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A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…
It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…
In this paper, we show that the dynamics of a wide variety of nonlinear systems such as engineering, physical, chemical, biological, and ecological systems, can be simulated or modeled by the dynamics of memristor circuits. It has the…
Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires…
Some biological systems operate at the critical point between stability and instability and this requires a fine-tuning of parameters. We bring together two examples from the literature that illustrate this: neural integration in the…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
The study of mechanistic interpretability aims to reverse-engineer a model to explain its behaviors. While recent studies have focused on the static mechanism of a certain behavior, the learning dynamics inside a model remain to be…
The presence of (partially) automated vehicles on the roads presents an opportunity to compensate the unstable behaviour of conventional vehicles. Vehicles subject to perturbations should (i) recover their equilibrium speed, (ii) react not…
Motion trajectory planning is one crucial aspect for automated vehicles, as it governs the own future behavior in a dynamically changing environment. A good utilization of a vehicle's characteristics requires the consideration of the…
Stochastic resonance holds much promise for the detection of weak signals in the presence of relatively loud noise. Following the discovery of nondynamical and of aperiodic stochastic resonance, it was recently shown that the phenomenon can…
Inferring control parameters in non-linear dynamical systems is an important task in analysing general dynamical behaviours, particularly in the presence of inherently deterministic chaos. Traditional approaches often rely on…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only…
An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers.…
In recent years, Neural Networks (NNs) have been employed to control nonlinear systems due to their potential capability in dealing with situations that might be difficult for conventional nonlinear control schemes. However, to the best of…
This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are…