverse engineering applications, physics modelling, and biological models, such as visual-motor tasks. Matrix Inequalities conditions are derived, for weighted L2-gain using a mixed strategy control along with exponential LP-stability of the closed-loop. A numerical example is given, where the merit of mixed control strategy comparing to deterministic control is demonstrated. Full article
(This article belongs to the Section Statistical Physics)
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12 pages, 829 KB  
Article
Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities
by Adrian-Mihail Stoica and Isaac Yaesh
Entropy 2024, 26(2), 115; https://doi.org/10.3390/e26020115 - 26 Jan 2024
Cited by 5 | Viewed by 1874
Abstract
The paradigm of stochastic antiresonance is considered for a class of nonlinear systems with sector bounded nonlinearities. Such systems arise in a variety of situations such as in engineering applications, in physics, in biology, and in systems with more general nonlinearities, approximated by [...] Read more.
The paradigm of stochastic antiresonance is considered for a class of nonlinear systems with sector bounded nonlinearities. Such systems arise in a variety of situations such as in engineering applications, in physics, in biology, and in systems with more general nonlinearities, approximated by a wide neural network of a single hidden layer, such as the error equation of Hopfield networks with respect to equilibria or visuo-motor tasks. It is shown that driving such systems with a certain amount of state-multiplicative noise, one can stabilize noise-free unstable systems. Linear-Matrix-Inequality-based stabilization conditions are derived, utilizing a novel non-quadratic Lyapunov functional and a numerical example where state-multiplicative noise stabilizes a nonlinear system exhibiting chaotic behavior is demonstrated. Full article
(This article belongs to the Special Issue Information Theory in Control Systems, 2nd Edition)
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