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For a class of $(N+1)$-dimensional systems of differential delay equations with a cyclic and monotone negative feedback structure, we construct a two-dimensional invariant manifold, on which phase curves spiral outward towards a bounding…
Terminal sliding mode (TSM) control algorithm and its non-singular refinement have been elaborated for two decades and belong, since then, to a broader class of the finite-time controllers, which are known to be robust against the matched…
The collective behavior of the ensembles of coupled nonlinear oscillator is one of the most interesting and important problems in modern nonlinear dynamics. In this paper, we study rotational dynamics, in particular space-time structures,…
The folded node is a singularity associated with loss of normal hyperbolicity in systems where mixtures of slow and fast timescales arise due to singular perturbations. Canards are special solutions that reveal a counteractive feature of…
Invariant-based inverse engineering is an elegant approach to quantum control with corresponding experimental implementations that perform tasks with applications in quantum information processing such as shuttling trapped ions. We build on…
We consider the rotational dynamics in an ensemble of globally coupled identical pendulums. This model is essentially a generalization of the standard Kuramoto model, which takes into account the inertia and the intrinsic nonlinearity of…
We introduce a new model to study the oscillations of opposite flows sharing a common bottleneck and moving on two Totally Asymmetric Simple Exclusion Process (TASEP) lanes. We provide a theoretical analysis of the phase diagram, valid when…
We demonstrate that chaos can be controlled using a multiplicative exponential feedback control. All three types of unstable orbits - unstable fixed points, limit cycles and chaotic trajectories can be stabilized using this control. The…
Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory…
Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. In this work, we consider a well investigated phase field model including contact line…
Almost sure asymptotic stabilization of a discrete-time switched stochastic system is investigated. Information on the active operation mode of the switched system is assumed to be available for control purposes only at random time…
We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…
We illustrate how the recent theory of Spectral Submanifolds (SSM) can capture global bifurcations and complex dynamics in mechanical systems even under delay and spatial discretization. Specifically, we build a parameter-dependent…
This paper is mainly concerned with the robustly stable adaptive control of single-input single-output impulse-free linear time-invariant singular dynamic systems of known order and unknown parameterizations subject to single external point…
The coherent control of scattering processes is considered, with electron impact dissociation of H$_2^+$ used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a…
The objective of this note is to share some reflections of the authors regarding the use of sliding mode designs in control systems. We believe the abundant, and ever increasing, appearance of this kind of works on our scientific…
Artificial time delay controller was conceptualised for nonlinear systems to reduce dependency on precise system modelling unlike the conventional adaptive and robust control strategies. In this approach unknown dynamics is compensated by…
Model-free algorithms are brought into the control system's research with the emergence of reinforcement learning algorithms. However, there are two practical challenges of reinforcement learning-based methods. First, learning by…
We study bifurcations associated with stability of the lowest stationary point (SP) of a damped parametrically forced pendulum by varying $\omega_0$ (the natural frequency of the pendulum) and $A$ (the amplitude of the external driving…
The concept of controlling non-linear systems is one the significant fields in scientific researches for the purpose of which intelligent approaches can provide desirable applicability. Fuzzy systems are systems with ambiguous definition…