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Finite-time coherent sets represent minimally mixing objects in general nonlinear dynamics, and are spatially mobile features that are the most predictable in the medium term. When the dynamical system is subjected to small parameter…
In this paper, we propose a suboptimal and reduced-order Model Predictive Control (MPC) architecture for discrete-time feedback-interconnected systems. The numerical MPC solver: (i) acts suboptimally, performing only a finite number of…
Time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current…
The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…
Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees…
This note studies the robust output feedback stabilization problem of a class of multi-input multi-output invertible nonlinear systems, for which an "ideal" state feedback based on feedback linearization can be designed under certain mild…
The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model…
Feedback optimization is a control paradigm that enables physical systems to autonomously reach efficient operating points. Its central idea is to interconnect optimization iterations in closed-loop with the physical plant. Since iterative…
The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs…
For a discrete dynamical system on $\R$ generated by a quadratic function, we show, using elementary computations, that the existence, number, and stability of 3-cycles are determined by a single parameter depending on the coefficients of…
The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital…
This paper deals with the output feedback stabilization problem of nonlinear multi-input multi-output systems having an uncertain input gain matrix. It is assumed that the system has a well-defined vector relative degree and that the zero…
Higher-order time integration methods that unconditionally preserve the positivity and linear invariants of the underlying differential equation system cannot belong to the class of general linear methods. This poses a major challenge for…
This paper studies static output feedback stabilization of continuous-time (incrementally) passive nonlinear systems where the control actions can only be chosen from a discrete (and possibly finite) set of points. For this purpose, we are…
This paper concerns the classical dynamics of three coupled rotors: equal masses moving on a circle subject to attractive cosine inter-particle potentials. It is a simpler variant of the gravitational three-body problem and also arises as…
In this paper, the notion of robust strict QSR-dissipativity is applied to solve the static output feedback control problem for a class of continuous-time nonlinear rational systems subject to input saturation and bounded parametric…
Identifying the mechanism of intercellular feedback regulation is critical for the basic understanding of tissue growth control in organisms. In this paper, we analyze a tissue growth model consisting of a single lineage of two cell types…
The main purpose of this paper is to study the local dynamics and bifurcations of a discrete-time SIR epidemiological model. The existence and stability of disease-free and endemic fixed points are investigated along with a fairly complete…
A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off…
The phase transition kinetics in three phase systems was investigated using the numerically efficient cell dynamics method. A phasefield model with a simple analytical free energy and single order parameter was used to study the kinetics…