Related papers: From chaos to order through mixing
Recently developed control methods with strong disturbance rejection capabilities provide a useful option for control design. The key lies in a general concept of disturbance and effective ways to estimate and compensate the disturbance.…
An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The…
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced…
We present an algorithm of control synthesis for nonlinear switched systems, based on an existing procedure of state-space bisection and made available for nonlinear systems with the help of validated simulation. The use of validated…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…
We consider stabilization and performance optimization of non-linear controlled systems, where the non-linearity satisfies a sector constraint asymptotically. This leads to optimization of the closed loop peak-to-peak system norm subject to…
We propose a simple method to estimate the parameters involved in discrete dynamical systems from time series. The method is based on the concept of controlling chaos by constant feedback. The major advantages of the method are that it…
The paper addresses the stabilization of nonlinear systems with semi-quadratic cost: quadratic with respect to controls and nonlinear for state variables. Paper presents the effective new feedback synthesis procedure. The novel feedback…
A simple method to perform chaos control without the need of complex numerical and analytical calculations is proposed. The method works for dynamical systems with bounded solutions and in the trivial case of constant Jacobians.
We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish…
This paper develops a robust safety-critical control method for nonlinear strictfeedback systems with mismatched disturbances. Using a state transformation and a linear time-varying disturbance observer, the system is converted into a form…
In the present work, we consider nonlinear control systems for which there exist structural obstacles to the design of classical continuous backstepping feedback laws. We conceive feedback laws such that the origin of the closed-loop system…
In this work we present a nonlinear adaptive suboptimal control strategy for uncertain nonlinear systems. Stochastic parametric uncertainty is dealt with by employing spectral decomposition of the random variables by means of the…
Control of chaotic systems to given targets is a subject of substantial and well-developed research issue in nonlinear science, which can be formulated as a class of multi-modal constrained numerical optimization problem with…
The study of chaos has long relied on computationally intensive methods to quantify unpredictability and design control strategies. Recent advances in machine learning, from convolutional neural networks to transformer architectures,…
This paper investigates the robust stabilisation of a class of fractional-order non-linear systems via fixed-order dynamic output feedback controller in terms of linear matrix inequalities (LMIs). The systematic stabilisation algorithm…
This paper presents an algorithm to apply nonlinear control design approaches in the case of stochastic systems with partial state observation. Deterministic nonlinear control approaches are formulated under the assumption of full state…
The stabilization of nonlinear systems under zero-state-detectability assumption or its analogues is considered. The proposed supervisory control provides a finite time practical stabilization of output and it is based on uniting local and…
The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications…
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…