Related papers: Controlling Canard Cycles
We show that there exist generic slow-fast systems with only one (time-scaling) parameter on the two-torus, which have canard cycles for arbitrary small values of this parameter. This is in drastic contrast with the planar case, where…
This paper studies the emulation-based stabilization of nonlinear networked control systems with two time scales. We address the challenge of using a single communication channel for transmitting both fast and slow variables between the…
We investigate the stability of the synchronization manifold in a ring and an open-ended chain of nearest neighbors coupled self-sustained systems, each self-sustained system consisting of multi-limit cycles van der Pol oscillators. Such…
We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the…
In this paper we propose an algorithm for stabilizing circular formations of fixed-wing UAVs with constant speeds. The algorithm is based on the idea of tracking circles with different radii in order to control the inter-vehicle phases with…
The aim of this work is to propose an alternative method for determining the condition of existence of "canard solutions" for three and four-dimensional singularly perturbed systems with only one fast variable in the folded saddle case.…
This work studies the stabilization for a periodic parabolic system under perturbations in the system conductivity. A perturbed system does not have any periodic solution in general. However, we will prove that the perturbed system can…
We consider application of the multiple time delayed feedback for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, the multiple one exhibits resonances between feedback and…
In this paper, we present a novel cascade control structure with formal guarantees of uniform almost global asymptotic stability for the state tracking error dynamics of a quadcopter. The proposed approach features a model predictive…
We present a simpler proof of the existence of an exact number of one or more limit cycles to the Lienard system $\dot{x}=y-F(x) $, $\dot {y}=-g(xt)$, under weaker conditions on the odd functions $F(x) $ and $g(x) $ as compared to those…
Model Predictive Control (MPC) is a widely known control method that has proved to be particularly effective in multivariable and constrained control. Closed-loop stability and recursive feasibility can be guaranteed by employing accurate…
We develop a predictor-feedback control design for multi-input nonlinear systems with distinct input delays, of arbitrary length, in each individual input channel. Due to the fact that different input signals reach the plant at different…
Analysis of the PPF chaos control method used in biological experiments shows that it can robustly control a wider class of systems than previously believed, including those without stable manifolds. This can be exploited to find the…
Van der Pol oscillators are prototypical self-sustaining oscillators which have been used to model nonlinear processes in biological and other classical processes. In this work, we investigate how quantum fluctuations affect phase-locking…
We study the implementation of a weak multiple delayed feedback for controlling coherence of chaotic oscillations. The specific system we treat is the Lorenz system with classical set of parameters. There are two reasons behind the interest…
Incorporating force bounds is crucial for realistic control implementations in physical systems. Here, we investigate the fastest possible synchronisation of a Li\'enard system to its limit cycle using a bounded external force. To tackle…
This article presents an adaptive nonlinear delayed feedback control scheme for stabilizing the unstable periodic orbit of unknown fractional-order chaotic systems. The proposed control framework uses the Lyapunov approach and sliding mode…
Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…
An exact and analytic control protocol of two types of finite dimensional quantum systems is proposed. The system can be drive to an arbitrary target state using cosine classical fields in finite cycles. The control parameters which are…
The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to…