Related papers: Controlling Canard Cycles
Power systems with a high penetration of renewable generation are vulnerable to frequency oscillation and voltage instability. Traditionally, the stability of power systems is considered either in terms of local stability or as an angle…
The paper revisits recently revealed regimes of the "nonconventional synchronization" in systems of coupled bi-stable Van der Pol oscillators. These regimes are characterized by periodic (or quasiperiodic) almost complete energy exchanges…
We report on the application of chaos control to the irregular motion of an electron under the combined influence of a Coulomb and a magnetic field, the so-called ``diamagnetic Kepler problem'' (DKP). We show how to stabilize the classical…
Dynamical systems can be coupled in a manner that is designed to drive the resulting dynamics onto a specified lower dimensional submanifold in the phase space of the combined system. On the submanifold, the variables of the two systems…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
Limitations of the delayed feedback control and of its extended versions have been fully treated in the literature. The oscillating delayed feedback control appears as a promising scheme to overcome this problem. In this work, two methods…
Robust global stabilization of nonlinear systems by observer-based feedback controllers is a challenging task. This article investigates the problem of designing observer-based stabilizing controllers for incrementally quadratic nonlinear…
We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a…
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…
Motivated by the dynamics of neuronal responses, we analyze the dynamics of the Fitzhugh-Nagumo slow-fast system with delayed self-coupling. This system provides a canonical example of a canard explosion for sufficiently small delays.…
Asymptotic stability is with no doubts an essential property to be studied for any system. This analysis often becomes very difficult for coupled systems and even harder when different timescales appear. The singular perturbation method…
Model predictive control (MPC) has become the most widely used advanced control method in process industry. In many cases, forecasts of the disturbances are available, e.g., predicted renewable power generation based on weather forecast.…
In large-scale neural networks, coherent limit cycle oscillations usually coexist with unstable incoherent equilibrium states, which are not observed experimentally. We implement a first-order dynamic controller to stabilize unknown…
A control design approach is developed for a general class of uncertain strict-feedback-like nonlinear systems with dynamic uncertain input nonlinearities with time delays. The system structure considered in this paper includes a nominal…
Chemical oscillation is an interesting nonlinear dynamical phenomenon which arises due to complex stability condition of the steady state of a reaction far away from equilibrium which is usually characterised by a periodic attractor or a…
Closed-loop control of turbulent flows is a challenging problem with important practical and fundamental implications. We perform closed-loop control of forced, turbulent jets based on a wave-cancellation strategy. The study is motivated by…
One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent letter [Phys.~Rev.~Lett. 130, 020201…
Time-delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states. We present an application of extended time delay autosynchronization introduced by Socolar et al. to an unstable focus. This…
This paper presents a control methodology for achieving orbital stabilization with simultaneous time synchronization of periodic trajectories in underactuated robotic systems. The proposed approach extends the classical transverse…
Researchers have developed hybrid Van der Pol Rayleigh Duffing type oscillators to model human induced forces; however, their analytical framework has largely relied on the Lindstedt Poincare perturbation method, energy balance approaches,…