Related papers: Equivariant Versions of Odd Number Theorem
A new class of control problems is discussed - homeostasis control. Homeostasis control problems can be considered as control problems with a given target set, in particular, as a problem of stabilizing the values of some target function,…
In this article, we investigate the problem of exponential stabilization via output feedback for a cascaded system composed of an ordinary differential equation (ODE) and a wave partial differential equation (PDE) under boundary control.…
It has recently been speculated that statistical properties of chaos may be captured by weighted sums over unstable invariant tori embedded in the chaotic attractor of hyperchaotic dissipative systems; analogous to sums over periodic orbits…
Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the…
The paper focuses on the numerical stability and accuracy of implicit time-domain integration (TDI) methods when applied for the solution of a power system model impacted by time delays. Such a model is generally formulated as a set of…
A Lyapunov-based method is presented for stabilizing and controlling of closed quantum systems. The proposed method is constructed upon a novel quantum Lyapunov function of the system state trajectory tracking error. A positive-definite…
Reliable controllers with high flexibility and performance are necessary for the control of intricate, advanced, and expensive systems such as aircraft, marine vessels, automotive vehicles, and satellites. Meanwhile, control allocation has…
We consider a terminal control problem for processes governed by a nonlinear system of fractional ODEs. In order to show existence of the control, we first consider the linear counterpart of the system and reprove a number of classical…
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…
Difference control schemes for controlling unstable fixed points become important if the exact position of the fixed point is unavailable or moving due to drifting parameters. We propose a memory difference control method for stabilization…
We develop an indirect-adaptive model predictive control algorithm for uncertain linear systems subject to constraints. The system is modeled as a polytopic linear parameter varying system where the convex combination vector is constant but…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
This paper studies the exponential stabilization on infinite dimensional system with impulse controls, where impulse instants appear periodically. The first main result shows that exponential stabilizability of the control system with a…
This paper explores transverse coordinates for the purpose of orbitally stabilizing periodic motions of nonlinear, control-affine dynamical systems. It is shown that the dynamics of any (minimal or excessive) set of transverse coordinates,…
In this paper we introduce a new method to design control laws for non-linear underactuated systems. Our method produces an infinite dimensional family of control laws, whereas most control techniques only produce a finite dimensional…
This paper is concerned with the problem of Model Predictive Control and Rolling Horizon Control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a…
We analyze the stabilization of unstable steady states by delayed feedback control with a periodic time-varying delay in the regime of a high-frequency modulation of the delay. The average effect of the delayed feedback term in the control…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
We employ an extension of ergodic theory to the random setting to investigate the existence of random periodic solutions of random dynamical systems. Given that a random dynamical system has a dissipative structure, we proved that a random…
In this contribution, the optimal stabilization problem of periodic orbits is studied via invariant manifold theory and symplectic geometry. The stable manifold theory for the optimal point stabilization case is generalized to the case of…